Euphractinae * Palaeopeltinae

Pachyarmatheriinae

Pampatheriinae

Glyptodontinae † Chlamyphorinae

Tolypeutinae Le Verger

F, Gerber S, Hautier L, Delsuc F, Amson E, Ladevèze S, Bardin J, Billet G. Ferreira-Cardoso

CINGULATA Peltephilidae † Dasypodidae Dasypodinae Chlamyphoridae

However, an even greater number of extinct taxa have been associated with or included within the extinct glyptodonts (see below). Following the proposal of Delsuc et al. (2016) (see above), the systematics of Cingulata at the subfamily level could be represented as follows (the taxa not treated by these authors are defined at an adapted taxonomic rank and indicated by *):

« Voici encore des arbres et je connais leur rugueux, de l'eau et j'éprouve sa saveur. Ces parfums d'herbe et d'étoiles, la nuit, certains soirs où le coeur se détend, comment nierais-je ce monde dont j'éprouve la puissance et les forces ? Pourtant toute la science de cette terre ne me donnera rien qui puisse m'assurer que ce monde est à moi. Vous me le décrivez et vous m'apprenez à le classer. Vous énumérez ses lois et dans ma soif de savoir je consens qu'elles soient vraies. Vous démontez son mécanisme et mon espoir s'accroît. Au terme dernier, vous m'apprenez que cet univers prestigieux et bariolé se réduit à l'électron. Tout ceci est bon et j'attends que vous continuiez. Mais vous me parlez d'un invisible système planétaire où des électrons gravitent autour d'un noyau. Vous m'expliquez ce monde avec une image. Je reconnais alors que vous en êtes venus à la poésie : je ne connaîtrai jamais. Ai-je le temps de m'en indigner ? Vous avez déjà changé de théorie. Ainsi cette science qui devait tout m'apprendre finit dans l'hypothèse, cette lucidité sombre dans la métaphore, cette incertitude se résout en oeuvre d'art. » Albert Camus. 1942. Le Mythe de Sisyphe, « Un raisonnement absurde : les murs de l'absurdes ».

"And here are trees and I know their gnarled surface, water and I feel its taste. These scents of grass and stars at night, certain evenings when the heart relaxeshow shall I negate this world whose power and strength I feel? Yet all the knowledge on earth will give me nothing to assure me that this world is mine. You describe it to me and you teach me to classify it. You enumerate its laws and in my thirst for knowledge I admit that they are true. You take apart its mechanism and my hope increases. At the final stage you teach me that this wondrous and multicolored universe can be reduced to the atom and that the atom itself can be reduced to the electron. All this is good and I wait for you to continue. But you tell me of an invisible planetary system in which electrons gravitate around a nucleus. You explain this world to me with an image. I realize then that you have been reduced to poetry: I shall never know. Have I the time to become indignant? You have already changed theories. So that science that was to teach me everything ends up in a hypothesis, that lucidity founders in metaphor, that uncertainty is resolved in a work of art."

Albert Camus. 1942. The Myth of Sisyphus, "An Absurd Reasoning: Absurd Walls". Translated from the French by Justin O'Brien (1955).

It has been three long years filled with adventures, but what particularly characterizes them is the constant headaches regarding the question of biological variation, which I am sure does not leave the mental health unscathed for those who try to understand it. I could not have completed this work without the unfailing support of several people whom I would like to thank infinitely.

First of all, I would like to thank my PhD supervisor, Guillaume Billet, who guided my research from the beginning to end, yet trusted me in such a way that it allowed me to progress within the exciting world of research. He was always kind and patient. No one could reproach him for being bothered by my pitiful English or my lack of rigor in certain aspects of the writing of draft versions. He always followed a rigorous, pedagogical, and friendly approach towards me while nourishing our discussions and flourishing ideas. Even on a personal note, he was always available to provide advice not related to my PhD. Guillaume, it was an honor to have been at your side during these three years. It is with emotion that I write these lines in the hope that this PhD is only the beginning of a long collaboration. I wish to give you my full gratitude and friendship. I can never thank you enough for everything... Goussard for your indispensable help with the 3D processing, as well as for our many discussions and your friendship. They saved me from having to redo the whole process at the mercy of computer whims. Thanks to Renaud Lebrun, from the University of Montpellier, for training me in 3D acquisition and allowing me to use the X-ray microtomograph to scan a large number of specimens. Thanks also for his kindness and his trust. Thanks to the technical teams, Charlène Letenneur, Sophie Fernandez, Colas Bouillet, Lilian Cazes, Yohan Despres, Philippe Loubry, Renaud Vacant and Jean-Charles Zajac for your friendship and help. Our interactions were always very friendly, and I learned a lot from them. Thanks to Marie-Astrid Angel for always helping me to consult the documents in the library of the Centre de Recherche en Paléontologie -Paris. Thanks to Maria Lages for her daily welcomes, always with a smile.

Finally, many thanks to my office mates, Véronique Barriel, Sandrine Ladevèze, Chloé Olivier, Nathalie Poulet, Claire Sagne, Guillaume Billet, Helder Gomes Rodrigues, Damien Olivier, Maxime Perretta and Vincent Pernègre, who have brightened up these three years with rich discussions and laughs. I would also like to thank the whole team of doctoral missions and my colleagues who accompanied me during my teaching missions.

The PhD is an opportunity to travel and acquire new data. Several people have allowed me to undertake these trips and for this, I would like to thank them. First of all, a huge thank I would also like to thank my colleagues who are co-authors for the versions of this research published or in preparation, without whom this work would never have seen the light of day. Thanks to Laureano for his kindness, friendship and interesting discussions on the diversity of cingulates. Thank you to Jérémie Bardin and Sylvain Gerber for having worked on the morphological integration with Guillaume and me. Thank you for our many discussions and for your help and support in all our studies. Special thanks to Jérémie who helped me with the R scripts with which I was not at all familiar. Thanks to Eli Amson for his discussions and pertinent remarks. Thanks to Frédéric Delsuc for his very interesting remarks and discussions, especially on the diversity of the extant groups. Huge thanks to Sergio Ferreira-Cardoso and Lionel Hautier. Thank you for your warm welcome in Montpellier, your help with the specimens to be scanned and your very enriching discussions. Many thanks to Sergio and his partner Laura for hosting me during my missions. To all of you, I convey my most sincere gratitude and friendship.

My thanks also go to all my other friends and colleagues in Paris, Montpellier, Fribourg and other places. From students to retirees, in and out of science, while I cannot mention everyone by name, I would like to thank them all for their unfailing friendship, passionate discussions, help and support for the various aspects of my PhD and personal life. Thank you to them for being faithful companions during these three years of my life and for believing in me.

Special thanks to Sandrine Ladevèze and Floréal Solé. It has been five years since we crossed paths on the winding university roads that lead students to meet their supervisors. And since then, a deep friendship has linked us. I thank them for helping me whenever they could, for their friendship, for their proofreading and for the projects they have involved me in, which have never ceased to multiply. The latter have notably allowed me not to sink completely into the subject of my PhD, but also to grow intellectually through other studies.

I would like to thank my roommates, who are my lifelong friends. It has been a privilege for me to spend a large part of these three years with them. There were ups and downs. It is not always easy to share one's daily life. But they were always there through the worst and the best times. I will be eternally grateful to them for that. Thank you, Lionel and Maxime. I would like to thank especially Maxime, who allowed me to use his computer during the lockdown thus saving my PhD.

I would like to thank my father, mother, brother, and sister. Without them, I would not be where I am today. They never questioned my professional choices, trying at all costs to bring the best to our family. Despite all the difficulties, they are an immense support to me. I thank them from the bottom of my heart.

Finally, my gratitude goes to Olivia, my partner. Without her, none of this would have been possible. She was always by my side, no matter what it cost, helping me with all the events of my life, both personal and professional. Her patience, kindness, and love were a solid foundation for me. Even if life has separated us geographically, multiplying emotions tenfold, she was always close to me. Olivia, I will never find the words to tell you how grateful I am to you. Thank you so much.

INTRODUCTION

Morphological variation is a pervasive biological phenomenon, which has long inspired naturalists and led them to propose classifications of organisms based on observed similarities and differences. From [START_REF] Linnaeus | Systema naturae per regna tria naturae, secundum classes, ordines, genera, species, cum characteribus, differentiis, synonymis, locis[END_REF] to the present day, biologists have never ceased to study the patterns produced by this variation and the processes that are its source. However, the more we examine morphological variation, the more we discover its extreme complexity. In recent decades, the use of morphological variation as a source of traits for phylogenetic analyses has been strongly questioned, despite the primacy of these data for the study of extinct taxa inaccessible to molecular analyses [START_REF] Wiens | The role of morphological data in phylogeny reconstruction[END_REF][START_REF] Asher | Morphology, paleontology, and placental mammal phylogeny[END_REF][START_REF] Springer | Morphology and placental mammal phylogeny[END_REF]. This primacy of morphological data for reconstructing relationships of extinct forms is hampered by critical assessments of its performance, particularly for analyses of interordinal relationships within placental mammals [START_REF] Scotland | Phylogeny reconstruction: the role of morphology[END_REF][START_REF] Springer | Morphology and placental mammal phylogeny[END_REF][START_REF] Springer | Technical comment on "The placental mammal ancestor and the post-K-Pg radiation of placentals[END_REF]. This observation is in line with the fact that many studies have called for an improvement of our phylogenetic methods using morphology (e.g., [START_REF] Dávalos | Integrating incomplete fossils by isolating conflicting signal in saturated and non-independent morphological characters[END_REF][START_REF] Goswami | The macroevolutionary consequences of phenotypic integration: from development to deep time[END_REF]Billet et al., 2015a;[START_REF] Harrison | Among-character rate variation distributions in phylogenetic analysis of discrete morphological characters[END_REF][START_REF] Lee | Morphological phylogenetics in the genomic age[END_REF][START_REF] Pyron | Post-molecular systematics and the future of phylogenetics[END_REF][START_REF] Wright | Modeling character change heterogeneity in phylogenetic analyses of morphology through the use of priors[END_REF][START_REF] Bardin | Ontogenetic data analyzed as such in phylogenies[END_REF][START_REF] Billet | Serial Homology and Correlated Characters in Morphological Phylogenetics: Modeling the Evolution of Dental Crests in Placentals[END_REF]. Efforts towards that goal must include a broader exploration of patterns of morphological variation and a better identification of the covariation among traits, as frequently underlined by these studies.

Cingulates are a group of placental mammals that belong to the superorder Xenarthra together with anteaters and sloths. The Cingulata includes the extant armadillos and extinct taxa such as glyptodonts. This clade represents an ideal case study for the exploration of morphological variation in a phylogenetic context. Their modest extant diversity permits a detailed exploration of the entire group, whereas their past diversity, exhibiting cranial shapes very unusual in mammals (Superina & Loughry, 2015), offers a wide range of investigations.

The major interest of this group for the subject treated in the present work lies in the lack of congruence between phylogenetic analyses using morphological versus molecular data (not at all level). The recent incorporation of a glyptodont's mitogenome in molecular analyses has clearly revealed these incongruences [START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF][START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF]. In this context, we propose to explore patterns of morphological variation of the skull within the Cingulata using different perspectives and to discuss the possible impact of our findings on the phylogenetic reconstructions proposed for the group.

In a first step (Chapter 1), we introduce the Cingulata group by specifying the state of the art concerning their taxonomic diversity and by summarizing all the existing hypotheses on their phylogenetic relationships. This overview enables us to highlight the lack of consensus among these hypotheses, and to underline gaps in our morphological knowledge of the group, especially with regard to internal anatomy and integration patterns (= tendency of traits to covary) of the skull. We show that an exploration of these two aspects will be useful to complete morphological matrices used in phylogenetic analysis but also to better understand the existing covariations among several anatomical structures and characters that can mislead morphological phylogenetics.

Our work starts with an in-depth study of the internal anatomy of the skull of the Cingulata, demonstrating that these poorly known structures can deliver new phylogenetic information (Chapter 2). This exploration allows us to complement our existing anatomical knowledge of the skull of cingulates and to highlight new characters, which can be incorporated to the existing matrices, with a signal focused on the position of the glyptodonts. We discuss the evolutionary scenarios corresponding to these new characters and their congruence with current phylogenetic hypotheses concerning the group.

The next part of our work explores the morphological integration of the cingulate skull in two steps (Chapters 3 & 4). We first focus on one of the most powerful factors responsible for morphological integration known in mammals, allometry, in order to target cranial covariation patterns related to size variation (Chapter 3). Our work on this aspect starts with an exploratory approach on one of the best sampled cingulate species, the nine-banded armadillo (Dasypus novemcinctus [START_REF] Linnaeus | Systema naturae per regna tria naturae, secundum classes, ordines, genera, species, cum characteribus, differentiis, synonymis, locis[END_REF]. It enables us to identify allometric patterns in this species at two scalesthe entire skull and cranial subunitsand at two levels of integrationthe static and ontogenetic levels. Based on this exploratory study, we test the existence of similar allometric patterns in two other extant and distantly related species of cingulates with the same approach. All these patterns are then compared to an evolutionary analysis of allometry gathering most extant cingulate species and most of the emblematic fossil groups (with a focus on glyptodonts). This comparison makes it possible to determine if certain allometric patterns detected at the species level were at play during the evolution of cingulates.

This last analysis highlights several covariations between the size and shape of the skull that seem to be present across the whole group.

The second step in our investigation of morphological integration is represented by an in-depth study of the strongest covariations among cranial linear distances in the three armadillo species initially sampled for allometry (Chapter 4). Our selective exploration of pairs of covarying distances highlight strong cranial correlations not detected in our previous study on allometry. The patterns obtained in the three species are then analyzed at the evolutionary level to identify whether these covariations were also present in the morphological evolution of the group. This new approach was then complemented by an analysis of cranial modularity without a priori about the possible modules in the three armadillo speciesmodularity "exists if integration is concentrated within certain parts or regions of a structure, the modules, but is relatively weak between these modules" (Klingenberg, 2014: pp. 2). This analysis reveals a partitioning of the integration into three anteroposteriorly distributed modules of the skull. In a complementary way, we carry out the very first exploration of the variations of cingulate cranial shape at the evolutionary level, using the modules detected at the preceding step, which allows us to cover a larger scope of potential covariations.

Finally, the implications of these studies are briefly discussed in a general conclusion (Chapter 5) regarding the already existing phylogenetic hypotheses and the cranial characters used in the matrices. Our results on cranial integration are compared with existing matrices and phylogenetic analyses in order to identify possible groups of traits that may covary and to discuss their impact on the phylogenetic reconstruction within the group. This exploratory work emphasizes the necessity to better understand the complexity of morphological variation in order to make progress in our phylogenetic investigations of extinct taxa.

CHAPTER 1 Cingulata, a Case Study in Mammalian Phylogeny

« Tous les tatous sont originaires de l'Amérique ; ils étaient inconnus avant la découverte du nouveau monde, les anciens n'en ont jamais fait mention ». Buffon. 1753. Quadrupède. Tome IV: p. 115.

"All armadillos originate from America; they were unknown before the discovery of the new world, the ancients never mentioned them". Buffon. 1753. Quadrupède. Tome IV: p. 115. Translated.

Extant and extinct diversity of Cingulata

1.1.1 Who are the Cingulata?

The Cingulata, which comprise all extant armadillos and a rich fossil diversity, correspond to one of the 21 orders of placental mammal [START_REF] Wilson | Handbook of the Mammals of the World: Insectivores, sloths and colungos[END_REF]. In Latin, this term means "the girdled ones", which emphasizes the main characteristic of the group, i.e. the presence of a bony carapace made of osteoderms covering the head, body and tail (most often mobile), a unique feature within mammals [START_REF] Mcdonald | Xenarthran skeletal anatomy: primitive or derived? (Mammalia, Xenarthra)[END_REF]. Earlier classifications grouped cingulates with sloths, anteaters, pangolins, and aardvarks in the super-order Edentata based on their reduction in dental complexity [START_REF] Cuvier | Tableau élémentaire de l'histoire naturelle des animaux[END_REF]; see [START_REF] Gunnell | Edentata" summary[END_REF] for a summary of the group). It is only at the end of the 19th century, following an earlier suggestion by [START_REF] Flower | On the mutual affinities of the animals composing the order Edentata[END_REF], that armadillos were gathered within the same group with sloths and anteaters: the Xenarthra Cope, 1889 (etymology: strange articulation). The monophyly of the Xenarthra is still supported today, and they constitute one of the four major clades of extant placental mammals [START_REF] Zachos | Mammalian Phylogenetics: A Short Overview of Recent Advances[END_REF]; see Section 1.2).

The extant Cingulata are composed of 21 extant species of armadillos grouped in nine genera and two families [START_REF] Gardner | Order Cingulata[END_REF][START_REF] Mcdonough | Family Dasypodidae (long-nosed armadillos)[END_REF][START_REF] Superina | Family Chlamyphoridae (Chlamyphorid armadillos)[END_REF] (Figure 1). Traditionally, all extant species were included in the same family: the Dasypodidae (e.g., [START_REF] Simpson | The principles of classification and a classification of mammals[END_REF]. Recent molecular studies incorporating extinct glyptodonts, and the accompanying newly proposed phylogenies, have questioned the existence of a single family, leading [START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF] to define two families for the extant diversity of armadillos: the Dasypodidae including the clade Dasypodinae (Figure 1) and the Chlamyphoridae including the other three extant clades Euphractinae, Chlamyphorinae and Tolypeutinae (Figure 1) 1 . 1 In their discussion [START_REF] Gaudin | Cranial osteology of the pampathere Holmesina floridanus (Xenarthra: Cingulata; Blancan NALMA), including a description of an isolated petrosal bone[END_REF] explain that this proposition is not the most consistent with what is known about fossil diversity. They propose to raise all sub-families to the family level for greater consistency.

Here, we will follow the nomenclature of [START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF] to facilitate comparisons between molecular and morpho-anatomical analyses and not to confuse discussions regarding previous works. Because of this choice, the fossil families will be readjusted to the subfamily rank if they are included within the Dasypodidae or Chlamyphoridae, as advocated by [START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF].

Figure 1. Mosaic of extant cingulate species with details of their taxonomic affiliation based on recent molecular analyses [START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF][START_REF] Gibb | Shotgun mitogenomics provides a reference phylogenetic framework and timescale for living xenarthrans[END_REF][START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF]. The family Dasypodidae contains 7 extant species all attributed to the clade Dasypodinae (in blue). The family Chlamyphoridae contains 14 extant species distributed within three clades: Euphractinae (in red); Chlamyphorinae (in purple) and Tolypeutinae (in yellow). The colors chosen follow [START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF], as for the rest of the manuscript. Specimens marked with an asterisk (*) correspond to species whose status is currently under discussion (see Chapter Extant cingulates are omnivorous or insectivorous (see [START_REF] Gaudin | Paleogene Xenarthra and the evolution of South American mammals[END_REF] but also include some more specialized species such as the myrmecophagous giant armadillo -Priodontes maximus [START_REF] Kerr | The animal kingdom or zoological system, of the celebrated Sir Charles Linnaeus. class I. Mammalia: contain a complete systematic description, arrangement, and nomenclature, of all the known species and varieties of Mammalia, or animals which give suck to their young; being a translation of that part of the Systema Naturae, as lately published, with great improvements[END_REF][START_REF] Desbiez | Insights into giant armadillo (Priodontes maximus Kerr, 1792) reproduction[END_REF]. Their weight varies between a few hundred grams (Calyptophractus retusus [START_REF] Burmeister | Ein neuer Chlamyphorus[END_REF] to about fifty kilos (Priodontes maximus). Together with other xenarthrans, armadillos most likely originated in South America (Vizcaíno & Loughry, 2008; see more specifically Aguiar & Fonseca, 2008, for extant species) and most of their subsequent evolution took place on this continent (the so-called "Splendid

Isolation" of [START_REF] Simpson | Splendid isolation: the curious history of South American mammals[END_REF]. Due to their long endemic evolution in South America and their unique characters (e.g., bony carapace), they are often regarded as morphologically exotic in comparison to Old World placental mammals (Superina & Loughry, 2015). It is only with the formation of the Isthmus of Panama, about 2.8 Ma, that one can find remains of cingulates outside the South American continent (Gilette & Ray, 1981;[START_REF] Carranza-Castañeda | Late Tertiary terrestrial mammals from central Mexico and their relationship to South American immigrants[END_REF][START_REF] Zurita | Neosclerocalyptus spp. (Cingulata: Glyptodontidae: Hoplophorini): cranial morphology and palaeoenvironments along the changing Quaternary[END_REF]. Today, only one species of armadillo is present much further in the north, as far as the United States, due to its northern migration that began 200 years agothe nine-banded armadillo, Dasypus novemcinctus [START_REF] Taulman | Recent range expansion and distributional limits of the nine-banded armadillo (Dasypus novemcinctus) in the United States[END_REF]. Although they currently represent the most diverse group within the xenarthrans, extant armadillos only represent a reduced portion of the great past diversity of cingulates.

What about past diversity?

The first xenarthran remains date back to approximately 55 Ma and correspond to osteoderm fragments and postcranial remains from Itaborai, Brazil [START_REF] Bergqvist | The Xenarthra (Mammalia) of Sao Jose de Itaboraí Basin (upper Paleocene, Itaborian), Rio de Janeiro, Brazil[END_REF][START_REF] Gaudin | Paleogene Xenarthra and the evolution of South American mammals[END_REF]. To date, there are almost 200 described genera referred to Xenarthra in the fossil record, a large proportion of which belong to the Cingulata (more than 100; [START_REF] Mckenna | Classification of mammals: above the species level[END_REF] probably due to a preservational bias in favor of osteodermal remains.

Traditionally (e.g., [START_REF] Simpson | The principles of classification and a classification of mammals[END_REF], most extant and extinct Cingulata were classified in two different families, marking a strong dichotomy in their morphological appearance: the Dasypodidae and the extinct Glyptodontidae (Figures 2,3 & 4see below for their updated systematics; and see Figure 1 and Section 1.2). The Glyptodontidae (= Glyptodontinae in our manuscript; see below) included the extinct glyptodonts (Figure 2D), a group of large cingulates defined by [START_REF] Owen | Description of a tooth and part of the skeleton of the Glyptodon, a large quadruped of the edentate order, to which belongs the tessellated bony armour figured by Mr. Clift in his memoir on the remains of the Megatherium, brought to England by Sir Woodbine Parish[END_REF] whose name means "engraved tooth" (see Section 1.1.3 for their characteristic) [START_REF] Fernicola | Nuevos aportes para la sistemática de los Glyptodontia Ameghino 1889 (Mammalia, Xenarthra, Cingulata)[END_REF]. The Dasypodidae included extant taxa and extinct forms (Figure 2B) closer to armadillos than glyptodonts in the old nomenclature. An additional extinct family of uncertain taxonomic affinities was the Peltephilidae (Figure 2A). Several extinct clades belong to the Cingulata, such as the enigmatic Pachyarmatheriinae and Palaeopeltinae [START_REF] Fernicola | A new species of Neoglyptatelus (Mammalia, Xenarthra, Cingulata) from the late Miocene of Uruguay provides new insights on the evolution of the dorsal armor in cingulates[END_REF]. The extinct Pampatheriinae (Figure 2C) were first considered to belong to the Dasypodidae [START_REF] Simpson | Holmesina septentrionalis, extinct giant armadillo of Florida[END_REF] although Paula Couto (1954) proposed that this sub-family be raised to the family level. They are now considered to be very closely related to glyptodonts [START_REF] Patterson | The Fossil Mammal Fauna of South America[END_REF][START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF][START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF][START_REF] Gaudin | Cranial osteology of the pampathere Holmesina floridanus (Xenarthra: Cingulata; Blancan NALMA), including a description of an isolated petrosal bone[END_REF].

Pampatheres and glyptodonts are considered herbivores [START_REF] Vizcaíno | The armadillos (Mammalia, Xenarthra, Dasypodidae) of the Santa Cruz formation (early-middle Miocene): An approach to their paleobiology[END_REF](Vizcaíno et al., , 2012a) ) whereas most other fossil taxa tend to have a diet similar to modern forms, except for Macroeuphractus Ameghino, 1887 for which a carnivorous diet is assumed (Vizcaíno & De Iuliis, 2003). The pampatheres and glyptodonts also stand out from other cingulates due to their larger body mass, which could reach up to 250 kg and over 2 tons respectively [START_REF] Vizcaíno | Proportions and function of the limbs of glyptodonts[END_REF]Vizcaíno et al., 2012a;[START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF]. Cingulates were mainly represented by osteoderms in the South American fossil record and the oldest sub-complete skulls for most groups date back to the Oligocene at best (Figure 3 - [START_REF] Gaudin | Paleogene Xenarthra and the evolution of South American mammals[END_REF]. Among the oldest cingulate cranial remains, an incomplete portion of caudal cranium is known for Utaetus buccatus [START_REF] Ameghino | Preliminary notes on new mammals from the Cretaceous terrains of Patagonia[END_REF][START_REF] Simpson | The beginning of the age of mammals in South America. Part 1. Introduction. Systematics: Marsupialia, Edentata, Condylarthra, Litopterna, and Notioprogonia[END_REF], of uncertain phylogenetic affinities, from the Middle Eocene of Patagonia (Barrancan subage - [START_REF] Gaudin | Paleogene Xenarthra and the evolution of South American mammals[END_REF]. Partial cranial remains of cingulates were also documented from the middle Eocene of northern Argentina (Vacan subage - [START_REF] Herrera | A new Eocene dasypodid with caniniforms (Mammalia, Xenarthra, Cingulata) from northwest Argentina[END_REF] and from the early Oligocene of Chile (Tinguirirican subage - [START_REF] Carlini | The phylogenetic and biostratigraphic significance of new armadillos (Mammalia, Xenarthra, Dasypodidae, Euphractinae) from the Tinguirirican (Early Oligocene) of Chile[END_REF] (Figure 3). More complete skulls were reported from the Upper Oligocene Beds of Salla, Bolivia, for the tolypeutines (Kuntinaru boliviensis [START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF] and peltephilids [START_REF] Shockey | New Early Diverging Cingulate (Xenarthra: Peltephilidae) from the Late Oligocene of Bolivia and Considerations Regarding the Origin of Crown Xenarthra[END_REF]. As regards glyptodonts, the earliest well-preserved cranial remains are known from the early Miocene of the Santa Cruz Formation in Argentina i.e. more than 20 Ma later than the first partial skull of dasypodines (Figure 3). These correspond to well-preserved complete skulls [START_REF] Scott | Mammalia of the Santa Cruz beds. I. Edentata[END_REF] (Figure 4A-D). The 16-17 Ma old Santa Cruz Formation, which also delivered complete skulls for other cingulate taxa, probably provided one of the most complete glimpses into the past evolutionary history of cingulates, both anatomically and taxonomically [START_REF] Lr | Los Cingulata (Mammalia, Xenarthra) del Mioceno temprano y medio de Patagonia (edades Santacrucense y "Friasense[END_REF]Vizcaíno et al., 2012b). Finally, the oldest skulls of pampatheres date from the middle Miocene [START_REF] De Iuliis | Vassallia maxima Castellanos, 1946 (Mammalia: Xenarthra: Pampatheriidae), from Puerta del Corral Quemado (late Miocene to early Pliocene), Catamarca Province, Argentina[END_REF][START_REF] Gaudin | Paleogene Xenarthra and the evolution of South American mammals[END_REF][START_REF] Gaudin | Cranial osteology of the pampathere Holmesina floridanus (Xenarthra: Cingulata; Blancan NALMA), including a description of an isolated petrosal bone[END_REF]. For the pachyarmatheres, only the postcranial remains and osteoderms are known, dating back to the middle Miocene period [START_REF] Madden | The Laventan Stage and Laventan Age: new chronostratigraphic and geochronologic units for the Miocene of South America[END_REF][START_REF] Cozzuol | The Acre vertebrate fauna: Age, diversity, and geography[END_REF][START_REF] Laurito | Paleobiogeografía del arribo de mamíferos suramericanos al sur de América Central de previo al Gran Intercambio Biótico Americano: un vistazo al GABI en América Central[END_REF][START_REF] Fernicola | A new species of Neoglyptatelus (Mammalia, Xenarthra, Cingulata) from the late Miocene of Uruguay provides new insights on the evolution of the dorsal armor in cingulates[END_REF]. For palaeopeltines, their taxonomic validity is much debated and, to our knowledge, this group is not represented by available cranial remains but only by a multitude of osteodermal remains that could not be assigned to other families (pers. com. Laureano González-Ruiz). A skull was described by [START_REF] Kraglievich | Orophodon Amegh: representante de una nueva superfamilia orophodontoidea del suborden Xenarthra;(nota preliminar)[END_REF] but has been lost since.

Although the earliest remains are relatively rare for most of these fossil groups, late Miocene through Pleistocene remains are particularly abundant in comparison (except for peltephilids). All these fossil specimens testify to the existence of a great past diversity for the Cingulata. This taxonomic diversity is accompanied by a great variety of cranial shapes ranging from the elongated snout of the small dasypodines (e.g., Figure 2B) to the giant cubical skulls of Pleistocene glyptodonts (e.g., Figures 2D &4E).

Figure 3. Temporal distribution of each major group inspired by [START_REF] Gaudin | Paleogene Xenarthra and the evolution of South American mammals[END_REF] with Cenozoic SALMAs (= South American Land Mammal Ages -based on [START_REF] Woodburne | Revised timing of the South American early Paleogene land mammal ages[END_REF] and indication of earliest remains for each quoted group (inspired by [START_REF] Gaudin | Paleogene Xenarthra and the evolution of South American mammals[END_REF]. The phylogenetic relationships are based on recent molecular analyses [START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF][START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF] to which have been added the potential phylogenetic positions of each fossil taxa (peltephilids and pampatheres from [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF][START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF][START_REF] Gaudin | Cranial osteology of the pampathere Holmesina floridanus (Xenarthra: Cingulata; Blancan NALMA), including a description of an isolated petrosal bone[END_REF]pachyarmatheres from Fernicola et al., 2017;palaeopeltines from Perea et al., 2014). The stratigraphic distribution is based on the oldest occurrences for each group [START_REF] Pascual | Land Mammals: Paradigm for Cenozoic South American Geobiotic Evolution[END_REF][START_REF] Edmund | A new giant Armadillo[END_REF][START_REF] Carlini | The phylogenetic and biostratigraphic significance of new armadillos (Mammalia, Xenarthra, Dasypodidae, Euphractinae) from the Tinguirirican (Early Oligocene) of Chile[END_REF][START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF][START_REF] Fernicola | A new species of Neoglyptatelus (Mammalia, Xenarthra, Cingulata) from the late Miocene of Uruguay provides new insights on the evolution of the dorsal armor in cingulates[END_REF][START_REF] Herrera | A new Eocene dasypodid with caniniforms (Mammalia, Xenarthra, Cingulata) from northwest Argentina[END_REF][START_REF] Shockey | New Early Diverging Cingulate (Xenarthra: Peltephilidae) from the Late Oligocene of Bolivia and Considerations Regarding the Origin of Crown Xenarthra[END_REF][START_REF] Barasoain | A new pygmy armadillo (Cingulata, Euphractinae) from the late Miocene of Andean Argentina reveals an unexpected evolutionary history of the singular Prozaedyus lineage[END_REF]. The red nodes correspond to the molecular dating of [START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF]. Those in black are not dated. The taxonomic nomenclature used corresponds to the proposition of [START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF]. The taxonomic level of fossil taxa has been adapted accordingly. For more details on this nomenclature see Section 1.2. Abbreviations: Quat., Quaternary. Symbols: *, Pleistocene then Holocene; **, Notohippus zone.

The Special Case of Glyptodonts

Glyptodonts are a group of large herbivorous cingulates whose body mass varied from 80 kg at the end of the lower Miocene up to several tons for the last representatives of the Pleistocene [START_REF] Vizcaíno | Proportions and function of the limbs of glyptodonts[END_REF]. Glyptodont remains are very abundant in the fossil record of South America during the Cenozoic (from the late Eocene onwards) but also in southern North America during the Pleistocene [START_REF] Gillette | Glyptodonts of North America[END_REF]. Glyptodonts have several autapomorphic characters including a thickened essentially immobile dorsal carapace, a variable number of tri-lobed teeth, elephantine limbs, and a telescopic chewing apparatus under the skull [START_REF] Hoffstetter | Xenarthra[END_REF][START_REF] Fariña | Carved teeth and strange jaws: how glyptodonts masticated[END_REF][START_REF] Fernicola | Nuevos aportes para la sistemática de los Glyptodontia Ameghino 1889 (Mammalia, Xenarthra, Cingulata)[END_REF]. Their first representative, Glyptatelus Ameghino, 1897, is documented by osteoderms from the middle/late Eocene of Patagonia in Argentina [START_REF] Scillato-Yané | Sobre un Dasypodidae (Mammalia, Xenarthra) de edad Riochiquense (Palaeoceno superior) de Itaboraí (Brazil)[END_REF], which could be compatible with molecular estimates for their origin (35 ± 3 Ma -Delsuc et al., 2016). Glyptodonts survived until the beginning of the Holocene in South America [START_REF] Messineo | New radiocarbon dates from the Campo Laborde site (Pampean Region, Argentina) support the Holocene survival of giant ground sloth and glyptodonts[END_REF] (Figure 3).

As noted above, no complete glyptodont skull is known from the Paleogene. The Santa Cruz Formation of Patagonia yielded the earliest well-preserved glyptodont crania, all of modest size (Figure 4A-D). Many remains were discovered for later glyptodonts increasing the diversity of the group to more than 65 genera [START_REF] Mckenna | Classification of mammals: above the species level[END_REF] and showing a trend towards gigantism and graviportal limbs (Vizcaíno & Bargo, 1998;[START_REF] Soibelzon | Los Xenarthra (Mammalia) del Ensenadense (Pleistoceno Inferior a Medio) de la Region Pampeana (Argentina)[END_REF][START_REF] Cione | The great American biotic interchange: a South American perspective[END_REF][START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF] (Figure 4). Although all glyptodonts have a distinctive cranial shape relative to other cingulates (i.e., "broad, deep and almost cubical skull", Scott, 1903: pp. 5), comparisons among glyptodont specimens from the lower Miocene and more recent taxa show strong differences in many respects (e.g., [START_REF] Scott | Mammalia of the Santa Cruz beds. I. Edentata[END_REF], which warrants further study. Moreover, because of their very distinctive anatomy, the phylogenetic position of glyptodonts within Cingulata has been heavily debated (see below).

Figure 4. 3D model plate illustrating the skulls of extinct specimens of different families of Cingulata. A) Eucinepeltus complicatus Ameghino, 1891 (Miocene, Santacrucian SALMA). B) "Cochlops" debilis Ameghino, 1891 (Santacrucian). C) "Metopotoxus" anceps Scott, 1903 (Santacrucian). D) Propalaehoplophorus minus Ameghino, 1891 (Santacrucian). E) Glyptodon sp. (Pleistocene, Lujanian SALMA). Scale = 2 cm.

Systematics and phylogenetic issues on cingulates

The place of Xenarthra in mammals

Xenarthrans are nearly unanimously regarded as one of the four major clades of extant placental mammals today (e.g., [START_REF] Upham | Inferring the mammal tree: Species-level sets of phylogenies for questions in ecology, evolution, and conservation[END_REF][START_REF] Zachos | Mammalian Phylogenetics: A Short Overview of Recent Advances[END_REF]. It is the only one that is strongly supported by both molecular and morpho-anatomical data (discussed for Afrotheriasee [START_REF] Sánchez-Villagra | Thoracolumbar vertebral number: the first skeletal synapomorphy for afrotherian mammals[END_REF]. Uncertainties remain regarding their exact position in the placental tree (Figure 5) and their date of origin [START_REF] Zachos | Mammalian Phylogenetics: A Short Overview of Recent Advances[END_REF]. There are 3 hypotheses regarding their relationship with the other three primary groups of placentals (= Afrotheria, Euarchontoglires, and Laurasiatheria) (Figure 5).

Figure 5. Illustration of the three current hypotheses concerning the relations between the 4 major placental clades: Xenarthra (= Cingulata, Folivora, Vermilingua); Afrotheria (= Proboscidea, Sirenia, Hyracoidea, Tubulidentata, Macroscelidea, Afrosoricida); Euarchontoglires (= Scandentia, Primates, Dermoptera, Rodentia, Lagomorpha); Laurasiatheria (= (Eu-)Lipotyphla, Chiroptera, Pholidota, Carnivora, (Cet-)Artiodactyla, Perissodactyla). The Epitheria hypothesis is the least broadly supported (e.g., O' Leary et al., 2013phenomic and genomic data). The Atlantogenata and Exafroplacentalia hypotheses are more clearly supported by molecular analyses (e.g., [START_REF] Romiguier | Less is more in mammalian phylogenomics: AT-rich genes minimize tree conflicts and unravel the root of placental mammals[END_REF][START_REF] Tarver | The interrelationships of placental mammals and the limits of phylogenetic inference[END_REF]for morphological data see [START_REF] Halliday | Resolving the relationships of Paleocene placental mammals[END_REF]. In recent years, Atlantogenata hypothesis is favored [START_REF] Tarver | The interrelationships of placental mammals and the limits of phylogenetic inference[END_REF][START_REF] Esselstyn | Investigating difficult nodes in the placental mammal tree with expanded taxon sampling and thousands of ultraconserved elements[END_REF][START_REF] Zachos | Mammalian evolution, diversity and systematics. Handbook of zoology, Mammalia[END_REF]Uphman et al., 2019). For a more extensive discussion of these hypotheses refer to [START_REF] Foley | Mammal madness: is the mammal tree of life not yet resolved?[END_REF] and Zachos (2020).

Systematics and phylogenetics of the Cingulata

As for most taxa, our knowledge of the taxonomic composition of Cingulata and their phylogenetic relationships has changed through time. From the end of the 19th century to the present day, many hypotheses have been put forward about the relationships within and among extant and extinct cingulate groups. It was long difficult to find a strong signal and hence consensus on many aspects of the cingulate systematics and phylogeny before the advent of molecular phylogenetics.

The monophyly of the clades Dasypodinae and Chlamyphorinae has never been seriously questioned (Figure 6). However, this is not the case for the Tolypeutinae and Euphractinae for which some morpho-anatomical analyses questioned their monophyly as well as the relationships among their members [START_REF] Engelmann | The evolution and ecology of armadillos, sloths and vermilinguas[END_REF]Gaudin & Wible, 2006 -Figure 6A, C), including in a recent contribution (Herrera et al., 2017 -Figure 6F). In 2006, Abrantes & Bergqvist (Figure 6B) published a phylogenetic analysis based on postcranial material that supported a clade grouping dasypodines and tolypeutines and another one grouping chlamyphorines and euphractines (Figure 6B). In the same year, [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF] performed an analysis based on craniodental characters grouping chlamyphorines and a paraphyletic version of euphractines; the tolypeutines were also paraphyletic in their study (Figure 6C). When their analysis was performed only on extant taxa, they recovered a monophyletic Euphractinae but not Tolypeutinae [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF]. Finally, [START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF] revised the matrix of [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF]. Their results supported the monophyly of extant clades while still supporting a closer relationship between chlamyphorines and euphractines (Figure 6D). On the other hand, when their analysis was performed only on extant taxa, the monophyly of euphractines and tolypeutines was not confirmed (Figure S1). In summary, morpho-anatomical analyses did not provide clear support to the 4 extant clades and to their relationships as recovered in molecular analyses [START_REF] Delsuc | Molecular phylogenetics unveils the ancient evolutionary origins of the enigmatic fairy armadillos[END_REF][START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF][START_REF] Abba | Systematics of hairy armadillos and the taxonomic status of the Andean hairy armadillo (Chaetophractus nationi)[END_REF][START_REF] Gibb | Shotgun mitogenomics provides a reference phylogenetic framework and timescale for living xenarthrans[END_REF]Mitchell et al., 2016 -Figure 6G, H).

Molecular analyses have brought to light additional questions about the diversity and systematics of extant cingulates. They have indicated that several species initially recognized on a morphological basis may in fact be considered a single species, such as Chaetophractus nationi Thomas, 1894 and Chaetophractus vellerosus Gray, 1865 [a proposition now confirmed by morpho-anatomical and molecular analyses within the euphractines (see [START_REF] Abba | Systematics of hairy armadillos and the taxonomic status of the Andean hairy armadillo (Chaetophractus nationi)[END_REF] for more details see Supporting Information 1]. A similar situation may exist between Cabassous unicinctus Linnaeus, 1758 and Cabassous centralis Miller, 1899, (for more details see Supporting Information 1). Molecular analyses have also detected cases in which one species may actually correspond to a species complex, such as in the nine-banded armadillo [START_REF] Huchon | Armadillos exhibit less genetic polymorphism in North America than in South America: nuclear and mitochondrial data confirm a founder effect in Dasypus novemcinctus (Xenarthra)[END_REF][START_REF] Gibb | Shotgun mitogenomics provides a reference phylogenetic framework and timescale for living xenarthrans[END_REF][START_REF] Arteaga | Conservation Genetics, Demographic History, and Climatic Distribution of the Nine-Banded Armadillo (Dasypus novemcinctus): An Analysis of Its Mitochondrial Lineages[END_REF], Dasypus novemcinctus, which previously represented the extant armadillo species with the largest geographic distribution [START_REF] Mcbee | Dasypus novemcinctus[END_REF]. Morpho-anatomical analyses have subsequently provided additional evidence for this novel hypothesis in nine-banded armadillos [START_REF] Billet | The hidden anatomy of paranasal sinuses reveals biogeographically distinct morphotypes in the nine-banded armadillo (Dasypus novemcinctus)[END_REF][START_REF] Hautier | Beyond the carapace: skull shape variation and morphological systematics of long-nosed armadillos (genus Dasypus)[END_REF][START_REF] Feijó | Taxonomic revision of the long-nosed armadillos, Genus Dasypus Linnaeus, 1758 (Mammalia, Cingulata)[END_REF][START_REF] Feijó | Phylogeny and molecular species delimitation of long-nosed armadillos (Dasypus: Cingulata) supports morphology-based taxonomy[END_REF]. Many of these issues still need further work and clarification.

This demonstrates that the systematics of extant cingulates is not yet fully understood. As

It is now generally accepted that peltephilids, with their very peculiar skull and dentition, represent the earliest-diverging family among cingulates (e.g., [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF][START_REF] Shockey | New Early Diverging Cingulate (Xenarthra: Peltephilidae) from the Late Oligocene of Bolivia and Considerations Regarding the Origin of Crown Xenarthra[END_REF]) (Figure 3). Although they are poorly documented (see above), historical records concerning palaeopeltines consider them as potential distant relatives of the glyptodonts, or at least as members of the Cingulata [START_REF] Kraglievich | Orophodon Amegh: representante de una nueva superfamilia orophodontoidea del suborden Xenarthra;(nota preliminar)[END_REF].

Pachyarmatheriinae is a clade proposed by [START_REF] Fernicola | A new species of Neoglyptatelus (Mammalia, Xenarthra, Cingulata) from the late Miocene of Uruguay provides new insights on the evolution of the dorsal armor in cingulates[END_REF] based on the results of a phylogenetic analysis using cranial and postcranial characters (whereas no skull is known in this family), and which links the genus Pachyarmatherium Downing & White, 1995 and the genus Neoglyptatelus Carlini, Vizcaíno & Scillato-Yané, 1997. The latter belonged to Glyptatelinae which were previously considered as the earliest diverging group of glyptodonts [START_REF] Carlini | Armored xenarthrans: a unique taxonomic and ecologic assemblage[END_REF]. Therefore, like palaeopeltines, the pachyarmatheres might be closely related to glyptodonts (Figure 3). The same applies to pampatheres, which were either considered to be the ancestor of the glyptodonts [START_REF] Patterson | The Fossil Mammal Fauna of South America[END_REF] or their closest relatives (e.g., [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF][START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF]. Therefore, apart from the fossils attributed to the extant clades and the peltephilids, many systematic issues regarding extinct cingulates may revolve around the history of the glyptodonts.

Figure 6. Summary of the molecular (red circle) and morpho-anatomical (blue circle) phylogenetic analyses for Cingulata (only including all extant clades). When present, non-glyptodont fossil taxa were pruned from the original cladograms. A) [START_REF] Engelmann | The evolution and ecology of armadillos, sloths and vermilinguas[END_REF]. B) [START_REF] Abrantes | Proposta filogenetica para os Dasypodidae (Mammalia: Cingulata)[END_REF]. C) [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF]. D) [START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF]. E) [START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF]. F) [START_REF] Herrera | A new Eocene dasypodid with caniniforms (Mammalia, Xenarthra, Cingulata) from northwest Argentina[END_REF]. G) [START_REF] Delsuc | Molecular phylogenetics unveils the ancient evolutionary origins of the enigmatic fairy armadillos[END_REF]; [START_REF] Abba | Systematics of hairy armadillos and the taxonomic status of the Andean hairy armadillo (Chaetophractus nationi)[END_REF]; [START_REF] Gibb | Shotgun mitogenomics provides a reference phylogenetic framework and timescale for living xenarthrans[END_REF]. (H) [START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF]; [START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF].

The special case of the Glyptodonts

The position of the glyptodonts has been debated for a long time since the first cranial description of glyptodont remains by [START_REF] Owen | Description of a tooth and part of the skeleton of the Glyptodon, a large quadruped of the edentate order, to which belongs the tessellated bony armour figured by Mr. Clift in his memoir on the remains of the Megatherium, brought to England by Sir Woodbine Parish[END_REF]. Both [START_REF] Owen | Description of a tooth and part of the skeleton of the Glyptodon, a large quadruped of the edentate order, to which belongs the tessellated bony armour figured by Mr. Clift in his memoir on the remains of the Megatherium, brought to England by Sir Woodbine Parish[END_REF] and [START_REF] Huxley | II. On the osteology of the genus Glyptodon[END_REF] described the cranial anatomy in the genus Glyptodon, but their work was not oriented toward comparison with other cingulates, but rather with giant extinct sloths. [START_REF] Flower | On the mutual affinities of the animals composing the order Edentata[END_REF] was one of the first to compare the glyptodonts with other armadillos, which he saw as their direct descendants. [START_REF] Ameghino | Filogenia: Principios de clasificación transformista basados sobre leyes naturales y proporciones matemáticas[END_REF][START_REF] Ameghino | Contribución al conocimiento de los mamíferos fósiles de la República Argentina[END_REF] then proposed an opposite scenario, with glyptodonts nested within armadillos, since he regarded the great dental and cranial complexity of the former [START_REF] Owen | Description of a tooth and part of the skeleton of the Glyptodon, a large quadruped of the edentate order, to which belongs the tessellated bony armour figured by Mr. Clift in his memoir on the remains of the Megatherium, brought to England by Sir Woodbine Parish[END_REF] as evidence of derived characters. He also regarded their rigid carapace as a derived character as opposed to a mobile carapace. This proposition was discussed by other authors underlining the very specialized cranial anatomy of glyptodonts [START_REF] Burmeister | Monografía de los glyptodontes en el Museo Público de Buenos Aires[END_REF][START_REF] Carlini | An introduction to cingulate evolution and their evolutionary history during the great American biotic interchange: biogeographical clues from Venezuela[END_REF][START_REF] Fariña | Megafauna: giant beasts of Pleistocene South America[END_REF]. A potential solution to the position of glyptodonts within Cingulata was provided by Scott (1903: pp. 103-104), who explained that "... the Santa Cruz glyptodonts [Figure 4] are decidedly more primitive than those of later epochs, and to a certain extent they bridge over the gap between the glyptodonts and the armadillos, for the primitive features are, for the most part, points of resemblance to the latter group". Following these observations, Ameghino's hypothesis (1884, 1889) (glyptodonts in an apical position among cingulates) was supported by many authors throughout the 20th century [START_REF] Castellanos | Nuevos géneros de gliptodontes en relación con su filogenia[END_REF][START_REF] Castellanos | Trascendencia de la obra de Florentino Ameghino[END_REF][START_REF] Hoffstetter | Xenarthra[END_REF][START_REF] Patterson | The Fossil Mammal Fauna of South America[END_REF]see Fernicola (2008) for a brief review). The work of [START_REF] Abrantes | Proposta filogenetica para os Dasypodidae (Mammalia: Cingulata)[END_REF] constitutes an exception, as they defined glyptodonts as an outgroup to armadillos and pampatheres a priori in their phylogenetic analysis of cingulates (Figure 6B). While the Ameghino hypothesis remains the consensus view today (e.g., [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF][START_REF] Fernicola | Nuevos aportes para la sistemática de los Glyptodontia Ameghino 1889 (Mammalia, Xenarthra, Cingulata)[END_REF][START_REF] Porpino | Revisiting the intertropical Brazilian species Hoplophorus euphractus (Cingulata, Glyptodontoidea) and the phylogenetic affinities of Hoplophorus[END_REF][START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF][START_REF] Fernicola | A new species of Neoglyptatelus (Mammalia, Xenarthra, Cingulata) from the late Miocene of Uruguay provides new insights on the evolution of the dorsal armor in cingulates[END_REF]; but see [START_REF] Engelmann | The evolution and ecology of armadillos, sloths and vermilinguas[END_REF], the exact position of glyptodonts within cingulates has long been a hard question to answer. Phylogenetic analyses based on morphology have delivered contradictory results (Figure 6). The earliest phylogenetic analyses of the group found glyptodonts to be closely related to Eutatini (Proeutatus Ameghino, 1891 and Eutatus Ameghino, 1887extinct armadillos generally linked to euphractines [START_REF] Scillato-Yané | Catálogo de los Dasypodidae fósiles (Mammalia, Edentata) de la República Argentina, in II Congreso Argentino de Paleontología y Bioestratigrafía y I Congreso Latinoamericano de Paleontología[END_REF], 1982;[START_REF] Mckenna | Classification of mammals: above the species level[END_REF][START_REF] Scillato-Yané | Las especies del género Chasicotatus Scillato-Yané (Eutatini, Dasypodidae)[END_REF]) and to form with the pampatheres the sister group to extant cingulates (e.g., Engelmann, 1985 -Figure 6A). More recent analyses using morphology favored instead a close relationship of glyptodonts with Proeutatus but not with Eutatus, in a nested position within extant armadillos [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF][START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF]. These studies also suggested that glyptodonts are more closely related to euphractines and chlamyphorines than to other extant armadillos (Figure 6C,D). The most recent analysis proposed a position of glyptodonts as a sister group to a clade formed by dasypodines and tolypeutines (Herrera et al., 2017 -Figure 6F). As with the extant clades, morpho-anatomical analyses have struggled to reach a consensus view on the position of the glyptodonts.

The advent of molecular analyses first challenged the previous phylogenetic hypotheses on extant cingulates based on morpho-anatomy (e.g., [START_REF] Delsuc | Molecular phylogeny of living xenarthrans and the impact of character and taxon sampling on the placental tree rooting[END_REF][START_REF] Delsuc | Molecular systematics of armadillos (Xenarthra, Dasypodidae): contribution of maximum likelihood and Bayesian analyses of mitochondrial and nuclear genes[END_REF]. In 2016, two teams succeeded in extracting and analyzing mitochondrial DNA of one of the last representatives of glyptodonts: Doedicurus Burmeister, 1874 [START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF][START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF]. This new data resulted in a completely new hypothesis: glyptodonts were recovered as the sister group of a clade formed by the extant chlamyphorines and tolypeutines (Delsuc et al., 2016;Mitchell et al., 2016 -Figure 6H). These results differed considerably from the various hypotheses proposed by morphological phylogenetics. Interestingly, [START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF] demonstrated that by using the same morphological matrix as [START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF] but applying a molecular backbone constraint, the analysis revealed several morphological characters that supported a close relationship between glyptodonts and chlamyphorines (in agreement with comments by [START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF] (Mitchell et al., 2016 -Figure 6E), but not with tolypeutines.

In conclusion, in addition to being debated among morphologists, the position of glyptodonts represents a major conflict between morpho-anatomical and molecular analyses.

This situation encourages us to assess whether a revision of morphological evidence can help to resolve these conflicts. In particular, such a re-evaluation could consist of i) examining poorly known anatomical regions in order to collect a wider spectrum of characters, and, ii) having a closer look at patterns of morphological covariation to see if they can affect phylogenetic analyses of the group.

Anatomy and Covariation Patterns on the Cingulate Skull:

State of the Art

External and Internal Anatomy in Cingulata

Cranial and postcranial skeletal anatomy are already well known for many groups within the Cingulata, representing one of the most intensively investigated topics for the group [START_REF] Superina | What do we know about armadillos? An analysis of four centuries of knowledge about a group of South American mammals, with emphasis on their conservation[END_REF]. This is particularly the case for glyptodonts, which have been the subject of numerous anatomical descriptions and discussions for more than 150 years, especially regarding the skull (e.g., [START_REF] Owen | Description of a tooth and part of the skeleton of the Glyptodon, a large quadruped of the edentate order, to which belongs the tessellated bony armour figured by Mr. Clift in his memoir on the remains of the Megatherium, brought to England by Sir Woodbine Parish[END_REF][START_REF] Scott | Mammalia of the Santa Cruz beds. I. Edentata[END_REF][START_REF] Lr | Los Cingulata (Mammalia, Xenarthra) del Mioceno temprano y medio de Patagonia (edades Santacrucense y "Friasense[END_REF]). Yet, many aspects of the internal cranial anatomy remain poorly known in the group although recent works have shown that internal cranial anatomy in the Cingulata could provide new phylogenetic information. This includes the study of the inner ear in extant xenarthrans (Billet et al., 2015a);

the study of the paranasal sinuses and the narial region, which has led to the discovery of synapomorphies in Pleistocene glyptodonts [START_REF] Zurita | Neosclerocalyptus spp. (Cingulata: Glyptodontidae: Hoplophorini): cranial morphology and palaeoenvironments along the changing Quaternary[END_REF][START_REF] Fernicola | A neomorphic ossification of the nasal cartilages and the structure of paranasal sinus system of the glyptodont Neosclerocalyptus Paula Couto 1957 (Mammalia, Xenarthra)[END_REF]; or the study of morphological similarities of the brain endocast in extinct and extant Cingulata species, including glyptodonts (Tambusso & Fariña, 2015a;Tambusso & Fariña, 2015b). Apart from these, there are still many understudied aspects of the internal cranial anatomy that could potentially provide phylogenetic insight into the origins of glyptodonts. These include internal cranial canals which are rarely described or discussed beyond the presence/absence of their external foramina (but see the descriptive work on Euphractus sexcinctus Linnaeus, 1758 by [START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF] although they may be of real systematic interest (e.g., in turtles - [START_REF] Albrecht | The cranial arteries and cranial arterial foramina of the turtle genera Chrysemys, Sternotherus, and Trionyx: a comparative study with analysis of possible evolutionary implications[END_REF][START_REF] Albrecht | The cranial arteries of turtles and their evolutionary significance[END_REF][START_REF] Gaffney | Comparative cranial morphology of recent and fossil turtles[END_REF]Rollot et al., in press;or in therapsids -Araujo et al., 2017). The morphological variation of the internal part of the dentition, hidden within dental alveoli, is also poorly known in the group. Tooth roots can extend very high in the snout in glyptodonts (e.g., [START_REF] González-Ruiz | Juvenile Glyptodont (Mammalia, Cingulata) from the Miocene of Patagonia, Argentina: Insights into Mandibular and Dental Characters[END_REF] and this root height may be much lower in other groups (e.g., Dasypus -Ciancio et al., 2012). More studies are needed to investigate these aspects. Figure 7 provides an overview of some internal cranial regions that remain to be explored in glyptodonts and in other cingulates. Added to our knowledge of external anatomy, the scrutiny of new internal structural features would allow us to have a more complete view of the cranial anatomy of glyptodonts. The greater the completeness of our anatomical knowledge, the more potential characters could be defined and used for morphological phylogenetics to search for the origin of glyptodonts among cingulates. These poorly studied anatomical structures will be explored in Chapter 2.

Morphology, phylogeny, and covariation pattern in the cingulate skull

Despite numerous studies on the evolutionary history of cingulates, disagreements and uncertainties remain regarding several systematic issues, as noted above (see Section 1.2). The number of hypotheses is particularly high among phylogenies based on morphological data, especially for glyptodonts [START_REF] Engelmann | The evolution and ecology of armadillos, sloths and vermilinguas[END_REF][START_REF] Abrantes | Proposta filogenetica para os Dasypodidae (Mammalia: Cingulata)[END_REF][START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF][START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF][START_REF] Herrera | A new Eocene dasypodid with caniniforms (Mammalia, Xenarthra, Cingulata) from northwest Argentina[END_REF]. Conversely, molecular studies provided more stable results on the group [START_REF] Delsuc | Molecular phylogeny of living xenarthrans and the impact of character and taxon sampling on the placental tree rooting[END_REF][START_REF] Delsuc | Molecular systematics of armadillos (Xenarthra, Dasypodidae): contribution of maximum likelihood and Bayesian analyses of mitochondrial and nuclear genes[END_REF][START_REF] Delsuc | Molecular phylogenetics unveils the ancient evolutionary origins of the enigmatic fairy armadillos[END_REF][START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF][START_REF] Abba | Systematics of hairy armadillos and the taxonomic status of the Andean hairy armadillo (Chaetophractus nationi)[END_REF]Gibb et al., 2016;[START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF] but they are restricted in terms of access to data for extinct taxa.

The oldest reconstituted nuclear DNA for extinct mammals is around 1.7 Ma [START_REF] Cappellini | Ancient biomolecules and evolutionary inference[END_REF]), but proteomics extended this limit beyond one million years by reconstructing several protein sequences recovered from fossil mammal teeth (the oldest of which are 1.8 million years in age [START_REF] Warren | Move over, DNA: ancient proteins are starting to reveal humanity's history[END_REF]) which can be exploited for phylogenetic analyses [START_REF] Warren | Move over, DNA: ancient proteins are starting to reveal humanity's history[END_REF]. As glyptodonts have recently disappeared, teams have been able to reconstruct mitochondrial DNA sequences of one of their last representatives [START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF][START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF].

However, the history of cingulates goes back at least to the beginning of the Eocene, and the history of glyptodonts at least to the late Eocene (Figure 3). Consequently, a large part of the history of cingulates cannot be covered by the molecular data alone, which confers a prime importance to morphological data for reconstructing their evolutionary history.

This observation is obviously not unique to cingulates and over the last twenty years, the primacy of morphological data to phylogenetically place those extinct taxa inaccessible to molecular analysis has been widely recognized [START_REF] Wiens | The role of morphological data in phylogeny reconstruction[END_REF][START_REF] Asher | Morphology, paleontology, and placental mammal phylogeny[END_REF][START_REF] Springer | Morphology and placental mammal phylogeny[END_REF]. Fossils and their morphology are of prime importance for the reconstruction of evolutionary scenarios and for evolutionary biology in general because of the crucial contribution of their historical information. Although the analysis of fossils can yield congruence between molecular and morphological analyses (e.g., [START_REF] Morlon | Reconciling molecular phylogenies with the fossil record[END_REF][START_REF] Legg | Arthropod fossil data increase congruence of morphological and molecular phylogenies[END_REF], phylogenetic analyses including extinct of cingulates did not reach a high level of agreement with molecular studies (see Section 1.2).

Strong criticism of the use of morphological data for phylogenetic analyses has been expressed by several authors in the last decades (e.g., [START_REF] Scotland | Phylogeny reconstruction: the role of morphology[END_REF][START_REF] Springer | Morphology and placental mammal phylogeny[END_REF][START_REF] Springer | Technical comment on "The placental mammal ancestor and the post-K-Pg radiation of placentals[END_REF]. For instance, they underlined the frequent ambiguity in the definition of the morphological characters and the difficulty posed by correlated homoplasy among morphological characters. It is certainly true that the usefulness of fossils and morphological data for reconstructing evolutionary scenarios is complicated by the complexity of extracting the phylogenetic signal contained in morphological variation. In line with this observation, many studies have called for an improvement of our approaches and methods, which logically includes a better modeling of morphological variation [START_REF] Dávalos | Integrating incomplete fossils by isolating conflicting signal in saturated and non-independent morphological characters[END_REF][START_REF] Goswami | The macroevolutionary consequences of phenotypic integration: from development to deep time[END_REF]Billet et al., 2015a;[START_REF] Harrison | Among-character rate variation distributions in phylogenetic analysis of discrete morphological characters[END_REF][START_REF] Lee | Morphological phylogenetics in the genomic age[END_REF][START_REF] Pyron | Post-molecular systematics and the future of phylogenetics[END_REF][START_REF] Wright | Modeling character change heterogeneity in phylogenetic analyses of morphology through the use of priors[END_REF][START_REF] Bardin | Ontogenetic data analyzed as such in phylogenies[END_REF][START_REF] Billet | Serial Homology and Correlated Characters in Morphological Phylogenetics: Modeling the Evolution of Dental Crests in Placentals[END_REF]. However, morphological variation is a very complex matter [START_REF] Hallgrímsson | Variation: a central concept in biology[END_REF] and designing adapted models of morphological evolution is therefore extremely challenging.

A limiting factor for the modeling of morphological variation corresponds first and foremost to a lack of knowledge of the nature and scope morphological variation in general [START_REF] Hallgrímsson | Variation: a central concept in biology[END_REF]. One of the major problems lies in the degree of integration between two morphological traits, which often remains unexplored or neglected (Emerson & Hasting, 1998). The concept of morphological integration is defined as "the tendency of different traits to vary jointly, in a coordinated manner, throughout a morphological structure or even a whole organism" (Klingenberg, 2014: pp. 2). A strong integration thus signals a dependence between morphological traits. It is now well-known that dependence between characters in a matrix can be a major source of misleading data in phylogenetic analyses (e.g., [START_REF] Wilkinson | A comparison of two methods of character construction[END_REF][START_REF] Emerson | Morphological correlations in evolution: consequences for phylogenetic analysis[END_REF]Goswami & Polly, 2010a;[START_REF] Goswami | The macroevolutionary consequences of phenotypic integration: from development to deep time[END_REF][START_REF] Guillerme | Influence of different modes of morphological character correlation on phylogenetic tree inference[END_REF]. Morphological integration may thus have a deleterious effect on morphological phylogenetics whose methods presuppose independence between characters [START_REF] Felsenstein | Maximum likelihood and minimum-steps methods for estimating evolutionary trees from data on discrete characters[END_REF][START_REF] Kluge | A concern for evidence and a phylogenetic hypothesis of relationships among Epicrates (Boidae, Serpentes)[END_REF][START_REF] Emerson | Morphological correlations in evolution: consequences for phylogenetic analysis[END_REF][START_REF] O'keefe | Inferring and testing hypotheses of cladistic character dependence by using character compatibility[END_REF][START_REF] Lewis | A likelihood approach to estimating phylogeny from discrete morphological character data[END_REF][START_REF] Felsenstein | Inferring phylogenies[END_REF]. Examples of highly covarying characters used in phylogenetics may be found among serial homologues which correspond to repeated structures sharing a large proportion of their genetic architecture and developmental trajectory (e.g., [START_REF] Young | Serial homology and the evolution of mammalian limb covariation structure[END_REF]. Teeth count as serial homologues and their serial variation is sometimes scored as multiple separated traits on successive loci in mammalian phylogenetics (e.g., [START_REF] Gd | Phylogeny of the Carnivora: basal relationships among the carnivoramorphans, and assessment of the position of 'Miacoidea' relative to Carnivora[END_REF][START_REF] O'leary | The placental mammal ancestor and the post-K-Pg radiation of placentals[END_REF]. This approach can be problematic as repeated characters on successive teeth can show a high degree of integration in mammals and may thus mislead phylogenetic analyses [START_REF] Naylor | Are the fossil data really at odds with the molecular data? Morphological evidence for cetartiodactyla phylogeny reexamined[END_REF][START_REF] Billet | Serial Homology and Correlated Characters in Morphological Phylogenetics: Modeling the Evolution of Dental Crests in Placentals[END_REF]. A high degree of integration may also be found in the skull or other anatomical regions (e.g., [START_REF] Olson | Morphological integration[END_REF]Cheverud, 1982a;[START_REF] Hallgrímsson | Evolution of covariance in the mammalian skull[END_REF][START_REF] Goswami | EMMLi: a maximum likelihood approach to the analysis of modularity[END_REF] and thus a better knowledge of patterns of covariation in general is a prerequisite towards an improvement in our morphological matrices and models of character evolution [START_REF] Billet | Serial Homology and Correlated Characters in Morphological Phylogenetics: Modeling the Evolution of Dental Crests in Placentals[END_REF].

As discussed above, morphological variation is extremely complex. In addition to having determinants that might be multiple and interconnected, variation is a pervasive phenomenon at all levels of the biological hierarchy [START_REF] Hallgrímsson | Variation: a central concept in biology[END_REF]. The same is certainly true for morphological integration, which can be studied at various levels [START_REF] Klingenberg | Studying morphological integration and modularity at multiple levels: concepts and analysis[END_REF]. Morphological integration can occur at the static level (within one species and ontogenetic stage), at the ontogenetic level (across developmental stages within one species), and at the evolutionary level (among several species) (Figure 8). A main goal of comparative studies scrutinizing morphological integration at various levels is to investigate whether we can identify common covariation patterns within one or several species, and how constrained these patterns are (e.g., [START_REF] Pélabon | On the relationship between ontogenetic and static allometry[END_REF]. Therefore, such studies can serve as a basis for screening morphological data matrices in search of characters that could relate to common covariation patterns and thus be potentially misleading in phylogenetic analyses (i.e., condition of the character independencesee above).

Figure 8. Examples of ontogenetic, static, and evolutionary levels of variation in three species of armadillos. The ontogenetic level concerns variation across developmental stages within one species. The static level is variation within one species and stage. The evolutionary level focuses on variation among species at any given stage (= interspecific) [START_REF] Klingenberg | Studying morphological integration and modularity at multiple levels: concepts and analysis[END_REF]. Abbreviation: novemcin., novemcinctus.

Despite the great number of studies on morphological integration in recent years, cranial covariation patterns in Cingulata remain poorly known. Some studies have focused on the covariation of specific cranial distances with a size variable (e.g., [START_REF] Moeller | Allometrische analyse der gürteltier schädel. Ein beitrag zur phylogenie der Dasypodidae Bonaparte, 1838[END_REF] or on covariations among shape variables in the inner ear region (e.g., inner ear - Billet et al., 2015a) using mainly adult specimens of extant species. A few studies based on extant and fossil species have also explored the covariation between cranial shape and functional aspects such as diet (e.g., [START_REF] Vizcaíno | Functional and phylogenetic assessment of the masticatory adaptations in Cingulata (Mammalia, Xenarthra)[END_REF]in glyptodont -Fariña & Vizcaíno, 2001). In addition, [START_REF] Hubbe | A case study of extant and extinct Xenarthra cranium covariance structure: implications and applications to paleontology[END_REF] analyzed the structure of phenotypic variance-covariance matrices based on 18 cranial linear distances within 7 genera of extant armadillos, in order to test whether such matrices in extant taxa can be used as surrogates for extinct ones. Their study, however, did not provide a detailed account of the covarying distances in the cingulate skull. Beside morphological integration, there are also few studies evaluating cranial shape variation in cingulates using 3D data (through almost none that incorporate fossils). Cranial shape variation has been analyzed among species of euphractines [START_REF] Abba | Systematics of hairy armadillos and the taxonomic status of the Andean hairy armadillo (Chaetophractus nationi)[END_REF] and among several species of the genus Dasypus Linnaeus, 1758 together with a preliminary report on allometric patterns (Hautier et al., 2017;[START_REF] Feijó | Taxonomic revision of the long-nosed armadillos, Genus Dasypus Linnaeus, 1758 (Mammalia, Cingulata)[END_REF]. Overall, there remain few detailed accounts of patterns of covariation among cranial traits in cingulates, whether at the evolutionary level, or at the ontogenetic or static levels. We explore these aspects in detail in Chapter 3 and Chapter 4.

CHAPTER 2 New Insights from Internal Anatomy

« Fais d'abord l'anatomie de l'aile, puis celle des pennes sans plumes, puis celles des pennes avec les plumes ». Leonard de Vinci.

"First do the anatomy of the wing, then the anatomy of the featherless pen, then the anatomy of the feathered pen". Leonard de Vinci.

Comparative anatomy and phylogenetic contribution of internal cranial

structures in extant armadillos and extinct glyptodonts (Xenarthra, Cingulata)

ABSTRACT

The evolutionary history of the Cingulata, as for many groups, remains a highly debated topic to this day, particularly for one of their most emblematic representatives: the glyptodonts.

There is no consensus among morphological and molecular phylogenies relative to their position within Cingulata. As demonstrated by recent works, the study of the internal anatomy constitutes a promising path for enriching morphological matrices for the phylogenetic study of armadillos. However, internal cranial anatomy remains under-studied in the Cingulata. Here we explored and compared the anatomy of intracranial osseous canals and cavities in a diverse sample of extant and extinct cingulates, including the earliest well-preserved glyptodont crania.

The virtual 3D reconstruction (using X-ray microtomography) of selected canals and cavities related to cranial vascularization, innervation or tooth insertion allowed us to compare the locations, trajectories and shape of these structures and to discuss their potential interest for cingulate systematics. We tentatively reconstructed evolutionary scenarios for eight selected traits on these structures, in which glyptodonts often showed a greater resemblance to pampatheres, to the genus Proeutatus and/or to chlamyphorines. This latter pattern was partly congruent with recent molecular hypotheses, but more research is needed on these resemblances and on the potential effects of development and allometry on the observed variations. Overall, these comparisons have enabled us to highlight new anatomical variation that may be of great interest to further explore the evolutionary history of cingulates and the origins of glyptodonts on a morphological basis.

Le Verger K, Gonzalez Ruiz L, Billet G. Article In Preparation.

Introduction

The peculiar morphology of xenarthrans, which include armadillos (Cingulata), sloths (Folivora) and anteaters (Vermilingua), has aroused the curiosity of anatomists since the end of the 18th century [START_REF] Cuvier | Tableau élémentaire de l'histoire naturelle des animaux[END_REF]. Compared to other mammals, the sum of their unique characteristics has led them to be considered by some earlier workers the most unusual mammals (Vizcaíno & Loughbry, 2008; for a summary see Superina & Loughry, 2015).

Cingulates represent the only known mammals with a carapace, which contains a variable number of mobile bands and is formed by a mosaic of osteoderms covering the head, body and tail (Vizcaíno & Loughry, 2008). Cingulates include extant and extinct armadillos, among them the four extant clades Dasypodinae, Euphractinae, Tolypeutinae, and Chlamyphorinae, as well as the extinct glyptodonts, a group of herbivorous and large bodied mammals appearing in the late Eocene and disappearing at the beginning of the Holocene [START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF]; see also [START_REF] Gaudin | Cranial osteology of the pampathere Holmesina floridanus (Xenarthra: Cingulata; Blancan NALMA), including a description of an isolated petrosal bone[END_REF] for an alternative classification). The phylogenetic position of glyptodonts within Cingulata is particularly difficult to resolve based on morphological data because of their highly specialized anatomy and the large morphological gap separating them from extant armadillos [START_REF] Burmeister | Monografía de los glyptodontes en el Museo Público de Buenos Aires[END_REF][START_REF] Carlini | An introduction to cingulate evolution and their evolutionary history during the great American biotic interchange: biogeographical clues from Venezuela[END_REF][START_REF] Fariña | Megafauna: giant beasts of Pleistocene South America[END_REF]. This difficulty was recently emphasized by ancient DNA studies showing that phylogenetic analyses of their mitogenomes support a position for glyptodonts at odds with that proposed in prior morphological studies [START_REF] Engelmann | The evolution and ecology of armadillos, sloths and vermilinguas[END_REF][START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF][START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF]Delsuc et al., 2016;[START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF][START_REF] Herrera | A new Eocene dasypodid with caniniforms (Mammalia, Xenarthra, Cingulata) from northwest Argentina[END_REF].

While it has long been accepted that glyptodonts were closely related to extant armadillos [START_REF] Huxley | II. On the osteology of the genus Glyptodon[END_REF], their exact relationships with the latter were never clearly resolved on the basis morphological data. [START_REF] Flower | On the mutual affinities of the animals composing the order Edentata[END_REF] initially proposed that glyptodonts were the ancestors of extant armadillos but [START_REF] Ameghino | Filogenia: Principios de clasificación transformista basados sobre leyes naturales y proporciones matemáticas[END_REF][START_REF] Ameghino | Contribución al conocimiento de los mamíferos fósiles de la República Argentina[END_REF] disputed this hypothesis, arguing that their great dental and postcranial complexity, as described by Owen (1839) was evidence of their derived nature. The nested position of glyptodonts among extant armadillos has been supported by many authors since then, including by recent phylogenetic analyses using morphological data [START_REF] Castellanos | Nuevos géneros de gliptodontes en relación con su filogenia[END_REF][START_REF] Castellanos | Trascendencia de la obra de Florentino Ameghino[END_REF][START_REF] Hoffstetter | Xenarthra[END_REF][START_REF] Patterson | The Fossil Mammal Fauna of South America[END_REF]see Fernicola (2008) for a brief review of the history of the group; [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF][START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF][START_REF] Herrera | A new Eocene dasypodid with caniniforms (Mammalia, Xenarthra, Cingulata) from northwest Argentina[END_REF]. However, the consensus stops here. [START_REF] Engelmann | The evolution and ecology of armadillos, sloths and vermilinguas[END_REF] proposed a close relationship of glyptodonts with the extinct Eutatini (Proeutatus and Eutatus) and pampatheres, whereas the analysis of [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF] retrieved glyptodonts in an apical position nested within a large clade gathering euphractines, chlamyphorines, the extinct pampatheres and some extinct eutatines. A similar hypothesis was also supported by other studies, but with much variation in the composition of this large apical clade [START_REF] Fernicola | Nuevos aportes para la sistemática de los Glyptodontia Ameghino 1889 (Mammalia, Xenarthra, Cingulata)[END_REF][START_REF] Porpino | Revisiting the intertropical Brazilian species Hoplophorus euphractus (Cingulata, Glyptodontoidea) and the phylogenetic affinities of Hoplophorus[END_REF][START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF][START_REF] Fernicola | A new species of Neoglyptatelus (Mammalia, Xenarthra, Cingulata) from the late Miocene of Uruguay provides new insights on the evolution of the dorsal armor in cingulates[END_REF][START_REF] Herrera | A new Eocene dasypodid with caniniforms (Mammalia, Xenarthra, Cingulata) from northwest Argentina[END_REF]. Most of these studies, however, unvaryingly proposed a close relationship between the extinct giant pampatheres and glyptodonts, in agreement with [START_REF] Patterson | The Fossil Mammal Fauna of South America[END_REF]. Thanks to the progress made in ancient DNA studies and the recent extinction of glyptodontsat the beginning of the Holocene [START_REF] Messineo | New radiocarbon dates from the Campo Laborde site (Pampean Region, Argentina) support the Holocene survival of giant ground sloth and glyptodonts[END_REF])the complete mitochondrial genome of the late diverging glyptodont Doedicurus could be successfully assembled, which gave rise to a completely new phylogenetic hypothesis [START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF][START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF]. Based on analyses of their mitogenomes, glyptodonts are nested within extant armadillos and represent the sister group of a clade formed by chlamyphorines and tolypeutines [START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF][START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF]. Although analyses of morphological matrices using a molecular backbone constraint can detect morphological characters congruent with the molecular pattern [START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF], the high level of disagreement between the two data partitions still calls into question the phylogenetic signal provided by morphological matrices on cingulates.

External cranial and postcranial skeletal anatomy are already well known for many groups within Cingulata, but the internal cranial anatomy remains understudied. However, its study has already provided data of systematic interest for both the extant and extinct xenarthran diversity [START_REF] Zurita | Neosclerocalyptus spp. (Cingulata: Glyptodontidae: Hoplophorini): cranial morphology and palaeoenvironments along the changing Quaternary[END_REF][START_REF] Fernicola | A neomorphic ossification of the nasal cartilages and the structure of paranasal sinus system of the glyptodont Neosclerocalyptus Paula Couto 1957 (Mammalia, Xenarthra)[END_REF]Billet et al., 2015a;Tambusso & Fariña, 2015a;Tambusso & Fariña, 2015b;[START_REF] Billet | The hidden anatomy of paranasal sinuses reveals biogeographically distinct morphotypes in the nine-banded armadillo (Dasypus novemcinctus)[END_REF][START_REF] Boscaini | Digital cranial endocasts of the extinct sloth Glossotherium robustum (Xenarthra, Mylodontidae) from the late Pleistocene of Argentina: description and comparison with the extant sloths[END_REF][START_REF] Boscaini | Cranial anatomy and paleoneurology of the extinct sloth Catonyx tarijensis (Xenarthra, Mylodontidae) from the late Pleistocene of Oruro, Southwestern Bolivia[END_REF]. Intracranial osseous canals provide important pathways for innervation and vascularization of the head [START_REF] Evans | Miller's Anatomy of the Dog[END_REF]. The diversity and phylogenetic signal of their intracranial trajectories are poorly known, as these hidden structures are rarely described in mammals in general, including xenarthrans (e.g., [START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF]. In contrast, their external openings on the skull are often described and scored in phylogenetic matrices (e.g., 37/131 of cranial characters - [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF].

Here we present a comparative investigation of intracranial osseous canals and cavities in a diverse sample of extant and extinct cingulates, including the earliest well-preserved glyptodont crania, using X-ray microtomography. The 3D virtual reconstruction of selected canals and cavities related to cranial vascularization, innervation or tooth insertion enabled us to compare the locations, trajectories and shape of each homologous structure and discuss their potential interest for cingulate systematics. We tentatively reconstructed the evolutionary history of these traits using a molecularly constrained phylogeny, and we discuss the potential effects of development and allometry on their variation. These comparisons, combined with information obtained from the literature, allowed us to propose new potential characters that may be used to further explore the origins of glyptodonts within cingulates on a morphological basis.

Materials and methods

Sampling

We examined the skulls of 33 extant and extinct xenarthran specimens. Two specimens belonging to the Pilosa (sloths and anteaters) were chosen as outgroups. The remaining 31 skulls belonged to Cingulata (Table 1). This sample included specimens representing the 9 extant genera, as well as three small developmental series in phylogenetically distant species (Cabassous unicinctus, Dasypus novemcinctus, Zaedyus pichiy), with the aim of better understanding the ontogenetic variation of the selected anatomical structures. The cingulate specimens also included 14 specimens belonging to fossil species, among them six glyptodonts (Table 1). This sample covered more than 40 million years of cingulate evolutionary history and includes all the major cingulate clades. The small number of well-preserved fossil specimens did not allow us to evaluate intraspecific variation, as we were unable to perform measurements on more than 1 or 2 specimens per species (Table S1). Species identification was based on collection data, geographical origin, cranial anatomy, and the literature on cingulate taxonomy (e.g., [START_REF] Scott | Mammalia of the Santa Cruz beds. I. Edentata[END_REF][START_REF] Mcbee | Dasypus novemcinctus[END_REF][START_REF] Wetzel | Taxonomy and distribution of armadillos, Dasypodidae[END_REF][START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF][START_REF] Wetzel | Order cingulata[END_REF]Hayssen, 2014a;[START_REF] Abba | Systematics of hairy armadillos and the taxonomic status of the Andean hairy armadillo (Chaetophractus nationi)[END_REF][START_REF] Carlini | Chaetophractus vellerosus (Cingulata: Dasypodidae)[END_REF][START_REF] Gaudin | Cranial osteology of the pampathere Holmesina floridanus (Xenarthra: Cingulata; Blancan NALMA), including a description of an isolated petrosal bone[END_REF][START_REF] Smith | Calyptophractus retusus (Cingulata: Dasypodidae)[END_REF]. Digital data of all specimens were acquired using X-ray microcomputed tomography (μCT). Specimens were scanned on X-ray tomography imagery platforms at the American Museum of Natural History (New York, USA); the Museum national d'Histoire naturelle (France) in Paris (AST-RX platform), the University of Montpellier (France) and the Museum für Naturkunde (ZMB) in Berlin (Germany). Three-dimensional reconstructions of the selected structures were performed using stacks of digital μCT images with MIMICS v. 21.0 software (3D Medical Image Processing Software, Materialize, Leuven, Belgium). The visualization of 3D models was also conducted with AVIZO v. 9.7.0 software (Visualization Sciences Group, Burlington, MA, USA).

Selected regions of interest and anatomical nomenclature

We selected several osseous anatomical complexes in the internal cranial anatomy of cingulates that are poorly known and of interest for this study such as dental alveoli and several specific intraosseous canals. The latter mostly correspond to vascular pathways and/or the courses of cranial nerves involved in the innervation of various cranial areas: the nasolacrimal canal, the palatine canal, the sphenopalatine canal, the canal for the frontal diploic vein, the transverse canal, the orbitotemporal canal, the canal for the capsuloparietal emissary vein and the posttemporal canal.

Except for Dasypus, which represents a special case (see [START_REF] Ciancio | Evolutionary implications of dental eruption in Dasypus (Xenarthra)[END_REF], the homologies in the dental row between the different species of Cingulata are not known mainly because of the drastic reduction in dental complexity [START_REF] Vizcaíno | The teeth of the "toothless": novelties and key innovations in the evolution of xenarthrans (Mammalia, Xenarthra)[END_REF]. For glyptodonts, previous studies conventionally designated the whole set of teeth as molariform but without further precision (e.g., [START_REF] González-Ruiz | First record of supernumerary teeth in Glyptodontidae (Mammalia, Xenarthra, Cingulata)[END_REF]. We therefore chose to use a positional nomenclature and to designate separately the teeth housed in the premaxillary (Pt) from the molariform teeth (Mf) borne by the maxillary (see [START_REF] Herrera | A new Eocene dasypodid with caniniforms (Mammalia, Xenarthra, Cingulata) from northwest Argentina[END_REF] for a different nomenclature).

Only those intracranial canals whose sampled variation appeared to bear clear systematic information were selected in this work (Figure 9). Non-selected canals generally showed asymmetric and intraspecific variation (e.g., hypoglossal canal; trajectory of the internal carotid arterysee [START_REF] Patterson | The ear region in xenarthrans (=Edentata, Mammalia). Part I. Cingulates[END_REF][START_REF] Gaudin | The ear region of edentates and the phylogeny of the Tardigrada (Mammalia, Xenarthra)[END_REF] or provided no new data (e.g., infraorbital canal) with respect to what was already described or scored for the systematics of the group [START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF][START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF][START_REF] Gaudin | Cranial osteology of the pampathere Holmesina floridanus (Xenarthra: Cingulata; Blancan NALMA), including a description of an isolated petrosal bone[END_REF]. Other nonselected canals were rarely visible in all specimens (often due to taphonomynot in place and/or obscured by a hard and dense matrix) and were therefore difficult to compare. Specimens that presented a canal that was too incomplete are not described in the relevant section. For the identification and nomenclature of the selected intracranial canals, our study used previous work describing intracranial anatomy in cingulates and eutherians in general [START_REF] Thewissen | Mammalian frontal diploic vein and the human foramen caecum[END_REF][START_REF] Wible | Cranial circulation and relationships of the colugo Cynocephalus (Dermoptera, Mammalia)[END_REF][START_REF] Gaudin | Phylogenetic relationships among sloths (Mammalia, Xenarthra, Tardigrada): the craniodental evidence[END_REF][START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF][START_REF] Evans | Miller's Anatomy of the Dog[END_REF][START_REF] Muizon De | Alcidedorbignya inopinata, a basal pantodont (Placentalia, Mammalia) from the early Palaeocene of Bolivia: anatomy, phylogeny and palaeobiology[END_REF][START_REF] Gaudin | Cranial osteology of the pampathere Holmesina floridanus (Xenarthra: Cingulata; Blancan NALMA), including a description of an isolated petrosal bone[END_REF]. We have indicated for each selected region of interest: the variation of these regions during ontogeny, a synthetic comparison among specimens, and the formalization of potential discrete or continuous characters to highlight potential evolutionary scenarios to be mapped onto the tree of cingulates. The formalization of new characters was performed based on observations that were stable among glyptodonts and were shared with some non-glyptodonts cingulates, so that they could provide pertinent information when investigating glyptodont origins.

Virtual reconstruction of the selected regions

Teeth were absent for many specimens, but they were reconstructed when present. When present, the most dorsal part of the teeth did not always fill the whole alveolar cavity, leaving a void between the roof of the alveolar cavity and the dorsal edge of the tooth. Because we selected the internal orientation and curvature of the whole dental row for study, the reconstruction of alveoli was preferred over the modelling of teeth, which were sometimes absent for our specimens. In some cases, the distinction between the limit of the alveolar wall, the tooth and the sediment were not identifiable. In this case we modelled only the distinguishable structures to allow comparison (e.g., Doellotatus sp. in Figure 10).

A canal corresponds to a duct completely enclosed in one or more bones, and which usually provides passageway to vessels and/or nerves. In some cases, a canal may not be continuously enclosed by bone, and thus turns into a groove for part of its course (e.g., orbitotemporal canal).

In such a case, we have reconstructed the course of the groove in a manner similarly to that of a canal, but we illustrated the areas corresponding to the groove with increased transparency.

In some cases, two canals were confluent in such a way that it was no longer possible to distinguish which part of the duct corresponds to the passage of which vessel or nerve. These regions of confluence were specified in each of our reconstructions by a shaded area (e.g., posttemporal canal and canal for the capsuloparietal emissary vein). Most selected canals were continuous with external or internal foramina. Figure S2 shows the location of each of these foramina in Euphractus sexcinctus.

Measurements

A few specific measurements were taken for comparison where quantification seemed to offer a better account of the observed variation than a qualitative description. Skull length, height and width were measured to calculate the geometric mean of each specimen (= geometric mean, an estimator of the size of a specimen defined by the cubic root of the product of the three variables [START_REF]Morphometrics with R[END_REF]). The geometric mean was log transformed to facilitate graphing of the data [START_REF]Morphometrics with R[END_REF]. Several other cranial measurements were selected, and their variation was compared to that of the geometric mean in our sample (Table S2 and Figure S3).

These measurements were selected in order to quantify the following aspects that appeared interesting to us after our anatomical observations: 1) the relative height of the dental row (i.e., GDRH/GSH = the ratio between the greatest dental row height and the greatest skull height);

2) the angle between the straight line marked by the ventral most point of the tentorial process and the dorsal most point of the annular ridge (see Wible & Spaulding, 2013) and the horizontal anteroposterior axis defined here by the straight line between the mesial edge of the first tooth and the distal edge of the last tooth in sagittal view to compare the internal vault inclination (IVI) among taxa. These measurements are further explained and summarized in Figure S3; they were taken using the linear distance and angle tools of MIMICS v. 21.0 software.

Reconstructing evolutionary scenarios for intracranial traits

In order to visualize possible evolutionary scenarios for the discrete and continuous intracranial traits defined based on our observations, we reconstructed a cladogram focused on the taxa in our sample by performing a parsimony analysis using PAUP v. 4.0a167 [START_REF] Swofford | PAUP: Phylogenetic analysis using parsimony (and other methods)[END_REF]. We used the morphological matrix of [START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF] (largely based on that of [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF], which we limited to the genera in our sample (Utaetus buccatus was also removed due to an overly large amount of missing data). The initial matrix included all the genera of our sample except for one extant genus (Calyptophractus), along with four fossil genera: three Santacrucian glyptodonts ("Cochlops", Eucinepeltus, and "Metopotoxus") and one Pleistocene glyptodont (Glyptodon). We therefore scored these fossil taxa based on our CTscanned specimens and added them to the analysis. After this stage, the matrix included 22 taxa scored for 125 characters (Supporting information 2). We performed the same analysis as [START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF], with a heuristic search involving 1000 random addition replicates, with 27 morphological characters treated as ordered and treating taxa with multiple states as polymorphic (Supporting information 2). Following the recent molecular works of Delsuc et al. (2016) and [START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF], we enforced a backbone constraint similar to that of [START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF]. Because this resulted in an unusual position for Proeutatus lagena (i.e., as the sister group of euphractines), contrary to its usual placement close to the glyptodonts in morphological analyses [START_REF] Engelmann | The evolution and ecology of armadillos, sloths and vermilinguas[END_REF][START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF][START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF][START_REF] Herrera | A new Eocene dasypodid with caniniforms (Mammalia, Xenarthra, Cingulata) from northwest Argentina[END_REF], we added a constraint on this taxon to assign it a priori to a position close to glyptodonts (Figure S4A). By using this approach, our aim was only to obtain a more consensual topology, based on recent morphological and molecular analyses, in order to discuss the relevance of our characters. This study is not intended to produce a new phylogenetic analysis. The strict consensus of the most parsimonious trees (with two polytomiesextant euphractines and glyptodont except for "Metopotoxus" anceps) obtained was then used to calculate branch lengths in order to explore evolutionary scenarios for our qualitative and quantitative observations over the entire topology of the tree. The strict consensus was used as a baseline cladogram (Figure S4B the strict consensus of the same analysis without constraint is illustrated in Figure S4C for indication). As the optimization options of the analysis can affect the length of the branches, we have chosen to favor the hypothesis of convergence (= DELTRAN) rather than reversion because they have been regarded as more likely [START_REF] Wake | Homoplasy: from detecting pattern to determining process and mechanism of evolution[END_REF]. For the reconstruction of evolutionary scenarios for intracranial discrete or continuous traits, one needs to complete missing data (n = 5 on 8 characters) and resolve polytomies. For the latter, we used the multi2di function of the ape package of R [START_REF] Paradis | ape 5.0: an environment for modern phylogenetics and evolutionary analyses in R[END_REF]. The function resolves polytomies by adding one or several additional node(s) and corresponding branch(es) of length 0. The duplicate nodes thus have the same values, allowing the removal of duplicates a posteriori. In order to facilitate the visualization of the evolutionary scenarios on the tree, we have rendered the tree ultrametric using the force.ultrametric function of the phytools package of R [START_REF] Revell | phytools: an R package for phylogenetic comparative biology (and other things)[END_REF]. For the discrete traits, the missing data (i.e., 1 taxon for characters 1 and 2 (not applicable), 7 taxa for character 4; 1 taxon for character 5see results) were completed according to their ancestor node optimization. In case of optimization uncertainties, we also favorized convergences for the same reason mentioned previously [START_REF] Wake | Homoplasy: from detecting pattern to determining process and mechanism of evolution[END_REF]. The reconstruction and mapping of ancestral states was performed using stochastic mapping with a symmetric condition matrix (i.e., one for which all transformation rates are considered equivalent; see [START_REF] Bollback | SIMMAP: stochastic character mapping of discrete traits on phylogenies[END_REF][START_REF] Revell | phytools: an R package for phylogenetic comparative biology (and other things)[END_REF]. This analysis was performed using the make.simmap function of the phytools package of R, with which we produced 100 simulations for each character. For continuous traits, missing data (i.e., 2 taxa for the character 8) were estimated using an approach combining the use of multiple imputations with procrustean superimposition of principal component analysis results [START_REF] Clavel | Missing Data Estimation in Morphometrics: How Much is Too Much?[END_REF] with the estim function of the mvMORPH package of R [START_REF] Clavel | mvMORPH: an R package for fitting multivariate evolutionary models to morphometric data[END_REF]. Then, the reconstruction of the ancestral states was performed using maximum likelihood using the contMap function of the phytools package of R [START_REF] Revell | phytools: an R package for phylogenetic comparative biology (and other things)[END_REF]. ZMB, Museum für Naturkunde, Berlin, Germany.

RESULTS -ANATOMICAL DESCRIPTION AND COMPARISON

Teeth and Alveolar Cavities -Orientation, Curvature and Height

The three species sampled intraspecifically do not show any ontogenetic variation in the orientation and curvature of the teeth compared to the pattern observed in adults (see below).

In Dasypus and Zaedyus the relative height of teeth shows an increase from the youngest to the oldest specimens, suggesting an increase in height during ontogeny (Figure 11). In Cabassous, which possess a reduced dentition, no clear ontogenetic trend has been observed (Figure 11).

Height--The relative height of the alveolar cavities distinguishes specimens with reduced teeth such as Dasypus, Stegotherium, Cabassous and Priodontes, from other cingulate species, some of which may even show extremely enlarged teeth, as is the case in glyptodonts (Figure 10, Table S2).

In taxa with reduced teeth, the height of the alveolar cavity in lateral view is practically the same for all teeth (Figure 10). In the other taxa, the dorsal profile of the dental row in lateral view is curved (dorsal convexity): teeth gradually increase in height backward until the middle of the dental series and then gradually decrease in height posteriorly. and most glyptodonts (at Mf5-6/Mf8). In addition, the GDRH/GSH ratio, which express the relative dental height according to the skull height, seems to be correlated to the body size (R² = 0.5363; P-value = 9.42E-06), showing that large-sized taxa have relatively taller dentitions. This is reminiscent of the increase in height of the dental row during ontogeny in Dasypus and

Zaedyus. The largest species in the sample, glyptodonts and Vassallia, do indeed show a strongly elevated dentition in relation to the skull depth (Figure 12). This is also the case in Peltephilus, for which the height of the skull is particularly low in relation to its length.

Although they are small (i.e., GSL< 43mm) and despite the allometric trends noted in Dasypus and Zaedyus, chlamyphorines show a tooth height comparable in proportion to the larger-sized

Chaetophractus, Proeutatus and Euphractus (Figure 12). Relative tooth height is lower in Tolypeutes, Zaedyus, Prozaedyus, and Cabassous, and extremely low in specimens with dental reduction -Dasypus, Stegotherium, and Priodontes (Figure 12). Curvature & Orientation--As visible in anterior and ventral views (Figure 10), taxa with reduced teeth and Peltephilus exhibit a rather homogenous curvature and orientation of teeth along the dental row while most cingulates show gradual changes in these aspects anteroposteriorly. In most cingulates, anterior teeth are tilted lingually, i.e. tilted with a medially offset apex, while most posterior teeth often tilt labially. The tilt of posterior teeth is often much less pronounced than for anterior teeth. Similarly, taxa that show curved crowns generally show anterior teeth with an inward curvature (lingual convexity) which can be strongest in the middle of the dental row, while the two posteriormost teeth often show a lesser degree of inward curvature or even an outward curvature (labial convexity Based on these observations, we propose scrutinizing evolutionary scenarios for the following two characters of the dentition (see Table 2).

Cranial Canals Frontal Diploic Vein canal

The course of this canal is entirely within the frontal bone. It opens externally at one or exceptionally two foramina located in the orbitotemporal fossa, slightly ventral to the most dorsal part of the orbital margin (Figure S2). This canal conveys the frontal diploic vein, an emissary of the dorsal cerebral vein/dorsal sagittal sinus or a vein issuing from the frontal diploë [START_REF] Thewissen | Mammalian frontal diploic vein and the human foramen caecum[END_REF][START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF][START_REF] Evans | Miller's Anatomy of the Dog[END_REF][START_REF] Muizon De | Alcidedorbignya inopinata, a basal pantodont (Placentalia, Mammalia) from the early Palaeocene of Bolivia: anatomy, phylogeny and palaeobiology[END_REF].

In early ontogeny, the canal of the frontal diploic vein is initially extremely thick in youngest specimens of Dasypus (see also [START_REF] Billet | The hidden anatomy of paranasal sinuses reveals biogeographically distinct morphotypes in the nine-banded armadillo (Dasypus novemcinctus)[END_REF] and Zaedyus and occupies a large part of the frontal bone (Figure 11). Its relative diameter is considerably reduced in older specimens of Dasypus and Zaedyus with no change in its curved trajectory in Zaedyus but becoming more strictly transverse in the adult stage in Dasypus (Figure 11). In Cabassous, it remains fairly similar from juvenile to adult stages in our sample (Figure 11).

In our adult sample, the canal is relatively straight, very thin, oriented posteromedially in dorsal view and without ramifications or only one small branch in Bradypus and Utaetus (Figure 13, Figure S5). In Tamandua, Peltephilus, Stegotherium, Dasypus, Euphractus, Priodontes and Cabassous, its overall course is transverse but with a posterior bend or convexity of varying degree (Figure 13). Ramifications and a posterior convexity are also found in Prozaedyus, Chaetophractus, Zaedyus and Proeutatus, but the overall course of their canal is more anteromedially oriented, as is also observed in Priodontes, Stegotherium and Cabassous (Figure 13). The same orientation is found in Doellotatus (incomplete), except that the course of the canal is completely straight and has no ramifications (Figure 13). Tolypeutes, on the other hand, shows a very peculiar course with a forked structure in dorsal view (Figure 13). The canal is merged with diploe in chlamyphorines but its presence is observable in Calyptophractus in which it has a straight and anteromedially oriented trajectory (Figure 13). This canal was not observed in all the glyptodonts sampled or in Vassallia. However, [START_REF] Gaudin | Phylogenetic relationships among sloths (Mammalia, Xenarthra, Tardigrada): the craniodental evidence[END_REF] notes the presence of this canal in glyptodonts and [START_REF] Gaudin | Cranial osteology of the pampathere Holmesina floridanus (Xenarthra: Cingulata; Blancan NALMA), including a description of an isolated petrosal bone[END_REF] mention it in pampatheres.

For the last group, there was a possible confusion with the anterior opening of the orbitotemporal canal (Figure S6). We suspect a taphonomic bias for some specimens (e.g., some Santacrucian glyptodonts) and call for a deeper study of this canal in cingulates before its variation can be scored.

Nasolacrimal Canal

The nasolacrimal canal originates posteriorly at the anterior orbital edge with the lacrimal foramen (Figures 9 & S2). It runs anteriorly within the lacrimal and the maxillary bones in its most posteriormost portion. More anteriorly, the canal is located between the inner wall of the maxillary and turbinates. It opens anteriorly (in front of the tooth row, except in Peltephilus) and ventromedially into the nasal cavity (Figures S2E & S7). This canal allows the transmission of fluids from the lacrimal sac to the nasal cavity and is potentially accompanied by a vein in Euphractus [START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF].

The course of the nasolacrimal canal barely changes during ontogeny in our sample (Figure 11). Its length changes, and follows the lengthening of the snout that accompanies the growth of the cranium (Chapter 3). In addition, Cabassous and, to a lesser degree, the adult stage of Zaedyus show a more medial orientation of the course of the nasolacrimal canal in its most posterior part which differs slightly from Dasypus and other stages of Zaedyus, where it runs more parallel to the external surface of the skull (Figure 11).

The position of the nasolacrimal canal and lacrimal foramen varies among taxa, although this feature was not scored in previous matrices (e.g., [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF]. The lacrimal foramen is particularly high relative to the orbital edge (closer to the most dorsal point of the orbit than to the jugal bone in lateral view) in chlamyphorines, Proeutatus and glyptodonts (Figure 14). The trajectory of the nasolacrimal canal is strongly sigmoid in Tamandua (Figure 14). In Bradypus, Peltephilus, Proeutatus, Chaetophractus, and Euphractus, the course of the nasolacrimal canal is slightly convex dorsally (Figure 14). The curvature is much pronounced in Vassallia in the posterior half of its course as it passes above the tooth row (Figure 14). In dasypodines, Prozaedyus, Zaedyus, tolypeutines, and chlamyphorines, the nasolacrimal canal is relatively straight or it bears a slight ventral convexity in its posterior part (Figure 14). In glyptodonts, the canal runs ventromedially and not anteriorly from the lacrimal foramen (Figures 14 & 15), and curves strongly inward anteriorly when approaching the sagittal plane of the skull (Figures 14 & 15).

Whereas glyptodonts appear to show a unique condition in the course of their nasolacrimal canal, the anterior opening of this canal is located halfway up in their nasal cavity as in Bradypus, Tamandua, Peltephilus, Doellotatus, Proeutatus and Vassallia. In comparison, this opening is closer to the palate in other specimens (Figure 14). This variation can be scored in the following character (see Table 2).

Palatine and Sphenopalatine Canals

Two large canals are enclosed within the maxillary and palatine bones forming the hard palate in cingulates: the palatine canal and the sphenopalatine canal [START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF].

The palatine canal is generally thinner, longer than and positioned medial to the sphenopalatine canal. The palatine canal transmits the major and minor palatine nerve, artery, and vein in Euphractus [START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF]. This canal opens externally at the caudal palatine foramen posteriorly and at the multiple foramina scattered throughout the hard palate (both in the palatine and maxillary) anteriorly (Figure S2). The sphenopalatine canal, which is often very wide in cingulates, transmits the caudal nasal nerve and the sphenopalatine artery and vein [START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF]. The sphenopalatine canal opens anteriorly in the nasal cavity and posteriorly in the pterygopalatine fossa just posterior to the dental row and close to or confluent with the caudal palatine foramen [START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF]; Figure S2). The palatine canal and sphenopalatine canal are confluent in part of their posterior course in many of the species in our sample.

The palatine canal and sphenopalatine canal vary little during ontogeny within the three species of our ontogenetic series (Figure 11). The branch of the palatine canal posterior to its region of confluence with the sphenopalatine canal in Dasypus and Cabassous appears in the subadult (or intermediate) stage and elongates further in the adult stage (Figure 11). In the youngest specimen of Zaedyus, the sphenopalatine canal is much wider relative to skull size than in later stages, and there is no region of confluence with the palatine canal (Figure 11). In the youngest Dasypus specimen, the sphenopalatine canal is absent. It is present only as a wide groove in the youngest to subadult stages, but is completely enclosed in the adult stage of Dasypus in our sample (Figure 11).

In our adult sample, the shape and trajectory of the palatine canal does not vary much among species (Figures 14 & 15). In glyptodonts, the palatine canal strongly ascends posteriorly (starting from Mf6) (Figure 14) and forms a groove running along the inner wall of the nasopharyngeal canal (Figure S8). In other cingulates, the palatine canal does not show such an ascending trajectory posteriorly. The sphenopalatine canal, which is thicker than the palatine canal, features a relatively straight trajectory in lateral view in Peltephilus, dasypodines, Prozaedyus, Euphractus, Zaedyus, Doellotatus and "Cochlops", whereas it shows a strong ventral curvature in Chaetophractus, tolypeutines, chlamyphorines and Glyptodon (Figure 14).

It should be further noted that the dorsal position of the sphenopalatine canal relative to the nasopharyngeal canal is a feature shared by Vassallia and Glyptodon (Figure S9). In Bradypus and Tamandua, the palatine canal does not contact the sphenopalatine canal (Figures 14 & 15).

The two canals are in contact in a small region of confluence in the dasypodines whereas the palatine canal becomes completely confluent with the sphenopalatine canal, and sometimes accompanied by ventrally oriented auxiliary branches of the palatine canal, in Peltephilus, tolypeutines, chlamyphorines and Glyptodon (Figures 14 & 15). In euphractines, the confluence between the sphenopalatine canal and the palatine canal is not as clear-cut as in the above-cited cingulates (Figures 14 & 15). The palatine canal of euphractines runs ventrally along the sphenopalatine canal in the same figure 8-shaped canal while being completely conjoined only in their most posterior part and at their posterior opening (Figures 14 & 15). The extent of this confluence is highly variable in Euphractus according to [START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF], and in other cingulates as well (Gaudin & Wible, 2006character 71). We observed the same variation as [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF] concerning the extent of this confluence in the vicinity of the posterior opening of the sphenopalatine canal for all the taxa in our sample. Several branches may emerge from this region of confluence (Figures 14 & 15), some of which present an interesting pattern.

One branch opens externally from the caudal foramen of the palatine canal in dasypodines, Cabassous and Priodontes (Figures 14 & 15). A second branch extends posteriorly into the hard palate, before disappearing in the bone diploe in dasypodines. In Euphractus, Zaedyus, Cabassous and Priodontes, two or more branches extend posteriorly into the hard palate, but they open in the nasopharyngeal canal (Figures 14 & 15). Several other ramifications of the palatine canal are present in our sample, but it remains to be determined how variable these are at the intraspecific level with a dataset larger than that of Table S1.

Based on the observation of these two canals, we proposed to scrutinize evolutionary scenarios for the following character (see Table 2).

Transverse Canal

When present, the transverse canal is marked externally by a foramen positioned anteroventrally to or within the foramen ovale in the alisphenoid (Figure S2). This canal crosses the cranium transversally at the level of the basisphenoid and transmits a large vein issued from the cavernous sinus [START_REF] Sánchez-Villagra | Patterns of evolutionary transformation in the petrosal bone and some basicranial features in marsupial mammals, with special reference to didelphids[END_REF][START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF]). Often, one or more branches originate from this canal and extend posteriorly towards the lateral edge of the basisphenoid to join the inferior petrosal sinus [START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF].

The transverse canal appears early in Dasypus and varies little during ontogeny.

Although, in Zaedyus and Cabassous, the connection between the transverse canal and the posterior branch extending towards the inferior petrosal sinus varies in both series, we have not observed a clear ontogenetic pattern of variation in our three species (Figure 11).

In Bradypus, Peltephilus, Stegotherium, Doellotatus, Tolypeutes and Glyptodon, there is no transverse canal, or it is not detectable (scored as present in Doellotatus and Stegotherium, variable in Tolypeutes by Gaudin & Wible, 2006character 111). Chlamyphorines have a transverse canal foramen opening directly within the braincase, and thus there is a very short canal that does not cross the midline of the cranium. Tamandua stands out in having a thin lateral part of the transverse canal which is not comparable to the condition in Cingulata (Figure 16). In Utaetus (Figure S5), Dasypus, euphractines, Prozaedyus, Cabassous and Priodontes, the branch starting from the transverse canal foramen is oriented posteromedially in ventral view (Figure 16). In the Santacrucian glyptodonts, it is medially oriented (Figure 16). In

Vassallia it is anteromedially oriented (Figure 16). This lateral branch of the transverse canal splits into a branch that crosses the midline in the basisphenoid bone and a branch that joins the inferior petrosal sinus (except in Utaetus (Figure S5) where the branch extends dorsolaterally to open into the roof of the basisphenoid) (Figure 16). In Proeutatus, this bifurcation occurs much closer to the transverse canal foramen than in other taxa (Figure 16). It is relatively more medial in euphractines, Prozaedyus, Cabassous and Priodontes (Figure 16). In Tamandua, Dasypus, Vassallia and Santacrucian glyptodonts, this bifurcation is closer to the sagittal plane than to the foramen (Figure 16). The transverse medial branch is anteromedially oriented in ventral view in Proeutatus, Cabassous and Prozaedyus, whereas it is medially oriented in the other taxa (Figure 16). Our specimens of Tamandua, euphractines (not complete in Chaetophractus) and Priodontes show an additional branch connecting the transverse medial branch to the posterior branch reaching the inferior petrosal sinus (Figure 16). In Vassallia and the Santacrucian glyptodonts, the posterior branch reaching the inferior petrosal sinus is much thinner than the rest of the canal, in contrast to the other taxa, in which the whole canal exhibits a relatively homogeneous width (Figure 16). Based on these observations of the transverse canal, we propose to scrutinize evolutionary scenarios for the following character (see Table 2).

Orbitotemporal and Posttemporal Canals

Within the braincase, the orbitotemporal canal provides passageway to the rostral extension of the ramus superior of the stapedial artery, or orbitotemporal artery (giving rise to the ramus supraorbitalis in the orbital region), and a few small veins [START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF] whereas the more posterior posttemporal canal transmits the arteria diploëtica magna and the large vena diploëtica magna [START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF]). These two canals can give rise to the arterial and venous rami temporales along the lateral wall of the braincase which exit via numerous foramina on the cranial roof to irrigate the temporalis muscle [START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF]; Figure S2). The posttemporal canal is connected posteriorly to an external groove in the petro-occipital region marking the passage of the occipital artery [START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF] Figure S2). From there, the posttemporal canal extends forward as a canal enclosed between the petrosal and squamosal (or only in the squamosal) and oriented mostly horizontally. More anteriorly, past the petrosal, the posttemporal canal is connected to the orbitotemporal canal, which runs further anteriorly within or on the inner surface of the lateral braincase wall of the braincase (formed by the squamosal, frontal and sometimes the parietal). The delimitation between the two canals generally occurs where the canal for the ramus superior joins them [START_REF] Muizon De | Alcidedorbignya inopinata, a basal pantodont (Placentalia, Mammalia) from the early Palaeocene of Bolivia: anatomy, phylogeny and palaeobiology[END_REF]. However, we were only able to observe a canal possibly transmitting the ramus superior in Tolypeutes (Figure S10), but not in the other specimens. Consequently, we followed the suggestion of [START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF], who separate the two canals at the level of the postglenoid foramen. In some taxa, the orbitotemporal canal is not completely enclosed for parts of its length, and appears instead as a groove on the internal wall of the braincase. The anterior opening of the orbitotemporal canal is located in the orbitotemporal region, just posteroventral to the postorbital constriction (Figure S2; [START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF]= cranioorbital foramen in [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF]; see also [START_REF] Muizon De | Alcidedorbignya inopinata, a basal pantodont (Placentalia, Mammalia) from the early Palaeocene of Bolivia: anatomy, phylogeny and palaeobiology[END_REF] for multiple illustrations of these canals in another placental taxon).

The orbitotemporal canal only appears as a short canal near the orbitotemporal region in the youngest specimens of all three species, whereas the canal (or groove) is clearly visible for its entire length in later stages (Figure 11). The connections of the orbitotemporal canal with canals for the numerous rami temporales occur in the two last stages in both Zaedyus and Cabassous (Figure 11). The posttemporal canal is already well formed in the youngest specimen of Dasypus and hardly changes during ontogeny (Figure 11). In Zaedyus, the posttemporal canal is not enclosed in the youngest stage. In Cabassous, the posttemporal canal is present in the youngest stage sampled, but it expands anteriorly during the two subsequent stages (Figure 11).

In our adult sample, Bradypus, Tamandua, euphractines, Vassallia and glyptodonts possess a posttemporal canal emerging at the center of the occiput in lateral view and at the level of the jugular foramen (Figure 17). In Peltephilus, it originates more ventrally, even with the most dorsal margin of the occipital condyles in lateral view (Figure 17). In dasypodines, tolypeutines and chlamyphorines, the posterior extremity of the canal is at an intermediate height (Figure 17). Apart from the position of the posterior opening of this canal (= posttemporal foramen of [START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF], we were unable to determine any systematically significant variation regarding its direction, length, or width.

In Bradypus and Tamandua, the orbitotemporal canal does not reach the orbitotemporal region (Figures 17 & 18). It reaches the orbitotemporal region in all the cingulates in our sample except for Priodontes (Figures 17 & 18). [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF] mention the absence of the anterior opening of the orbitotemporal canal in Priodontes (character 78), but also in Chlamyphorus and

Vassallia for which we observe a clear opening in the orbitotemporal region (Figure 17). In Bradypus, Tamandua and Peltephilus, this canal bears a ventral curvature (strong in Peltephilus), whereas its trajectory exhibits a more or less strong dorsal curvature in all the other taxa (Figure 17). In Utaetus (Figure S5), Peltephilus, Dasypus, Prozaedyus, euphractines, Cabassous, Tolypeutes, chlamyphorines, Proeutatus and Santacrucian glyptodonts, the orbitotemporal canal becomes a groove on the internal lateral wall of the braincase before being enclosed again as a canal close to its external anterior opening (Figure 17). In Calyptophractus, Proeutatus and glyptodonts, the anterior half of the orbitotemporal canal displays a pronounced downward trajectory, and its anterior opening is located lower than its posterior connection with the posttemporal canal (Figure 17). Calyptophractus stands out, however, in having two branches that connect the orbitotemporal and posttemporal canals (Figure 17). A large region of confluence between the orbitotemporal and posttemporal canals and the canal for the capsuloparietal emissary vein is identified in Tamandua, Peltephilus, Stegotherium, Dasypus, Chaetophractus, Priodontes, Vassallia and the glyptodonts (and potentially also in Proeutatus but the orbitotemporal canal is not distinct in this region; Figures 17 & 18). This confluent region is reminiscent of the petrosquamosal fossa in Alcidedorbignya [START_REF] Muizon De | Alcidedorbignya inopinata, a basal pantodont (Placentalia, Mammalia) from the early Palaeocene of Bolivia: anatomy, phylogeny and palaeobiology[END_REF].

The orbitotemporal and posttemporal canals connect with the rami temporales through multiple small canals whose number remains quite variable at the intraspecific level. However, a high density of rami temporales for the orbitotemporal canal is particularly noticeable in euphractines, Cabassous, Calyptophractus and glyptodonts (Figure 17). This density is coded by [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF], who counted the number of foramina for rami temporales in the temporal fossa of parietal (0, equal to or less than five; 1, greater than fivecharacter 97). In their matrix, almost all cingulates are coded as having more than 5 foramina. The variations in the density of the canals for the rami temporales observed in our study call for further investigation of these structures, which could potentially carry an interesting phylogenetic signal among cingulates.

Based on these observations of the orbitotemporal canal, we propose to scrutinize evolutionary scenarios for the following character (see Table 2).

Character 6 (discrete -unordered): Downward trajectory of the orbitotemporal canal. State (0): Canal does not reach the orbitotemporal region.

State (1):

The anterior part of the canal has a slight downward trajectory ending at the same or almost the same height as its origin from the posttemporal canal.

State (2):

The canal has a strong downward anterior trajectory, and its anterior opening is much lower than its posterior connection to the posttemporal canal.

Canal of the Capsuloparietal Emissary Vein

The canal for the capsuloparietal emissary vein opens anteroventrally at the postglenoid and suprameatal foramina, and connects to the groove for the transverse sinus posterodorsally [START_REF] Wible | Cranial circulation and relationships of the colugo Cynocephalus (Dermoptera, Mammalia)[END_REF][START_REF] Muizon De | Alcidedorbignya inopinata, a basal pantodont (Placentalia, Mammalia) from the early Palaeocene of Bolivia: anatomy, phylogeny and palaeobiology[END_REF]. From the cranial roof, the transverse sinus runs posteroventrally in a wide groove excavated in the inner surface of the parietal and extends anteroventrally within a canal formed by the petrosal medially and the squamosal laterally. This canal opens externally through the suprameatal foramen, the postglenoid foramen and accessory foramina at the posterior base of the zygomatic arch (e.g., [START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF]; Figure S2).

It transmits the capsuloparietal emissary vein (= retroarticular vein in Canis [START_REF] Evans | Miller's Anatomy of the Dog[END_REF]; postglenoid vein in Cynocephalus [START_REF] Wible | Cranial circulation and relationships of the colugo Cynocephalus (Dermoptera, Mammalia)[END_REF] and Dasypus [START_REF] Wible | Petrosal anatomy of the nine-banded armadillo, Dasypus novemcinctus Linnaeus, 1758 (Mammalia, Xenarthra, Dasypodidae)[END_REF]).

In our sample, this canal is often partly confluent with the posttemporal and orbitotemporal canal in its posterodorsal portion (Figure S11).

The canal for the capsuloparietal emissary vein is already well formed in the youngest specimen of Dasypus and hardly changes during ontogeny, except that it becomes relatively thinner (Figure 11). In Zaedyus, it is only partly formed in the youngest specimen, and its trajectory is better marked in older stages (Figure 11). In the youngest Cabassous, this canal is noticeably short and only marked in its most ventral part (glenoid region). It is only in older stages that the canal elongates posterodorsally (Figure 11).

The canal is absent and the passage of the vein is only indicated by a groove in Bradypus, Chlamyphorus and Utaetus (maybe due to the absence of the petrosal in the Utaetus specimen illustrated on Figure S5). The groove is very wide in the latter two (Figure 17). In Utaetus,

several rami temporales open into the cranial roof, and the groove becomes a short canal opening into the glenoid region (Figure S5). The canal of the capsuloparietal emissary vein opens through the postglenoid foramen and potentially in the suprameatal foramen as well (see rami temporales opening in the squamosal whose number varies in our intraspecific sampling (Table S1)) in Peltephilus, euphractines, Prozaedyus, Doellotatus, Proeutatus, chlamyphorines,

Vassallia and the glyptodonts (as notably scored for the glenoid region by Gaudin & Wible, 2006character 119;Figures 17 & 18). In tolypeutines, the canal always opens by a suprameatal foramen with a well-marked branch, whereas its opening via the postglenoid foramen may sometimes be absent, as we have occasionally observed the absence of a postglenoid foramen in our intraspecific sample of Cabassous unicinctus (Table S1). For all our taxa except Bradypus, the canal extends anteroventrally the cranial roof (Figure 17).

However, its inclination varies considerably from one species to another. It is steeply inclined in dasypodines, slightly less so in euphractines, Prozaedyus, Doellotatus and Proeutatus, and much less so in tolypeutines, Calyptophractus, Vassallia and glyptodonts (Figure 17). 17). Chlamyphorines and Zaedyus show a relatively thicker canal, as compared with the very thin canal in Vassallia. The fact that small taxa have a relatively thicker canal is reminiscent of young specimens of Dasypus as compared to older and larger specimens of the same species (Figure 11) and suggest a potential allometric pattern.

Based on these observations, we propose to scrutinize evolutionary scenarios for the following character related to the anterolateral extremity of the canal (see Table 2).

Character 7 (discrete -unordered): Canal of the capsuloparietal emissary vein inclination in lateral view. State (0): Anterodorsal orientation or canal very short. State (1): Inclination anteroventral from the posterior opening to the anterior opening. State (2): Less anteroventrally inclined, with an almost anteroposterior orientation close to the anterior opening.

Inclination of the cranial roof

Digital study of the braincase of our sample enabled observation of notable variations in the internal vault inclination (= IVI) relative to the anteroposterior axis of the cranium. The values of the IVI angle show an interesting pattern in our sample that does not correlate (R² = 0.1768; P-value = 0.3246) with size (Figure 19). Whereas Glyptodon is distinguished from the other cingulates by an exceedingly high inclination combined with a large size, the large-sized

Vassallia has a very low cranial roof inclination (Figure 19). Miocene glyptodonts, Proeutatus, Stegotherium, Chlamyphorus and the adult specimen of Dasypus are also characterized by high inclinations (Figure 19). The juvenile Cabassous also displays a strong inclination, which decreases with age whereas the inclination increases with age in Dasypus (Figure 19).

Calyptophractus shows an intermediate cranial roof inclination (Figure 19). The outgroups,

Cabassous (adult) and euphractines exhibit low values, and the remaining tolypeutines and

Peltephilus are even characterized by a negative tilting of IVI (Figure 19). We propose to treat the IVI as a continuous character to scrutinize evolutionary scenarios (see Table 2).

Character 8 (continuous): Internal Vault Inclination.

DISCUSSION

Due to their very unusual anatomy, even within the Cingulata, the phylogenetic placement of glyptodonts has been long debated [START_REF] Burmeister | Monografía de los glyptodontes en el Museo Público de Buenos Aires[END_REF][START_REF] Scott | Mammalia of the Santa Cruz beds. I. Edentata[END_REF][START_REF] Carlini | An introduction to cingulate evolution and their evolutionary history during the great American biotic interchange: biogeographical clues from Venezuela[END_REF][START_REF] Fariña | Megafauna: giant beasts of Pleistocene South America[END_REF]. Recent molecular analyses have proposed a new hypothesis (i.e., as sister group of the clade tolypeutines + chlamyphorines - [START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF][START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF] at odds with the multiple hypotheses based on morphological analyses [START_REF] Engelmann | The evolution and ecology of armadillos, sloths and vermilinguas[END_REF][START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF][START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF][START_REF] Herrera | A new Eocene dasypodid with caniniforms (Mammalia, Xenarthra, Cingulata) from northwest Argentina[END_REF]. The recent investigation of the internal anatomy in the Dasypus novemcinctus species complex [START_REF] Billet | The hidden anatomy of paranasal sinuses reveals biogeographically distinct morphotypes in the nine-banded armadillo (Dasypus novemcinctus)[END_REF] underlined the potential phylogenetic signal hidden in the internal cranial structures of cingulates. Comparative studies on the paranasal sinuses and on brain endocasts of cingulates have been performed, but could not provide consistent information on the placement of glyptodonts within the Cingulata [START_REF] Zurita | Neosclerocalyptus spp. (Cingulata: Glyptodontidae: Hoplophorini): cranial morphology and palaeoenvironments along the changing Quaternary[END_REF][START_REF] Fernicola | A neomorphic ossification of the nasal cartilages and the structure of paranasal sinus system of the glyptodont Neosclerocalyptus Paula Couto 1957 (Mammalia, Xenarthra)[END_REF]Tambusso & Fariña, 2015a). Our comparative study complements these previous efforts by adding the analysis of the dental alveolar cavities (previously only explored in the glyptodont genus Eucinepeltus -González-Ruiz et al., 2020) and of various canals involved in the vascularization and innervation of the skull (see [START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF]. Based on an extensive sample of extant and extinct cingulates, our survey enabled us to describe many new aspects of the internal cranial anatomy in the group, and to propose 8 potential characters with helpful phylogenetic information to aid in determining the placement of glyptodonts within Cingulata.

The anatomical variation of the dental alveolar cavities in cingulates comprises many aspects including the height, curvature, and orientation of teeth, along with their number and distribution on the rostrum [START_REF] Vizcaíno | The teeth of the "toothless": novelties and key innovations in the evolution of xenarthrans (Mammalia, Xenarthra)[END_REF]. Among our observations, we have proposed two characters with potential bearing on the affinities of glyptodonts. The first corresponds to the position of the most dorsal point of these cavities in lateral view (character 1). The dorsal margins of the alveoli for a dorsally convex line for the whole dental row in most cingulates, except in taxa with reduced teeth. This point is situated posteriorly (i.e., at Mf5-6) in glyptodonts, pampatheres, chlamyphorines, Prozaedyus and Zaedyus in our sample. The distribution of this character would be congruent with the hypothesis of a close relationship between glyptodonts and pampatheres, as suggested by many previous authors [START_REF] Patterson | The Fossil Mammal Fauna of South America[END_REF][START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF][START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF][START_REF] Herrera | A new Eocene dasypodid with caniniforms (Mammalia, Xenarthra, Cingulata) from northwest Argentina[END_REF], but also supports the clade formed by the latter two with chlamyphorines, as proposed by the morphological analysis of [START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF] constrained by the molecular backbone (Figure 20). On the other hand, Proeutatus, generally considered to be a close relative of the clade glyptodonts + pampatheres [START_REF] Engelmann | The evolution and ecology of armadillos, sloths and vermilinguas[END_REF][START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF][START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF][START_REF] Gaudin | Cranial osteology of the pampathere Holmesina floridanus (Xenarthra: Cingulata; Blancan NALMA), including a description of an isolated petrosal bone[END_REF], has its most dorsal point situated much further anteriorly (i.e., ca. Mf1-3).

The second character derived from dental alveolar cavities corresponds to the curvature of the anterior teeth in anterior view (character 2). As for character 1, chlamyphorines and pampatheres resemble glyptodonts in this aspect, exhibiting an inward curvature. Tolypeutes, Doellotatus and Peltephilus also show a similar condition (Figure 20). As shown by the reconstructed evolutionary scenario (Figure 20), this character could still support the morphological hypothesis of [START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF] of a close relationship between glyptodonts and chlamyphorines. The distribution of this character on the baseline cladogram shows some homoplasy, however, with the condition in Proeutatus contrasting with that of glyptodonts, while the early diverging Peltephilus resemble the latter (Figure 20). Another point of interest concerning the variation of dental alveolar cavities is the potential allometric pattern identified by the correlation between the relative height of the dental row and skull size (Figure 12). This needs to be analyzed further, but if confirmed, such an allometric pattern pertaining to the relative height of the dentition may be closely related to the variation in shape of the rostrum.

Extremely high teeth, if not strongly curved, should occupy a large dorsoventral space and would thus require a relatively high rostrum. This hypothesis is reinforced by the existence of a common allometric pattern in mammals corresponding to the relative elongation of the snout as size increases [START_REF] Cardini | Larger mammals have longer faces because of size-related constraints on skull form[END_REF]Cardini, 2019). However, we do not know whether allometry could affect the variation of the two aforementioned alveolar cavity characters, but the resemblance of small taxa (i.e., chlamyphorines) and large taxa (i.e., glyptodonts and pampatheres) seems to argue against this. In any case, our study brings to light interesting new variation regarding the upper tooth roots/alveolar cavities of cingulates, which have in the past been compared to one another on the basis of their number, the presence/absence of teeth in the premaxillary, tooth wear, histology, and the orientation of the long axis of the teeth relative to the long axis of the dental row (characters 1, 3 to 8 - [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF] ; see discussion for glyptodonts regarding these characters [START_REF] Scott | Mammalia of the Santa Cruz beds. I. Edentata[END_REF][START_REF] Ferigolo | Evolutionary trends of the histological pattern in the teeth of Edentata (Xenarthra)[END_REF][START_REF] González-Ruiz | First record of supernumerary teeth in Glyptodontidae (Mammalia, Xenarthra, Cingulata)[END_REF]. Our initial observations point towards a resemblance between glyptodonts, chlamyphorines and pampatheres on the overall spatial organization of the alveolar cavities, which would be partly compatible with molecular results [START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF][START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF]. However, we believe further information could be gained by more detailed quantified analyses of shape to more fully reflect the complex spatial variation of the dental alveolar cavities.

Our analysis of selected intracranial canals described various aspects of their variation, which were unknown in cingulates until now. Furthermore, it enabled us to propose five characters, that provide potentially significant phylogenetic information. This analysis also demonstrated the need to further examine the variation of several structures (e.g., canal of the frontal diploic vein).

Both the trajectory and position of the nasolacrimal canal vary within the sample. A trajectory that is first directed medially at its posterior opening (i.e., the lacrimal foramen) represents a unique characteristic of glyptodonts within the Cingulata (Figures 14 & 15). The most informative feature on this canal regarding the relationships of glyptodonts with other cingulates is the relative height of its anterior opening within the nasal cavity (character 3 -Figure 20). In most cingulates, this opening is positioned ventrally in the nasal cavity, close to the hard palate, whereas in glyptodonts it is near the vertical midpoint of the cavity. The distribution of this character on the baseline cladogram supports the node linking the glyptodonts, pampatheres and Proeutatus (Figure 20), as in several previous morphological analyses [START_REF] Engelmann | The evolution and ecology of armadillos, sloths and vermilinguas[END_REF][START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF][START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF][START_REF] Gaudin | Cranial osteology of the pampathere Holmesina floridanus (Xenarthra: Cingulata; Blancan NALMA), including a description of an isolated petrosal bone[END_REF].

The course and connection between the sphenopalatine canal and the palatine canal is characterized by a complex pattern which is very peculiar in glyptodonts (Figures S8 &S9).

The degree of fusion between the two canals was variable within our sample. Because of taphonomic issues, only "Cochlops" and Glyptodon allowed us to observe a fusion of the two canals in glyptodonts. However, this fusion was also present as in the chlamyphorines. The uncertain condition in pampatheres and Proeutatus does not allow us to draw clear conclusions (character 4 -Figure 20), but the distribution of this character on the baseline cladogram could be congruent with the morphological hypothesis of [START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF] (Figure 20). However, caution is warranted, because the confluence between the sphenopalatine foramen and the caudal palatine foramen is known to exhibit substantial intraspecific variation in several taxa (see character 71, [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF] including Euphractus [START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF]). In addition, the condition in pampatheres needs further investigation, since a caudal palatine foramen has been identified in the floor of the sphenopalatine canal in Holmesina [START_REF] Gaudin | Cranial osteology of the pampathere Holmesina floridanus (Xenarthra: Cingulata; Blancan NALMA), including a description of an isolated petrosal bone[END_REF]. Our study also reveals a strong resemblance between pampatheres and glyptodonts, which share a dorsal position of the sphenopalatine canal in relation to the nasopharyngeal canal (Figure S9). This feature could have been coded as a character, but an investigation of potential allometry for this trait is required before coding this trait.

The course, orientation and connections of the transverse canal also vary in our sample.

We were unable to identify this canal in Glyptodon, Tolypeutes and chlamyphorines, as well as

Bradypus, Peltephilus and Stegotherium. Its presence in the Santacrucian glyptodonts, pampatheres, Proeutatus and many other cingulates suggests that it has been lost in Glyptodon.

Apart from this potential loss, the distribution on the baseline cladogram of the character corresponding to the orientation of the branch directly connected to the transverse canal foramen may support the common morphological hypothesis of a close relationship among glyptodonts, pampatheres, and Proeutatus (character 5 -Figure 21; see also [START_REF] Engelmann | The evolution and ecology of armadillos, sloths and vermilinguas[END_REF][START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF][START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF][START_REF] Gaudin | Cranial osteology of the pampathere Holmesina floridanus (Xenarthra: Cingulata; Blancan NALMA), including a description of an isolated petrosal bone[END_REF]. Moreover, our work is congruent with the matrix of [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF] regarding the presence/absence of the tranverse canal foramen for most taxa (character 111) with the exceptions of Stegotherium (coded as present in [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF], Tamandua (coded as absent in [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF], and Doellotatus. In the case of the latter, the specimen available for our study was poorly preserved for this character (coded as present in [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF]. Our study also allows us to confirm the hypothesis of [START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF], which suggested that the canal crosses the midline of the skull in Euphractus sexcinctus. In their fetuses, they did not observe this transverse pattern, and doubted whether it existed in adult specimens [START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF].

We can confirm this pattern in our specimen (Figure 16). This well-known circulation pattern in several marsupials is much less clear in placentals, for which the occurrence of a foramen for the transverse canal (often without knowing whether it crosses the skull midline) is most often interpreted as a case of convergence [START_REF] Sánchez-Villagra | Patterns of evolutionary transformation in the petrosal bone and some basicranial features in marsupial mammals, with special reference to didelphids[END_REF]. In addition, our analysis of the youngest specimen of Zaedyus also suggests that the transverse canal is not formed in young euphractine individuals, according with the observations of [START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF]. However, in young dasypodines, we clearly observe this feature (Figure 11). For a large majority of taxa in our sample, we can confirm that a transverse canal crossing the midline is present in cingulates.

Figure 21. Reconstructed evolutionary scenarios for the endocranial characters 5-8 plotted on the reference cladogram with ancestral state estimation for internal nodes (see Material & Methods, Supporting information 2 and Figure S4). Each character is illustrated and the relationship between color and coding is explained within the figure. † represents extinct genera. For character 8 (= IVI), the angle between the anteroposterior axis of the cranium (defined by the line connecting the most posterior (a) and anterior (b) edges of the tooth row) and the straight line connecting the most dorsal point of the annular ridge (c) and the most ventral point of the tentorial process (d). Scale = 1 cm.

The distribution on the baseline cladogram of the character corresponding to the anterior course of the orbitotemporal canal also provided interesting information (character 6 -Figure 21). Calyptophractus, Proeutatus and glyptodonts share a strong downward trajectory of this canal, with an anterior opening located much lower in lateral view than its posterior connection of the orbitotemporal canal to the posttemporal canal. The evolutionary scenario for this character is, however, unclear for glyptodonts and their close allies, and homoplasy seem to be present (Figure 21). Our study also highlights the presence of a foramen for the anterior opening of the orbitotemporal canal in all cingulates except Priodontes whereas this foramen was scored as absent in Vassallia and Chlamyphorus in Gaudin & Wible (2006, character 78), and is often unknown for other cingulate taxa. Based on our observation, there is no doubt that the canal opens in the orbitotemporal region in Vassallia, while this opening is described as absent in Holmesina floridanus [START_REF] Gaudin | Cranial osteology of the pampathere Holmesina floridanus (Xenarthra: Cingulata; Blancan NALMA), including a description of an isolated petrosal bone[END_REF]. The opposite discrepancy exists regarding the foramen for the frontal diploic vein, absent in Vassallia and described as present in Holmesina floridanus by [START_REF] Gaudin | Cranial osteology of the pampathere Holmesina floridanus (Xenarthra: Cingulata; Blancan NALMA), including a description of an isolated petrosal bone[END_REF]. As these two foramina are usually located relatively close to each other in the orbitotemporal region (bearing many foramina), we suggest that misidentifications may have occurred between the opening of these two canals, if they are presents, and ethmoidal foramina (Figure S6). The only way to confirm this hypothesis would be to scan [START_REF] Gaudin | Cranial osteology of the pampathere Holmesina floridanus (Xenarthra: Cingulata; Blancan NALMA), including a description of an isolated petrosal bone[END_REF] specimens of Holmesina floridanus.

Another character we investigated concerned the inclination of the canal for the capsuloparietal emissary vein in lateral view (character 7 -Figure 21). All tolypeutines, Calyptophractus, Vassallia and glyptodonts share a less steep inclination than that observed in other cingulates, with a part close to the anterior opening oriented almost directly anterior direction. The distribution of this character could provide support for the molecular hypothesis of a closer relationship of the glyptodonts with chlamyphorines and tolypeutines [START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF][START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF]Figure 21). However, the condition is reversed in Chlamyphorus and Proeutatus, creating homoplasy that casts doubt on the evolution of this trait. The trajectory of this canal has never been scored in prior phylogenetic analyses of the Cingulata. In the literature, only two characters have been scored that indirectly concern this canal, characters 119 and 120 of [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF], related to the presence/absence of the postglenoid foramen and suprameatal foramen, respectively. These characters deliver contrasting grouping among cingulates [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF].

Finally, the internal inclination of the cranial vault relative to the anteroposterior axis of the cranium also helps identify some cingulate taxa that may resemble glyptodonts in this regard (character 8; Figure 21). The distribution of this quantitative trait on the baseline cladogram indicates that the glyptodonts, Proeutatus, Chlamyphorus, Calyptophractus and Dasypodinae exhibit a strong angle, whereas Vassallia possesses a very weak angle. The variation of this trait was not explained by allometry in our sample. A highly inclined vault may have been evolved independently in the dasypodines and in glyptodonts and their allies. Its distribution could provide support for a relationship between glyptodonts, Proeutatus and chlamyphorines to the exclusion of pampatheres or they may have undergone a reversal (Figure 21). The vault inclination in these taxa seems to be partly congruent with the distribution of a character proposed by [START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF] and discussed by [START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF], i.e., the dorsal position of the ventral surface of the auditory region relative to the palate (character 78 - [START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF]. This is a characteristic of glyptodonts, pampatheres, Eutatini and chlamyphorines in Billet et al.'s (2011) analysis. The potential relationship of these two aspects of the braincase should be tested in future studies.

In conclusion, our investigation of the cranial canals and alveolar cavities highlighted several endocranial characters that support a resemblance of glyptodonts with chlamyphorines, Proeutatus and pampatheres. Except for character 7, our investigation did not bring to light new, and strong resemblances between glyptodonts and tolypeutines that would support their close relationship as suggested by molecular studies [START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF][START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF].

In short, our study of internal anatomy lends further credence to recent reports of a greater morphological resemblance between glyptodonts and chlamyphorines than tolypeutines [START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF][START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF]. These results are reinforced by the low statistical support for the chlamyphorines + tolypeutines relationship relative to other clades in molecular analyses of cingulate phylogeny [START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF][START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF].

The congruence of these new internal characters with past morphological phylogenetic analyses of the group is difficult to evaluate since the results of the latter have been rather unstable (e.g., [START_REF] Engelmann | The evolution and ecology of armadillos, sloths and vermilinguas[END_REF][START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF][START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF]. However, a close resemblance of glyptodonts to the eutatine Proeutatus and the pampatheres is also supported by several characters in our study, which would be congruent with several recent phylogenetic hypotheses based on morphological data [START_REF] Engelmann | The evolution and ecology of armadillos, sloths and vermilinguas[END_REF][START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF][START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF][START_REF] Gaudin | Cranial osteology of the pampathere Holmesina floridanus (Xenarthra: Cingulata; Blancan NALMA), including a description of an isolated petrosal bone[END_REF]. However, even if our study shows similarities among chlamyphorines, pampatheres, glyptodonts, and Proeutatus, new analyses are needed that incorporate this new data before firmer phylogenetic conclusions can be reached. Our study provides a nonexhaustive account of internal canals of the skull, but internal structures still need to be studied to select new characters in particular for endocranial traits that we briefly describe but do not explore in detail. This is notably the case of the canal for the frontal diploic vein or the relative position of the sphenopalatine canal in relation with the nasopharyngeal canal, whose patterns of variation remain unclear at the moment. Another promising way forward was also revealed by our developmental series in which Cabassous varies in a manner different from that of Zaedyus and Dasypus as far as the inclination of the cranial roof is concerned (Figure 19). A better exploration of the developmental series with more specimens per species and more developmental series could provide a better understanding of the covariation patterns, especially since their trajectories can be coded for phylogenetic analyses (e.g., [START_REF] Bardin | Ontogenetic data analyzed as such in phylogenies[END_REF]. Further studies are also needed to better understand the patterns of variation of the internal characters highlighted here, which in some respects may be affected by allometry as we have highlighted for alveolar cavities and the canal for the capsuloparietal emissary vein.

82

CHAPTER 3

Cranial Allometry in Cingulata Analyses were conducted at the ontogenetic and static levels, and for successive developmental stages. Our results support craniofacial allometry as the global pattern along with more local allometric trends, such as the relative posterior elongation of the infraorbital canal, the tooth row reduction on the maxillary, and the marked development of nuchal crests on the supraoccipital with increasing skull size. Our study also reports allometric proportions of shape variation varying substantially among cranial units and across ontogenetic stages. The multi-scale approach advocated here allowed unveiling previously unnoticed allometric variations, indicating an untapped complexity of cranial allometric patterns to further explain mammalian morphological evolution.

Le Verger K, Hautier L, Bardin J, Gerber S, Delsuc F, Billet G. 2020. Ontogenetic and static allometry in the skull and cranial units of nine-banded armadillos (Cingulata: Dasypodidae: Dasypus novemcinctus). Biological Journal of the Linnean Society 131: 673-698 p.

INTRODUCTION

Variation in size is a major component of tetrapod evolution and diversity. Among them, mammals developed a wide range of body sizes since the onset of the Cenozoic era [START_REF] Smith | The evolution of maximum body size of terrestrial mammals[END_REF], with multiple independent events of size increase [START_REF] Baker | Adaptive evolution toward larger size in mammals[END_REF][START_REF] Bokma | Testing for Depéret's rule (body size increase) in mammals using combined extinct and extant data[END_REF].

The extant mammalian diversity extends over eight orders of magnitude in size [START_REF] Price | The macroevolutionary relationship between diet and body mass across mammals[END_REF], and this variation has accompanied ecological diversification [START_REF] Sibly | Effects of body size and lifestyle on evolution of mammal life histories[END_REF][START_REF] Price | The macroevolutionary relationship between diet and body mass across mammals[END_REF]. This size variation was also accompanied with major allometric trends during the course of mammalian evolution, particularly on the skull. Recent studies suggested that craniofacial allometry, i.e. larger faces relative to the rest of the skull in larger individuals, is a general evolutionary trend of morphological change in placentals, and possibly in other groups of vertebrates [START_REF] Cardini | Larger mammals have longer faces because of size-related constraints on skull form[END_REF]Cardini, 2019a;[START_REF] Linde-Medina | Testing the cranial evolutionary allometric 'rule' in Galliformes[END_REF]. Craniofacial allometry is also observable intraspecifically in developmental series of extant mammals [START_REF] Cardini | Larger mammals have longer faces because of size-related constraints on skull form[END_REF] but is absent in early diverging amniotes and in stem-mammals such as cynodonts [START_REF] Hoffman | Jurassic stem-mammal perinates and the origin of mammalian reproduction and growth[END_REF]. This shows that the craniofacial allometry might represent a mammal-specific trend at both the evolutionary and ontogenetic levels. Other common allometric aspects previously suggested in the mammalian skull, and generally based on bivariate analyses, include the negative allometry of middle-ear ossicles relative to the skull dimensions (e.g., [START_REF] Nummela | Scaling of the mammalian middle ear[END_REF], the negative allometry of the inner ear relative to the petrosal (Billet et al., 2015a), and more generally the negative allometry of sense organs relative to other skull parts (e.g., [START_REF] Sánchez-Villagra | Embryos in deep time: the rock record of biological development[END_REF].

Many recent studies analyzed cranial allometry in mammalian species using 3D geometric morphometrics methods (GMM) in relation to functional morphology, phylogeny or cranial integration [START_REF] Marroig | Cranial evolution in sakis (Pithecia, Platyrrhini) I: interspecific differentiation and allometric patterns[END_REF][START_REF] Slater | Allometry and performance: the evolution of skull form and function in felids[END_REF][START_REF] Hautier | Beyond the carapace: skull shape variation and morphological systematics of long-nosed armadillos (genus Dasypus)[END_REF]Cardini, 2019a). Most of these GMM studies considered the entire skull, and only a few of them touched upon this concept using an atomistic approach, i.e. focusing on more specific anatomical regions. Although it lacks the 3D approach of GMM, the use of linear distances showed on several instances that large cranial regions display different allometries relative to the entire skull [START_REF] Slijper | Whales[END_REF][START_REF] Monteiro | Ontogenetic variation in skull shape of Thrichomys apereoides (Rodentia: Echimyidae)[END_REF][START_REF] Ross | Bone strain gradients and optimization in vertebrate skulls[END_REF][START_REF] Marroig | Cranial evolution in sakis (Pithecia, Platyrrhini) I: interspecific differentiation and allometric patterns[END_REF]). These studies have highlighted complex allometric trends on the mammalian skull, which are likely determined by multiple and interacting developmental processes [START_REF] Hallgrímsson | Integration and the Developmental Genetics of Allometry[END_REF]. In fact, much remains to be discovered about these complex morphological patterns especially in the way that allometric growth differentially affects the various parts of the skull and induces cranial shape changes during ontogeny.

Armadillos have been poorly studied regarding allometry despite the fact that the group experienced a spectacular body mass increase in some lineages, especially in glyptodonts [START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF]. The smallest armadillo species do not exceed 0.115 kg while some glyptodonts weighed more than 2,000 kg [START_REF] Superina | Family Chlamyphoridae (Chlamyphorid armadillos)[END_REF]Vizcaíno et al., 2012). Size was generally treated separately from other biological traits in taxonomic or evolutionary contributions on this group (e.g., [START_REF] Wetzel | The subgenera and species of long-nosed armadillos, genus Dasypus L[END_REF], while other studies addressed allometry in the postcranial skeleton of armadillos from the functional, metabolic or physiological viewpoints (e.g., [START_REF] Frappell | How stiff is the armadillo? A comparison with the allometrics of mammalian respiratory mechanics[END_REF][START_REF] Vizcaíno | Structure and function in armadillo limbs (Mammalia: Xenarthra: Dasypodidae)[END_REF][START_REF] Costa | Analysis of the spatio-temporal parameters of gaits in Dasypus novemcinctus (Xenarthra: Dasypodidae)[END_REF]. However, Cardini (2019) demonstrated that extant armadillos exhibit a craniofacial evolutionary allometry similar to that of other placental mammals, a trend also detected in a comparative investigation of allometric variations between several armadillo genera [START_REF] Moeller | Allometrische analyse der gürteltier schädel. Ein beitrag zur phylogenie der Dasypodidae Bonaparte, 1838[END_REF]) and in two more detailed studies on euphractines [START_REF] Abba | Systematics of hairy armadillos and the taxonomic status of the Andean hairy armadillo (Chaetophractus nationi)[END_REF] and dasypodines [START_REF] Hautier | Beyond the carapace: skull shape variation and morphological systematics of long-nosed armadillos (genus Dasypus)[END_REF]. Apart from craniofacial allometry, no other quantitative analysis of cranial allometry exists for armadillos and no cranial shape change related to size was described in the group.

Our study focuses on describing ontogenetic and static allometric patterns in the skull of the most common, best studied, and widely distributed extant cingulate: the nine-banded armadillo (Dasypus novemcinctus ssp. [START_REF] Linnaeus | Systema naturae per regna tria naturae, secundum classes, ordines, genera, species, cum characteribus, differentiis, synonymis, locis[END_REF]. Being distributed on the two American continents, this taxon can be split in as much as four different geographical morphotypes, some or all of which may represent distinct species or subspecies: Southern, Central, Northern, and Guianan (Billet et al., 2017;[START_REF] Hautier | Beyond the carapace: skull shape variation and morphological systematics of long-nosed armadillos (genus Dasypus)[END_REF], as also suggested by molecular studies based on mitochondrial markers [START_REF] Huchon | Armadillos exhibit less genetic polymorphism in North America than in South America: nuclear and mitochondrial data confirm a founder effect in Dasypus novemcinctus (Xenarthra)[END_REF][START_REF] Gibb | Shotgun mitogenomics provides a reference phylogenetic framework and timescale for living xenarthrans[END_REF][START_REF] Feijó | Taxonomic revision of the long-nosed armadillos, Genus Dasypus Linnaeus, 1758 (Mammalia, Cingulata)[END_REF][START_REF] Feijó | Phylogeny and molecular species delimitation of long-nosed armadillos (Dasypus: Cingulata) supports morphology-based taxonomy[END_REF][START_REF] Arteaga | Conservation Genetics, Demographic History, and Climatic Distribution of the Nine-Banded Armadillo (Dasypus novemcinctus): An Analysis of Its Mitochondrial Lineages[END_REF].

Based on a large sample covering three of these four morphotypes, our study aims at understanding how allometric variation is distributed in their skull and seeks to further characterize the covariation between shape and size across different cranial units, while controlling for potential effects of geography. More precisely, we analyzed allometry in: i) the entire skull, and ii) virtually isolated cranial units, looking at both ontogenetic and static allometry. We report heterogeneous cranial allometric patterns in time and space and discuss potential underlying processes.

MATERIAL AND METHODS

Sampling

We sampled 96 cranial specimens stored in the collections of the Muséum national S3 for a complete list of specimens). The sample is largely similar to that of [START_REF] Hautier | Beyond the carapace: skull shape variation and morphological systematics of long-nosed armadillos (genus Dasypus)[END_REF], although some specimens could not be considered here, as they were too incomplete for the proposed set of landmarks (see below). We also added new specimens to complete the ontogenetic series (details available in Table S3). In order to minimize phylogenetic effects, we did not include specimens belonging to the "Guianan morphotype" [START_REF] Hautier | Beyond the carapace: skull shape variation and morphological systematics of long-nosed armadillos (genus Dasypus)[END_REF][START_REF] Billet | The hidden anatomy of paranasal sinuses reveals biogeographically distinct morphotypes in the nine-banded armadillo (Dasypus novemcinctus)[END_REF] as recent morpho-anatomical and molecular studies considered it to be clearly distinct from other D. novemcinctus populations, and to likely represent a new species [START_REF] Huchon | Armadillos exhibit less genetic polymorphism in North America than in South America: nuclear and mitochondrial data confirm a founder effect in Dasypus novemcinctus (Xenarthra)[END_REF][START_REF] Gibb | Shotgun mitogenomics provides a reference phylogenetic framework and timescale for living xenarthrans[END_REF][START_REF] Billet | The hidden anatomy of paranasal sinuses reveals biogeographically distinct morphotypes in the nine-banded armadillo (Dasypus novemcinctus)[END_REF][START_REF] Hautier | Beyond the carapace: skull shape variation and morphological systematics of long-nosed armadillos (genus Dasypus)[END_REF][START_REF] Feijó | Taxonomic revision of the long-nosed armadillos, Genus Dasypus Linnaeus, 1758 (Mammalia, Cingulata)[END_REF][START_REF] Feijó | Phylogeny and molecular species delimitation of long-nosed armadillos (Dasypus: Cingulata) supports morphology-based taxonomy[END_REF][START_REF] Arteaga | Conservation Genetics, Demographic History, and Climatic Distribution of the Nine-Banded Armadillo (Dasypus novemcinctus): An Analysis of Its Mitochondrial Lineages[END_REF]. These studies have also shown that other morphotypes recognizable within D. novemcinctus may represent sub-species or even distinct species, hence our use of D.

novemcinctus ssp. to refer to this potential species complex. Pending more definite conclusions on these aspects, the northern, central, and southern morphotypes were included together in our study and their distribution systematically scrutinized within the allometric analyses. In addition, all analyses of ontogenetic allometry were performed on two different datasets for comparison: on the whole sample and on the best-sampled morphotype only (i.e. southern; n = 48). Finally, potential differences between allometric trajectories among morphotypes were also tested. No specimen belonging to the hairy long-nosed armadillo (Dasypus pilosus) was included in the study as it is very divergent morphologically, although recent molecular studies have shown that this species may also be part of the Dasypus novemcinctus ssp. complex [START_REF] Gibb | Shotgun mitogenomics provides a reference phylogenetic framework and timescale for living xenarthrans[END_REF][START_REF] Feijó | Phylogeny and molecular species delimitation of long-nosed armadillos (Dasypus: Cingulata) supports morphology-based taxonomy[END_REF].

Geometric morphometrics

Digital data were acquired using X-ray µCT facilities at the University of Montpellier (France), at the Natural History Museum (BMNH), and at the AST-RX platform of the Muséum national d'Histoire naturelle (MNHN). Image stacks were improved in contrast, rotated, cropped, and reduced to 8 bits using the ImageJ software [START_REF] Schneider | NIH Image to ImageJ: 25 years of image analysis[END_REF]. Three-dimensional reconstruction and visualization of the skulls and of the virtually isolated bones were performed using stacks of digital images with MIMICS v. 21.0 software (3D Medical Image Processing Software, Materialize, Leuven, Belgium). Cranial shapes were quantified with 131 anatomical landmarks (Figure 22 and Table 3, 4, S4) placed on the exported 3D models using AVIZO v. 9.7.0 software (Visualization Sciences Group, Burlington, MA, USA). The landmarks corresponding to external cranial structures were based on well-established landmark sets from previous studies on mammalian taxa [START_REF] Goswami | EMMLi: a maximum likelihood approach to the analysis of modularity[END_REF][START_REF] Hautier | Beyond the carapace: skull shape variation and morphological systematics of long-nosed armadillos (genus Dasypus)[END_REF], and new landmarks were added on internal structures. Landmarks were selected to provide a good overall representation of skull shape, isolated bones, and characters traditionally used in cingulate phylogenetic analyses of the group [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF][START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF]. The last criterion was set for future studies aiming at integrating knowledge on allometry and covariation patterns for the construction of phylogenetic characters. All landmarks were positioned on suture contacts or at the maximum of curvature, or extreme points of bony processes, fossae or foramina except for landmark #131 (Figure 22), which corresponds to the dorsal projection of the most posterior point of the frontal sinuses (see [START_REF] Billet | The hidden anatomy of paranasal sinuses reveals biogeographically distinct morphotypes in the nine-banded armadillo (Dasypus novemcinctus)[END_REF] on the midline in dorsal view (it was landmarked with the transparency option in Avizo). This point was added to the landmark set in order to include an anatomical landmark on the large dorsal exposure of the frontal bone. We then performed a generalized Procrustes analysis [START_REF] Rohlf | Extensions of the Procrustes method for the optimal superimposition of landmarks[END_REF]) using function gpagen in the R package geomorph version 3.1.0 [START_REF] Adams | Geomorph: Software for geometric morphometric analyses[END_REF], and intra-individual asymmetries [START_REF] Klingenberg | Shape analysis of symmetric structures: quantifying variation among individuals and asymmetry[END_REF] were removed using the function symmetrize in the R package Morpho version 2.6 [START_REF] Schlager | Morpho and Rvcg -Shape Analysis in R: R-Packages for Geometric Morphometrics, Shape Analysis and Surface Manipulations[END_REF]. When some landmarks were missing on one side of the skull, their position was estimated using the function fixLMmirror in the Morpho R package (see Table S5). The logarithm of the centroid size was used as a size variable for the different cranial structures. 3 andTable 4. (2017). The combination of these three variables allowed confirming the ontogenetic separation of specimens in five stages. Some specimens could not be allocated to a particular stage because they preserved no teeth. In this case, these specimens were not included in the analyses where information on ontogenetic stage was needed (see Supporting S6 & S7 for details of the protocol and results

Information 3, Figures S12, S13 & S14, Table
concerning the determination of ontogenetic stages).

Ontogenetic and static allometry

Only complete specimens (n = 76, Table S3) were included in the analyses of allometry performed on the entire skull (ES). The ES Procrustes alignment was realized on the entire set of cranial landmarks, including both sides of the skull. For the ES analysis of ontogenetic allometry, the whole sample corresponds to 76 specimens with 48 specimens belonging to the "Southern group", 11 specimens to the "Central group", and 17 specimens to the "Northern group" as defined by [START_REF] Hautier | Beyond the carapace: skull shape variation and morphological systematics of long-nosed armadillos (genus Dasypus)[END_REF] and [START_REF] Billet | The hidden anatomy of paranasal sinuses reveals biogeographically distinct morphotypes in the nine-banded armadillo (Dasypus novemcinctus)[END_REF]. Only adult specimens were considered in the ES analysis of static allometry (i.e., 51 specimens in total, with 35 from the Southern, five from the Central, and 11 from the Northern groups).

Under the Bone-By-Bone (3B) approach, the analyzed objects corresponded to a virtually isolated bone or group of bones that we defined in this study as Operational Bone Units (OBUs).

We used the same samples for both the ES and 3B analyses of allometry (n = 76 for ontogenetic allometry; n = 51 for static allometry). Each 3B Procrustes alignment was realized on a reduced set of landmarks corresponding to the OBU under consideration. The allometric component in the shape variation of OBUs was analyzed using the skull centroid size as a measure of size. We performed the 3B analyses only on the left cranial side, which was more complete in most cases.

These 3B analyses were only performed on one side since many paired bones were not contiguous and to avoid taking into account symmetrized structures (see above). For the 3B analyses, 13 OBUs were defined, including 11 single bones: premaxillary (pmx); maxillary (mx); nasal (na); frontal (fr); lacrimal (lac); jugal (ju); palatine (pal); parietal (pa); squamosal (sq); supraoccipital (so); petrosal (pe). Two OBUs corresponding to bone complexes (alisphenoid-orbitosphenoidpterygoid-basisphenoid, as-os-pt-bs; basioccipital-exoccipital, bo-eo) were also defined as some of their bony components (alisphenoid-orbitosphenoid; basioccipital-exoccipital) were often fused in adults, and because only OBUs represented by more than three landmarks could be considered.

In the whole landmark dataset, only landmark #114 was not included in the 3B approach as it could not be associated with any of the 13 OBUs.

For both the ES and 3B analyses of allometry, we performed a multivariate regression of Procrustes shape coordinates [START_REF] Izenman | Multivariate regression[END_REF] on size (Log Centroid Size) using the function procD.lm of the R package geomorph. The R² (coefficient of determination) of these analyses represents the percentage of the total shape variation explained by the independent variable, here size [START_REF] Goodall | Procrustes methods in the statistical analysis of shape[END_REF][START_REF] Klingenberg | Geometric morphometrics of developmental instability: analyzing patterns of fluctuating asymmetry with Procrustes methods[END_REF][START_REF] Drake | The pace of morphological change: historical transformation of skull shape in St Bernard dogs[END_REF]. We referred to this percentage as the "allometric proportion of the total shape variation". We assessed the statistical significance of the regressions against the null hypothesis of isometric variation using permutation tests with 10,000 iterations [START_REF] Good | Permutation tests: a practical guide to resampling methods for testing hypotheses[END_REF]. We also present the values for the R² of non-significant regressions (at p-value>0.05) and comment them cautiously following recent recommendations by [START_REF] Dushoff | I can see clearly now: reinterpreting statistical significance[END_REF].

Common allometry among morphotypes

For the ES approach, differences in allometric trajectories among morphotypes at the ontogenetic and static levels were investigated. For this analysis, we performed a HOS (Homogeneity of Slope Test) using a Procrustes ANOVA [START_REF] Goodall | Procrustes methods in the statistical analysis of shape[END_REF] for morphotypes, size, and interaction between both variables [START_REF] Collyer | Phenotypic trajectory analysis: comparison of shape change patterns in evolution and ecology[END_REF]. The HOS performs statistical assessment of the terms in the model using Procrustes distances among specimens, rather than explained covariance matrices among variables, which is equivalent to distance-based ANOVA designs [START_REF] Anderson | A new method for non-parametric multivariate analysis of variance[END_REF]. The HOS calculates the amount of shape variation explained by size, computes the allometric slopes for each category of the independent variable, and quantifies the influence of a given factor on the shape variation. Statistical significance was evaluated with a residual randomization permutation procedure with 10,000 iterations [START_REF] Collyer | A method for analysis of phenotypic change for phenotypes described by high-dimensional data[END_REF]. If the null hypothesis of HOS (= parallel slopes) is rejected, then morphotypes differ in their patterns of allometric growth. The HOS analysis was conducted using the procD.allometry function of the geomorph package version 3.0.7 (Adams et al., 2018). More precisely, these analyses were performed to identify the interaction between geographic distribution (morphotypes) and allometry on shape variation by including pairwise comparisons between groups (distribution) to assess significant differences of both the direction (angles) and magnitude (amount of change in shape with size) of allometric trajectories. The pairwise comparisons were performed with advanced.procD.lm from the geomorph package version 3.0.7. When trajectories significantly differed between morphotypes, allometric patterns were analyzed both within the whole sample and within the southern morphotype subsample only.

Common allometry between ontogenetic stages

Multivariate regressions of shape on the logarithm of the skull centroid size were also performed for the different ontogenetic stages determined (see Results) in order to compare the allometric proportions between stages for a given OBU. We then tested the allometric differences between each ontogenetic stage for a given OBU. This preliminary investigation could not be conducted within particular morphotypes because their sampling per ontogenetic stage for each was too low. For this analysis, we also performed a HOS test using a Procrustes ANOVA on each OBU for ontogenetic stage, size, and interaction between both variables. In order to reduce biases linked to sample size, we calculated the angles of each slope for a given OBU versus the horizontal axis to test whether the different ontogenetic stages for a given OBU share a common allometry (see [START_REF] Klingenberg | Size, shape, and form: concepts of allometry in geometric morphometrics[END_REF]. The ratio between the OBU relative size and its average for a given ontogenetic stage was also calculated for each stage and for the entire sample in order to analyze the growth dynamics of the OBU.

RESULTS

Allometry and geography

The regression of shape on log centroid size in our ontogenetic series of D. novemcinctus ssp. accounts for 27.62% of the total shape variation (p-value < 0.0001, Figure 23; Figure S15).

The geographical distribution explains 16.64% of the total shape variation (p-value < 0.0001, Figure S15). At the ontogenetic level, the morphotypes show a slight difference in their allometric trajectory attesting to an interaction between geography and allometry on shape variation during ontogeny (Figure S15). However, this effect seems to be minimal (3.16 %; Figure S15). The HOS test pairwise comparisons of ontogenetic allometric trajectories suggests no difference between the Central and Southern morphotypes, but a significant difference between the latter two and the Northern morphotype. These results should be taken with caution as the p-value is very close to the statistically significance threshold in the comparison between the Central and Southern morphotypes (p-value = 0.0515) and the difference revealed with the Northern morphotype may be due to the lack of specimens as young as for the other two morphotypes. Because these results

suggest that the ontogenetic allometries may slightly differ among morphotypes, the allometric shape changes during ontogeny were analyzed both within the whole sample (see below) and within the Southern morphotype subsample (Figure S16).

The regression of shape on the logarithm of the centroid size in our adult sample of D.

novemcinctus ssp. accounts for only 6.31% of the total shape variation (p-value < 0.0001, Figure 23; Figure S15). The effect of geographical distribution is proportionally higher, expressing 22.81% of the total shape variation (p-value < 0.0001, Figure S15). At the static level, the morphotypes share a common allometric trajectory and no interaction between geography and allometry is statistically supported, although the p-value is close to the significance threshold (pvalue = 0.0619). It should also be noted that the central morphotype has relatively low sample size (Figure S15). The HOS test pairwise comparisons of static allometric trajectories suggests no difference between each morphotype. Because these results suggest that the static allometries are similar among morphotypes, the allometric shape changes at the adult stage were analyzed within the whole sample only (see below).

Figure 23. Ontogenetic and static allometry on the entire skull (ES) of nine-banded armadillos. Ontogenetic stages are represented with different colors (juvenile = green; subadult = yellow; adult = red; see text for more detail). For graphical display, we used the projected regression scores of the shape data to represent shape variation related to changes in log centroid size [START_REF] Adams | A field comes of age: geometric morphometrics in the 21st century[END_REF]. Shape changes were visualized as vectors from the minimal shape (green) to the maximal shape (red) of the shape regression scores corresponding to the projection of the data points in shape space on to an axis in the direction of the regression vector (see [START_REF] Drake | The pace of morphological change: historical transformation of skull shape in St Bernard dogs[END_REF]. A. Multivariate regression of skull shape on log skull centroid size at the ontogenetic level, representing 27.62% of the total shape variation. B. Same analysis, at the static level (6.31% of total shape variation) (see text).

Allometric variations on the entire skull (ES)

Ontogenetic allometry Three main regional trends of skull allometric variation can be recognized in our ontogenetic series. Adult cranial proportions clearly differed from juvenile ones in the relative size of the snout and zygomatic arches compared to the braincase (Figure 23A; Table S8). The snout undergoes an anteroposterior elongation with size increase. This elongation is bidirectional (one particularly distinctive for its strong relative posterior displacement. The dental row is relatively shorter in larger specimens, with an anterior displacement of the posterior portion of the dental row (#29-30) while the anterior portion varies very slightly (#27-28). The analysis of the ES ontogenetic allometry in the southern morphotype revealed remarkably similar shape changes to the ones described above (Figure S16).

directed

Static allometry

An increase in size, at the static level, is only associated with minor shape variations of the skull (Figure 23B; Table S8), similar to the pattern detected with the ontogenetic analyses of allometry, albeit to a lesser degree and with some variations specific to this level (see below). The most anterior part of the nasal bone shows a relative anterior displacement, just like the W-shaped processes in front of the premaxillary (as defined by landmarks #8; #11-14; Figure 22). The rest of the face shows a relative narrowing as size increases. The shape changes of the zygomatic arches elongation of the palatine is detected at the static level. For all other landmarks, the allometric changes appear very weak when compared to their changes in the analysis of ontogenetic allometry.

Allometric variations studied bone by bone (3B) Comparison between OBUs

We observe differences in the proportions of allometric shape variation between different OBUs both at the ontogenetic and static levels. In both cases (Figure 24), the regression of shape on size shows no statistical support for the lacrimal (Figure 24; Table 5; Figures S17 &S18). This is not the case for other OBUs, for which at least the analyses at the ontogenetic level show a significant allometric effect.

Figure 24. Bar graphs showing the allometric proportions (R²) of each cranial unit's (OBU) total shape variation under the 3B approach (see text), at the ontogenetic (A) and static (B) levels. Allometric proportions are shown with the log skull centroid size taken as a size variable. On the virtually dislocated skull (in right lateral view), the allometric proportions are reported in corresponding colors. White bars indicate a statistically unsupported (NS) allometry for a given OBU (at p value > 0.05). Abbreviations of OBUs: as-os-pt-bs, alisphenoid-orbitosphenoid-pterygoidbasisphenoid complex; bo-eo, basioccipital-exoccipital complex; fr, frontal; ju, jugal; lac, lacrimal; mx, maxillary; na, nasal; pa, parietal; pal, palatine; pe, petrosal; pmx, premaxillary; so, supraoccipital; sq, squamosal. At the ontogenetic level, the premaxillary has the lowest proportion of shape variation explained by size of all OBUs (lacrimal excluded; Figure 24A & Table 5). The jugal, petrosal, parietal, as-os-pt-bs OBU, nasal, palatine have a proportion of shape variation explained by size varying between 5% and 10% (Figure 24A & Table 5). The maxillary, supraoccipital and squamosal show allometric proportions between 10% and 12% (Figure 24A & Table 5). Finally, the last two OBUs showing the highest proportion of variation explained by size at the ontogenetic level are the bo-eo OBU and the frontal, the latter with more than twice the proportion values find in the other OBUs (Figure 24A & Table 5). At the static level, the allometric proportion is much lower than at the ontogenetic level for most OBUs. Only five OBUs show a statistically wellsupported allometric effect at this level. Among them, the petrosal and the as-os-pt-bs OBU show an allometric proportion lower than 5% (Figure 24B & Table 5). The frontal shows a drastic reduction in its allometric proportion (5.96%) (Figure 24B & Table 5). Finally, the parietal and palatine have an allometric proportion almost equivalent to that obtained at the ontogenetic level for the palatine, it is even higher to that of the entire skull (Figure 24B & Table 5).

All descriptions of the allometric shape changes below describe the maximal shapes as compared to the minimal shapes per OBU at the ontogenetic level. This was done only for the OBUs whose allometric variation is statistically well-supported (p-value < 0.05). Only landmarks on the left side of the skull are mentioned (see Table 3 and Table 4 for their symmetrical landmark/counterparts). The same analyses were performed using the Southern morphotype only.

We obtained very similar results (Figure S16) as the ones described hereafter for the entire dataset.

The only notable differences are generally in the norm (i.e., lesser) of the vectors and not in their direction. The results and shape changes explained by size for the static level on the whole sample are illustrated in Figure S19 and those changes that differ from the ontogenetic level are described in Supporting Information 4.

Alisphenoid-Orbitosphenoid-Pterygoid-Basisphenoid complex (Figure 25.A1-A3)

When the skull size increases, the foramen ovale (#70) shows very little variation, while the transverse canal foramen (#68) takes a more medial position. The pterygoid wings (#66) are more extended posteriorly. The optical foramen is located more dorsolaterally (#75). Internally, the most lateral point of the dorsal transverse ridge (#130), which delimits the ethmoidal fossa anteriorly, is more laterally positioned. Finally, the contact between the frontal, the squamosal, and the alisphenoid (#44) is located much more anteromedially.

Basioccipital-Exoccipital complex (Figure 25.B1-B3)

As size increases, the basioccipital becomes mediolaterally wider (#90). The concavity that constitutes the posterior part of the jugular foramen is less marked (#96). The occipital condyles are relatively larger and more anterolaterally oriented (#92; #100). The foramen magnum (#92;

#101) is relatively narrower mediolaterally, its ventral portion being more ventral. The exoccipital meets the supraoccipital much further dorsoanteriorly (#94).

Frontal (Figure 25.C1-C3)

The allometric changes mainly involve the posterior development of the frontal sinuses (#131), the deepening of the post-orbital constriction (#42), and a more posteroventral location of the ventral intersection of the annular ridge and cribriform plate (#113). While the frontal sinuses are poorly developed in the juvenile stage, they extend much farther posteriorly in older specimens (see also [START_REF] Billet | The hidden anatomy of paranasal sinuses reveals biogeographically distinct morphotypes in the nine-banded armadillo (Dasypus novemcinctus)[END_REF]. The anterior part of the frontal extends further anteriorly in larger individuals (#2; #34; #36) while its posterior part is relatively shortened anteroposteriorly and compressed dorsoventrally, as expressed by the landmarks #44, #78, and #81. Finally, the anterior edge of the orbit is placed only slightly more medially (#38).

Jugal (Figure 25.D1-D3)

Two main allometric trends can be recognized for the jugal. Its anterior part, in contact with the lacrimal and the maxillary (#50), shows a relative shortening as size increases. The second trend corresponds to a dorsoventral increase of the zygomatic arch (#23; #54; #56), which is stronger in its anteroventral and posterodorsal parts.

Maxillary (Figure 25.E1-E3)

From the juvenile stage to the adult stage, the maxillary shows a relative anterior elongation as shown by the landmarks in contact with the premaxillary (#4; #5; #7), especially ventrally at the level of the midline. The landmarks in contact with the palatine (#19; #21) are shifted anterodorsally and the dorsal part of the snout (#34; #36) more posteroventrally. While the maxillary is bulging in its dorsal mid-part in juveniles, it is much shorter dorsoventrally in larger specimens, as marked by the landmark in contact with the nasal and the frontal (#34). Large specimens also display a proportionally reduced dental row (#29; #31). The zygomatic process of the maxillary shows a more ventrolateral position (#23). Finally, the relative length of the infraorbital canal varies strongly from juveniles to adults, the maxillary foramen being more posterior in larger specimens, as expressed by the landmark #25.

Figure 25. Vector representation of the allometric shape changes detected for a given cranial unit (OBU), represented between its minimal (greensmaller centroid size) and maximal (redlarger centroid size) shape (see Figure 23). Results of the analysis performed at the ontogenetic level, and with the log skull centroid size taken as the size variable (see text). For each OBU, the changes are shown in three subsections organized horizontally: 1, vectors from minimal to maximal shape with minimal OBU shape; 2, same as 1) with maximal OBU shape; 3, minimal OBU shape in transparency with vectors. A) alisphenoid-orbitosphenoid-pterygoid-basisphenoid complex; A1-A2, lateral view; A3, dorsal view. B) basioccipital-exoccipital complex; B1-B2, dorsal view; B3, ventral view. C) frontal; C1-C2, lateral view; C3, ventral view. D) jugal; D1-D2, lateral view; D3, medial view. E) maxillary; E1-E2, lateral view; E3, medial view. F) nasal; F1-F2, dorsal view; F3, ventral view. Landmark numbers and orientation arrows were added for more readability as well as the overall representation of the unpaired bone (basioccipital). Abbreviations: A, anterior; D, dorsal; L, lateral; V, ventral.

Nasal (Figure 25.F1-F3)

The nasal is relatively narrower mediolaterally in larger specimens with a much more pronounced internal curvature. Only the landmarks in contact with the premaxillary (#4; #10) show a slight anterior elongation in the medial part of the bone.

Palatine (Figure 26.G1-G3)

The palatine becomes relatively more elongated anteroposteriorly and narrower mediolaterally as size increases. This elongation is particularly visible between the anterolateral edge of the palatine and the caudal palatine foramen that became more distant from one another as size increases (#19; #21; #46).

Parietal (Figure 26.H1-H3)

The parietal is slightly more elongated anteroposteriorly and narrower mediolaterally in larger specimens (#78; #79; #81; #83). The tentorial process forms a higher ventrally-directed crest as size increases (#73).

Petrosal (Figure 26.I1-I3)

On the promontorium, size has little effect on shape variation except at the anterior and medial borders, which are slightly more reduced as size increases (#104; #124). In larger specimens, the mastoid process (#106) is much more pronounced ventrally, the dorsal tip of the crista petrosa (#118) is more anterodorsal, and the bottom of the fossa subarcuata shows a relatively more posterior position (#126).

Figure 26. Vector representation of the allometric shape changes detected for a given cranial unit (OBU), represented between its minimal (greensmaller centroid size) and maximal (redlarger centroid size) shapes (see Figure 23). Results of the analysis performed at the ontogenetic level, and with the log skull centroid size taken as the size variable (see text). For each OBU, the changes are shown in three subsections organized horizontally: 1, vectors from minimal to maximal shape with minimal OBU shape; 2, same as 1) with maximal OBU shape; 3, minimal OBU shape in transparency with vectors. G) palatine; G1-G2, ventral view; G3, dorsal view. H) parietal; H1-H2, ventral view; H3, dorsal view. I) petrosal; I1-I2, medial view; I3, lateral view. J) premaxillary; J1-J2, ventral view; J3, medial view. K) squamosal; K1-K2, lateral view; K3, ventral view. L) supraoccipital; L1-L2, lateral view; L3, occipital view. Landmark numbers and orientation arrows were added for more readability as well as the overall representation of the unpaired bone (supraoccipital). Abbreviations: A, anterior; L, lateral; V, ventral.

Premaxillary (Figure 26.J1-J3)

The premaxillary is slightly more elongated dorsally in larger specimens while the situation is more complex ventrally. Medially, the premaxillary shortens (#5; #8) while it elongates laterally (#7; #14). The W-shaped process located in the anterior part of the bone (Figure 22) is more pronounced laterally with a deeper curvature (#12) and longer processes (#14). However, the Wshaped process is less sharp medially as its midline point is positioned more posteriorly (#8). The incisive foramen becomes relatively shorter anteroposteriorly mainly due to the anterior displacement of the most posterior point of these foramina (#18).

Squamosal (Figure 26.K1-K3)

The relative allometric reduction of the braincase is also visible on the dorsal edge of the squamosal of larger specimens (#81; #83). As for the jugal, we observe a dorsoventral increase of the zygomatic process of the squamosal (#54; #56). The posterior root of the zygomatic arch (#62) is also relatively more posterior. The posterior opening of the posttemporal canal [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF]) is more dorsal in larger specimens (#88). The postglenoid process (#58) is more pronounced anterolaterally and the postglenoid foramen (#60) is positioned slightly more medially. Therefore, the postglenoid process and postglenoid foramen are relatively more distant from one another on larger skulls. The sulcus for the external acoustic meatus (#64) is shallower and positioned more medially in larger specimens. Finally, the most posteroventral point between the alisphenoid and squamosal (#72) and the tip of the entoglenoid (#77) are shifted posteriorly.

Supraoccipital (Figure 26.L1-L3)

The increase in size is accompanied by a slight lateromedial narrowing (#83) and a dorsoventral elongation (#102) of the supraoccipital. The processes of the nuchal crests undergo a strong posteromedial development in larger specimens (#86). The external occipital crest (#84) is less prominent. In the inner part of the supraoccipital, the lateral occipital vertical ridges (#116) are more developed in the anterior part of the caudal cerebral fossa.

Allometry at different stages

The allometric proportion of shape variation varies between the juvenile, subadult, and adult stages for a given OBU and for the entire skull in the whole sample (Figure 27A; Table 6; Table S9). For the entire skull, the allometric proportion decreases from juvenile to adult stages.

In the 3B approach, the stage with the highest allometric proportion of shape variation varies from one OBU to another. The juvenile stage shows the highest allometric proportion for the maxillary, the frontal, the basioccipital-exoccipital complex, and the petrosal (Figure 27A; Table 6; Table S9). Allometric effects are often not statistically supported in older stages for these OBUs, as exemplified by the bo-eo OBU that only shows a strongly supported allometric effect at the juvenile stage. The allometric proportion of the maxillary shape variation in juveniles is only slightly higher than that retrieved at the subadult stage. The subadult stage shows the highest allometric proportion for the premaxillary, lacrimal, jugal, palatine, parietal, squamosal, and supraoccipital (Figure 27A; Table 6; Table S9). Allometric effects are statistically supported only at the subadult stage for the lacrimal, jugal, premaxillary, squamosal, and supraoccipital among these OBUs. The allometric proportion of shape variation is generally very low at the adult stage.

The frontal, palatine, parietal, as-os-pt-bs OBU, and petrosal all display allometry at this stage (Figure 27A; Table 6; Table S9). The nasal bone is the only OBU that shows no stage with a supported static allometry. Stages with the highest allometric proportion for a given OBU generally show a higher slope (Table 6). Thus, the subadult stage is usually characterized by the highest slope coefficients for most OBUs. The comparison of the angles of each regression slope with respect to the horizontal axis shows that several OBU stages may share a common allometry (Figure S20, Table 6, Table S9-S10). By cross-checking these results with the statistical support values obtained for the allometric analyses of a given OBU at a given stage (Table 6 andFigure 27A), we find that only the juvenile and subadult stages of the maxillary (for which the angles are negative) and the juvenile and adult stages of the petrosal show a common allometry in our sample.

This analysis also reveals a significantly different allometric effect between the subadult and adult stages of the palatine and parietal. (Figure S20, Table 6, Table S9-10). 6). B) Boxplot showing the variation of size for each OBU relative to its mean per stage (green, juvenile; yellow, subadult; red, adult), and for the whole sample (in black), as measured by the following ratio for every specimen: log OBU centroid size / mean log OBU centroid size at a given stage. Abbreviations of OBUs: as-os-pt-bs, alisphenoidorbitosphenoid-pterygoid-basisphenoid complex; bo-eo, basioccipital-exoccipital complex; fr, frontal; ju, jugal; lac, lacrimal; mx, maxillary; na, nasal; pa, parietal; pal, palatine; pe, petrosal; pmx, premaxillary; so, supraoccipital; sq, squamosal. The variation in size of an OBU relative to its mean size is different from one OBU to another and among ontogenetic stages (Figure 27B). At the juvenile stage, the OBUs with the largest size variations from their mean are the maxillary, nasal, lacrimal, jugal, palatine, squamosal, supraoccipital, and bo-eo OBUs. At the subadult level, OBUs with the largest variation in size constitute the anterior part of the snout (i.e., premaxillary, maxillary, and nasal). In the adult stage, the OBUs with the greatest variation in size from their mean correspond to the lacrimal, jugal, and palatine. Finally, over the entire sample and stages, the size variation of an OBU compared to its average size enables us to sort the OBUs into two categories: those with a large size range (i.e., premaxillary, maxillary, nasal, frontal, lacrimal, jugal, and palatine) and those with a small size range (i.e., parietal, squamosal, as-os-pt-bs OBU, supraoccipital, bo-eo OBU, and petrosal) (Figure 27B). These patterns of size variation do not reflect the allometric proportions per OBU and per stage. However, the two size categories clearly separate an anterior from a posterior block of OBUs, which recall the allometric pattern detected on the entire skull (Figure 23 and see Discussion).

DISCUSSION

Allometric and geographical interaction

In mammals with a wide geographical distribution, such as the Pan-American nine-banded armadillos, allometric patterns can vary with geography and across environments (e.g., Meloro et al. 2014;[START_REF] Bubadué | Ecogeographical variation in skull shape of South-American canids: abiotic or biotic processes?[END_REF][START_REF] Ferreira-Cardoso | Skull shape variation in extant pangolins (Pholidota: Manidae): allometric patterns and systematic implications[END_REF]. Recent work on nine-banded armadillos has shown that variation in cranial shape had an important geographic imprint in this widely distributed species [START_REF] Hautier | Beyond the carapace: skull shape variation and morphological systematics of long-nosed armadillos (genus Dasypus)[END_REF]. In conjunction with evidence from internal anatomy and molecular data, these observations suggested the existence of four morphotypes (Southern, Central, Northern and Guianan) that potentially correspond to different species or subspecies [START_REF] Huchon | Armadillos exhibit less genetic polymorphism in North America than in South America: nuclear and mitochondrial data confirm a founder effect in Dasypus novemcinctus (Xenarthra)[END_REF][START_REF] Gibb | Shotgun mitogenomics provides a reference phylogenetic framework and timescale for living xenarthrans[END_REF][START_REF] Billet | The hidden anatomy of paranasal sinuses reveals biogeographically distinct morphotypes in the nine-banded armadillo (Dasypus novemcinctus)[END_REF][START_REF] Hautier | Beyond the carapace: skull shape variation and morphological systematics of long-nosed armadillos (genus Dasypus)[END_REF][START_REF] Feijó | Taxonomic revision of the long-nosed armadillos, Genus Dasypus Linnaeus, 1758 (Mammalia, Cingulata)[END_REF][START_REF] Feijó | Phylogeny and molecular species delimitation of long-nosed armadillos (Dasypus: Cingulata) supports morphology-based taxonomy[END_REF][START_REF] Arteaga | Conservation Genetics, Demographic History, and Climatic Distribution of the Nine-Banded Armadillo (Dasypus novemcinctus): An Analysis of Its Mitochondrial Lineages[END_REF]. Regarding allometry, our results show that the percentage of variation in skull shape due to the interaction between geography and size is weak at the ontogenetic level (R² = 3.16% -Figure S15) and statistically unsupported at the static level. The slight difference in ontogenetic allometric trajectories among morphotypes of D. novemcinctus ssp. must be considered cautiously as it may be due to insufficient juvenile samplings in the Northern morphotype. A weak relationship between geography and allometry was also described in subspecies of the widespread Eurasian red squirrel [START_REF] Marr | Geographical variation in Eurasian red squirrel (Sciurus vulgaris L., 1758) mandibles and the issue of subspecies-level organization: a failure of history?[END_REF], for which subtle and continuous mandibular shape changes were retrieved.

Our comparison of allometric patterns between the whole sample and the Southern morphotype in nine banded armadillos further demonstrates that overall cranial allometric patterns are well conserved within this potential species complex. While ecological factors such as diet can influence allometric patterns [START_REF] Wilson | Allometric disparity in rodent evolution[END_REF], the distinction suggested by [START_REF] Smith | The anatomy and function of the feeding apparatus in two armadillos (Dasypoda): anatomy is not destiny[END_REF] between Central and South American populations (feeding more on termites and ants) and North American populations (more omnivorous) questions the influence of diet on allometric variation.

But, the weak link between geography and allometry in nine-banded armadillos also suggests that there is no clear influence of diet on overall cranial allometric patterns either.

Main allometric variations

Entire Skull approach

Allometry was recognized as an important component of mammalian skull variation, often accounting for about a third of the cranial variation at intra-and interspecific levels in mammals [START_REF] Frost | Cranial allometry, phylogeography, and systematics of large-bodied papionins (primates: Cercopithecinae) inferred from geometric morphometric analysis of landmark data. The Anatomical Record Part A: Discoveries in Molecular[END_REF][START_REF] Hallgrímsson | Deciphering the palimpsest: studying the relationship between morphological integration and phenotypic covariation[END_REF][START_REF] Cassini | Skull geometric morphometrics and paleoecology of Santacrucian (Late Early Miocene; Patagonia) native ungulates (Astrapotheria, Litopterna, and Notoungulata)[END_REF][START_REF] Hallgrímsson | Morphometrics, 3D imaging, and craniofacial development[END_REF]. Ninebanded armadillos are no exception with nearly 28% of the total cranial shape variation explained by size at the ontogenetic level. The two major ontogenetic allometric trends detected here were the relative snout elongation and the reduction of braincase proportions, which is reminiscent of previous results dealing with mammalian species [START_REF] Drake | The pace of morphological change: historical transformation of skull shape in St Bernard dogs[END_REF][START_REF] Moyano | Skull Ontogeny of the Hyraxes Procavia capensis and Dendrohyrax arboreus (Procaviidae: Hyracoidea)[END_REF][START_REF] Heck | Why the long face? Comparative shape analysis of miniature, pony, and other horse skulls reveals changes in ontogenetic growth[END_REF]. This pattern, often designated as craniofacial allometry, was also detected at the evolutionary level in many groups of mammals [START_REF] Cardini | Larger mammals have longer faces because of size-related constraints on skull form[END_REF][START_REF] Cardini | Why the long face? Kangaroos and wallabies follow the same 'rule' of cranial evolutionary allometry (CREA) as placentals[END_REF][START_REF] Tamagnini | Anyone with a long-face? Craniofacial Evolutionary Allometry (CREA) in a family of short-faced mammals, the Felidae[END_REF]. Cardini (2019) proposed that craniofacial allometry could represent a much widespread pattern of vertebrate morphological evolution.

In nine-banded armadillos, our analysis highlights some important additional allometric patterns on the entire skull, which could be summarized as follows:

(i)

The elongation of the snout is accompanied by a relative dorsoventral flattening and a lateromedial narrowing. At the intraspecific level, previous studies have also characterized a similar narrowing (e.g., [START_REF] Segura | A quantitative approach to the cranial ontogeny of Lycalopex culpaeus (Carnivora: Canidae)[END_REF] or flattening (e.g., [START_REF] Ferreira-Cardoso | Skull shape variation in extant pangolins (Pholidota: Manidae): allometric patterns and systematic implications[END_REF] of the snout.

(ii) When size increases and the snout elongates, the length of the dental row (excluding the M1; see Material and Methods) shortens relatively to the entire skull at both the ontogenetic and static levels (Figure 23), which might suggest that its size does not increase much during ontogeny. Several species belonging to the genus Dasypus stand out among extant armadillos in showing dental replacement of most of their cheek teeth [START_REF] Ciancio | Evolutionary implications of dental eruption in Dasypus (Xenarthra)[END_REF]. Further research is needed to establish whether this allometric reduction of the dental row proportion is specific to nine-banded armadillos or more widespread in other xenarthran species. It is indeed worth noting that this variation is known to be reversed in other mammals such as pronghorns [START_REF] Moyano | Skull ontogeny of the pronghorn (Antilocapra americana) in the comparative context of native North American ungulates[END_REF], zokors [START_REF] Kang | Geometric morphometric analysis of the plateau zokor (Eospalax baileyi) revealed significant effects of environmental factors on skull variations[END_REF] or howler monkeys (Meloro et al., 2014) in which the relative length of the upper dental row increases relative to the length of the skull.

(iii)

The orbitotemporal region shows a relative widening as the size increases, with a deeper postorbital constriction, a dorsoventally higher zygomatic arch and a wider temporal fenestra. An allometric relationship between these two parts of the orbitotemporal region has already been described in a canid species [START_REF] Segura | A quantitative approach to the cranial ontogeny of Lycalopex culpaeus (Carnivora: Canidae)[END_REF] while in horses the opposite variation is observed [START_REF] Heck | Why the long face? Comparative shape analysis of miniature, pony, and other horse skulls reveals changes in ontogenetic growth[END_REF]. It was noted that the effect of allometry throughout the orbitotemporal region is highly contrasted at the evolutionary level within mammalian groups, which is probably due to the functional relationship between the masticatory muscles and normal oculomotor function [START_REF] Heesy | Function of the mammalian postorbital bar[END_REF].

(iv) Much of the allometric shape changes found at the static level were already detected with clearly higher proportions at the ontogenetic level, except for the parietal and palatine bones (Figure 28A). The high proportion of static allometry for these two bones suggests that much of their size-related shape variation occurs late during ontogeny (Figure 27A), exhibits high phenotypic plasticity or is subject to high selective pressure [START_REF] Pélabon | On the relationship between ontogenetic and static allometry[END_REF]. This result is particularly interesting in the case of long-nosed armadillos as their palatal region bears several diagnostic traits for the genus Dasypus [START_REF] Feijó | Taxonomic revision of the Dasypus kappleri complex, with revalidations of Dasypus pastasae (Thomas, 1901) and Dasypus beniensis Lönnberg, 1942 (Cingulata, Dasypodidae)[END_REF]. It would be worth performing the same analyses in other Dasypus species to see if this allometric pattern is conserved within dasypodines and how it relates to the diagnostic features used to distinguish species [START_REF] Feijó | Phylogeny and molecular species delimitation of long-nosed armadillos (Dasypus: Cingulata) supports morphology-based taxonomy[END_REF].

Bone-By-Bone (3B) approach and the complexity of cranial allometry

Most studies on cranial allometry involved analyses of covariation between local cranial distances and the skull length (e.g., [START_REF] Goswami | Ontogenetic morphology and allometry of the cranium in the common European mole (Talpa europaea)[END_REF][START_REF] Wilson | Comparison of prenatal and postnatal ontogeny: cranial allometry in the African striped mouse (Rhabdomys pumilio)[END_REF][START_REF] Wilson | Allometric disparity in rodent evolution[END_REF][START_REF] Wilson | The evolution of ontogenetic allometric trajectories in mammalian domestication[END_REF], or multivariate regressions over a set of cranial landmarks (GMM data) using a whole-skull Procrustes alignment (e.g., [START_REF] Monteiro | Ontogenetic variation in skull shape of Thrichomys apereoides (Rodentia: Echimyidae)[END_REF][START_REF] Cardini | Post-natal ontogeny of the mandible and ventral cranium in Marmota species (Rodentia, Sciuridae): allometry and phylogeny[END_REF][START_REF] Heck | Why the long face? Comparative shape analysis of miniature, pony, and other horse skulls reveals changes in ontogenetic growth[END_REF]this study). A few studies, however, detailed allometric patterns on specific regions of the skull with the use of linear distances (e.g., Billet et al., 2015a). Our 3B analysis may represent a novel approach, to our knowledge, as it uses geometric morphometrics to pinpoint and compare allometric variations at a smaller anatomical scale, such as individual bones, while changing the referential for the Procrustes alignment. Such an approach enabled us to detect previously unnoticed allometric variations and to reveal an untapped complexity of allometric patterns. The scrutiny of different spatial scales has important implications for studies on morphological integration and modularity, because growth patterns and allometry are essential factors for morphological integration [START_REF] Porto | Size variation, growth strategies, and the evolution of modularity in the mammalian skull[END_REF][START_REF] Klingenberg | Cranial integration and modularity: insights into evolution and development from morphometric data[END_REF][START_REF] Mitteroecker | Morphometric Variation at Different Spatial Scales: Coordination and Compensation in the Emergence of Organismal Form[END_REF]. Such detailed characterization of shape variation linked to size should also help towards a better knowledge and more appropriate treatment of correlated characters in morphological phylogenetics [START_REF] Billet | Serial Homology and Correlated Characters in Morphological Phylogenetics: Modeling the Evolution of Dental Crests in Placentals[END_REF].

The differences in allometric variation found in specific regions of the skull, with the entire skull (ES) and 3B approaches at the ontogenetic and static levels, show that the whole cranial allometric variation results from a complex superimposition of different allometric patterns expressed at different times and locations. At the ontogenetic level, our 3B analyses enabled to highlight major cranial allometric variations for most cranial units (OBUs; see Material & Methods), which differ from the ones retrieved using the ES. For instance, a size-related dorsoventral elongation and mediolateral shortening of the supraoccipital was detected with the 3B approach but not with the ES analyses (Figure 23, Figure 26.L1-L3). These results partly agree with the bivariate analyses of [START_REF] Goswami | Ontogenetic morphology and allometry of the cranium in the common European mole (Talpa europaea)[END_REF], which showed that the width of the supraoccipital followed an isometric growth in the common European mole (Talpa europaea Linnaeus, 1758) while its height displayed positive allometry. Our 3B analyses also highlighted that the processes of the nuchal crests undergo a strong posteromedial development as size increases. Obviously, different allometric patterns could potentially be detected when considering different scales (e.g., focus on the basicranium region instead of a given bone).

Heterogeneity of cranial allometry in space and time

Our study shows that the degree of allometric shape variation is not homogeneously distributed among the skull bones of nine-banded armadillos. Our 3B analyses most particularly revealed that the allometric proportions of shape variation are regionalized. Cranial units displaying the highest allometric proportions are not necessarily located close to one another (Figure 24). The relation with cranial size differs between OBUs, which is in line with bivariate analyses demonstrating that most distances measured on mammalian skulls follow different allometric trends (e.g., [START_REF] Abdala | Postweaning ontogeny of the skull of Didelphis albiventris[END_REF][START_REF] Marroig | Cranial evolution in sakis (Pithecia, Platyrrhini) I: interspecific differentiation and allometric patterns[END_REF][START_REF] Goswami | Ontogenetic morphology and allometry of the cranium in the common European mole (Talpa europaea)[END_REF][START_REF] Wilson | Comparison of prenatal and postnatal ontogeny: cranial allometry in the African striped mouse (Rhabdomys pumilio)[END_REF][START_REF] Segura | A quantitative approach to the cranial ontogeny of Lycalopex culpaeus (Carnivora: Canidae)[END_REF][START_REF] Moyano | Skull Ontogeny of the Hyraxes Procavia capensis and Dendrohyrax arboreus (Procaviidae: Hyracoidea)[END_REF]. This heterogeneity of allometric proportions per cranial unit could not be explained by the variation in size during ontogeny (see

Results and Figures 27A-B & 28A

). Similarly, both the prenatal skull ossification sequence (Figure 28B see [START_REF] Hautier | Skeletal ossification and sequence heterochrony in xenarthran evolution[END_REF] and the embryonic origin of each bone (Figure 28C see [START_REF] Piekarski | Evolutionary innovation and conservation in the embryonic derivation of the vertebrate skull[END_REF] could not explain the differences in allometric proportions observed. Slight methodological artefacts (e.g., number of landmarks per object) and the multiplicity of developmental and genetic processes at stake during local cranial morphogenesis [START_REF] Hallgrímsson | Integration and the Developmental Genetics of Allometry[END_REF] may explain the heterogeneous pattern found in our study. In addition, the proportion of total shape variation of each cranial unit explained by an independent variable, here size, may also depend on how much other variables (e.g., environment) explain total shape variation and how these overlap with size.

Figure 28. Comparison between the allometric proportion of shape variation, the variation in size and developmental characteristics for each cranial unit treated in this paper (see Discussion). A) Allometric proportions at ontogenetic (light orange circles) and static (light green squares) levels (unfilled figures correspond to non-supported allometric effects, see text) and variation range of each OBU's size around its mean (light blue triangles). The latter is calculated as the interval between the first and third quartile of the ratio used in Figure 27B, for the whole sample. B) Ossification chain according to [START_REF] Hautier | Skeletal ossification and sequence heterochrony in xenarthran evolution[END_REF]. C) Distribution of embryonic origin of each bone according to [START_REF] Piekarski | Evolutionary innovation and conservation in the embryonic derivation of the vertebrate skull[END_REF]. Abbreviations: as-os-pt-bs, alisphenoid-orbitosphenoid-pterygoid-basisphenoid complex; bo-eo, basioccipital-exoccipital complex; fr, frontal; ju, jugal; lac, lacrimal; mx, maxillary; na, nasal; pa, parietal; pal, palatine; pe, petrosal; pmx, premaxillary; so, supraoccipital; sq, squamosal. Scale-bar = 1 cm.

We demonstrated that cranial units located in the anterior half of the skull vary more in size during postnatal development than those in the posterior half

(Figures 27B & 28A -see Segura &
Prevosti, 2012 for another example in Canidae). This result echoes the ontogenetic pattern of allometric variation of the entire skull where a clear separation could be made between the snout and braincase (Figure 23). In contrast to the mosaic distribution of allometric proportions, such a division of the skull into two parts (or modules) is more congruent with the skull ossification sequence and the embryonic origin of each bone (with the exclusion of the squamosal) (Figure 28).

Considering several ontogenetic stages contribute to a better understanding of the relative influences of the various developmental periods to the observed allometric patterns [START_REF] Klingenberg | Static, ontogenetic, and evolutionary allometry: a multivariate comparison in nine species of water striders[END_REF][START_REF] Mitteroecker | A brief review of shape, form, and allometry in geometric morphometrics, with applications to human facial morphology[END_REF]. Although preliminary, and pending confirmation for each morphotype, our results show that the allometric proportion of shape variation regularly decreases with age for the entire skull, as well as for most cranial units (Figure 27A), as could be expected for mammals (finite growth). However, the allometric proportions over time differ between cranial units as illustrated by OBUs having higher allometric proportions at the juvenile stage than at other stages (maxillary, frontal, bo-eo OBU and petrosal), and OBUs displaying higher or better supported allometric proportions in subadults and adults than in juveniles (palatine and parietal) (Figure 27A). We thus characterized a partition across developmental stages in each cranial unit, superimposed to the partition in the allometric proportion of shape variation among cranial bones. This heterogeneity of cranial allometry in time and space in nine-banded armadillos strongly suggests the existence of a complex modular architecture. Such modularity might facilitate the evolvability of the phenotype and be a prerequisite for heterochronic evolutionary changes, which are often local and mosaic [START_REF] Mitteroecker | Regional dissociated heterochrony in multivariate analysis[END_REF][START_REF] Gerber | Mosaic heterochrony and evolutionary modularity: the trilobite genus Zacanthopsis as a case study[END_REF].

Several authors [START_REF] Zumpano | Growth-related shape changes in the fetal craniofacial complex of humans (Homo sapiens) and pigtailed macaques (Macaca nemestrina): a 3D-CT comparative analysis[END_REF][START_REF] Goswami | Ontogenetic morphology and allometry of the cranium in the common European mole (Talpa europaea)[END_REF][START_REF] Sardi | Allometries throughout the late prenatal and early postnatal human craniofacial ontogeny[END_REF][START_REF] Wilson | Comparison of prenatal and postnatal ontogeny: cranial allometry in the African striped mouse (Rhabdomys pumilio)[END_REF] have shown that birth may constitute a clear-cut transition in the growth dynamics of several cranial units in rodents and primates, especially for the cranial roof. Since nine-banded armadillos are precocial [START_REF] Derrickson | Comparative reproductive strategies of altricial and precocial eutherian mammals[END_REF][START_REF] Krmpotic | Development of the integument of Dasypus hybridus and Chaetophractus vellerosus, and asynchronous events with respect to the postcranium[END_REF], much of the allometric variation patterns found in our postnatal sample may also be expressed prenatally [START_REF] Zelditch | The ontogenetic dynamics of shape disparity[END_REF]Wilson;2018), a hypothesis that could be tested on a sample including fetuses. These analyses of allometric patterns could also be performed in different armadillo species, at both the intraspecific and interspecific levels, to see how allometric patterns are comparable between species and whether they are maintained at an evolutionary scale (e.g., [START_REF] Gerber | Allometric space and allometric disparity: a developmental perspective in the macroevolutionary analysis of morphological disparity[END_REF][START_REF] Esquerré | Evolution of extreme ontogenetic allometric diversity and heterochrony in pythons, a clade of giant and dwarf snakes[END_REF][START_REF] Wilson | The evolution of ontogenetic allometric trajectories in mammalian domestication[END_REF].

Comparative study of cranial allometry in Cingulata

ABSTRACT

Allometry represents a pervasive pattern in morphological evolution. Recognition of a common allometric pattern across species requires comparative studies because analyses of sizerelated shape changes within a species are not sufficient to infer allometric patterns within other species or in an entire clade. Here, we used 3D geometric morphometric methods to study allometric patterns of the entire skull and cranial units at the ontogenetic and static levels in two phylogenetically distant armadillo species in the genera Cabassous and Zaedyus, which we compare to the armadillo Dasypus novemcinctus (Section 3.1) to identify common patterns of covariation. We then compare these intraspecific patterns to an evolutionary analysis of allometry, gathering most extant cingulate species and most of the emblematic fossil groups (with a focus on glyptodonts), using the same approach. Our results reveal a widespread craniofacial allometry, i.e., relative skull lengthening and reduction of braincase proportions as size increases, in all cingulates.

Our study also demonstrates that an increase in skull size in cingulates is generally accompanied by a relatively greater postorbital constriction, more protruding nuchal crests, broader temporal fossae, and a flatter cranial roof. The analyses conducted on cranial subunits show that widespread allometric patterns are also found more locally, such as for the relative position of the hypoglossal foramen, the proportions of the foramen magnum, and the protrusion of the posterior root of the zygomatic arch and of the mastoid process. This analysis also highlights an effect of size on shape variation for internal cranial structures, with a shallower fossa subarcuata and a thickening of the frontal bone resulting from size increases. These results evidence strong and widespread allometric patterns affecting cranial shape variation in cingulates, and represent a solid basis for the establishment of a mapping of strong covariation patterns to be discussed with respect to morphological characters employed in phylogenetic analysis.

Le Verger K, Hautier L, Bardin J, Gerber S, Delsuc F, Amson E, Gonzalez Ruiz L, Billet G. Article In Preparation.

INTRODUCTION

Variation in size constitutes a major determinant for variation in many biological traits.

Studies have shown that the size-related changes of traits, called allometry, indeed represent a pervasive pattern in morphological evolution [START_REF] Gould | Allometry and size in ontogeny and phylogeny[END_REF][START_REF] Hallgrímsson | Integration and the Developmental Genetics of Allometry[END_REF]. However, the variation of this pattern, within and among species, remains poorly known for many taxa.

Recognition of a common allometric pattern among species requires the production of comparative studies. Allometric variation may indeed differ between closely related species (e.g., [START_REF] Frost | Cranial allometry, phylogeography, and systematics of large-bodied papionins (primates: Cercopithecinae) inferred from geometric morphometric analysis of landmark data. The Anatomical Record Part A: Discoveries in Molecular[END_REF], and thus analyses of size-related shape changes within one species are not sufficient to infer allometric patterns within other species or within an entire clade. Allometry constitutes a complex and highly polygenic phenomenon [START_REF] Zelditch | The ontogenetic dynamics of shape disparity[END_REF][START_REF] Klingenberg | Evolution and development of shape: integrating quantitative approaches[END_REF][START_REF] Pélabon | Evolution of morphological allometry[END_REF][START_REF] Hallgrímsson | Integration and the Developmental Genetics of Allometry[END_REF]. Various factors (e.g., ecology) may influence size variation and thus indirectly impact morphological variation through allometric processes in several species (e.g., Esquérré et al., 2017). In turn, size variation may be a driving force behind an evolutionary trend or a constraint in morphological variation (Gould,1989;[START_REF] Sidlauskas | Continuous and arrested morphological diversification in sister clades of characiform fishes: a phylomorphospace approach[END_REF][START_REF] Klingenberg | Evolutionary covariation in geometric morphometric data: analyzing integration, modularity, and allometry in a phylogenetic context[END_REF][START_REF] Klingenberg | Size, shape, and form: concepts of allometry in geometric morphometrics[END_REF]. Allometric trajectories or patterns can therefore be biological traits under selection [START_REF] Adams | Ontogenetic convergence and evolution of foot morphology in European cave salamanders (Family: Plethodontidae)[END_REF][START_REF] Klingenberg | Evolution and development of shape: integrating quantitative approaches[END_REF][START_REF] Urošević | Patterns of cranial ontogeny in lacertid lizards: morphological and allometric disparity[END_REF][START_REF] Porto | Size variation, growth strategies, and the evolution of modularity in the mammalian skull[END_REF][START_REF] Giannini | Quantitative developmental data in a phylogenetic framework[END_REF]. Yet, the evolutionary mechanisms responsible for changes in allometric trajectories remain poorly understood. Allometry is expressed at various levels of the biological hierarchy and comparative studies can thus adopt complementary approaches to gain a global understanding of its variation within a group [START_REF] Klingenberg | Multivariate allometry[END_REF].

A first approach is to analyze allometric patterns and trajectories at the intraspecific level in several species and to compare them [START_REF] Strauss | Ontogenetic body form changes in three ecological morphotypes of anuran tadpoles[END_REF][START_REF] Zelditch | The ontogenetic dynamics of shape disparity[END_REF][START_REF] Adams | Ontogenetic convergence and evolution of foot morphology in European cave salamanders (Family: Plethodontidae)[END_REF]Frédérich & Sheets, 2010;[START_REF] Piras | The role of post-natal ontogeny in the evolution of phenotypic diversity in Podarcis lizards[END_REF][START_REF] Urošević | Patterns of cranial ontogeny in lacertid lizards: morphological and allometric disparity[END_REF]Esquérré et al., 2017;[START_REF] Wilson | The evolution of ontogenetic allometric trajectories in mammalian domestication[END_REF][START_REF] Ferreira-Cardoso | Skull shape variation in extant pangolins (Pholidota: Manidae): allometric patterns and systematic implications[END_REF][START_REF] Simons | Ontogenetic allometry and scaling in catarrhine crania[END_REF]. This comparison of intraspecific patterns allows a determination of whether the integration between size and shape is expressed in the same way in several taxa that are closely related. Looking at several intraspecific levels of variation (i.e., static or ontogenetic) also makes it possible to compare allometric patterns across various ontogenetic stages (see [START_REF] Pélabon | On the relationship between ontogenetic and static allometry[END_REF]. Many studies have used these approaches, providing evidence of both widespread intraspecific allometric patterns shared among several species (e.g., [START_REF] Shea | Allometry and heterochrony in the African apes[END_REF][START_REF] Shea | Bivariate and multivariate growth allometry: statistical and biological considerations[END_REF][START_REF] Ferreira-Cardoso | Skull shape variation in extant pangolins (Pholidota: Manidae): allometric patterns and systematic implications[END_REF] as well as diverging patterns among close relatives (e.g., [START_REF] Weston | Evolution of ontogeny in the hippopotamus skull: using allometry to dissect developmental change[END_REF]. Several authors have argued that allometric trajectories within species are biological traits under selection and can promote a greater diversity of shape [START_REF] Frankino | Natural selection and developmental constraints in the evolution of allometries[END_REF][START_REF] Adams | Ontogenetic convergence and evolution of foot morphology in European cave salamanders (Family: Plethodontidae)[END_REF][START_REF] Wilson | Diversity trends and their ontogenetic basis: an exploration of allometric disparity in rodents[END_REF][START_REF] Klingenberg | Evolution and development of shape: integrating quantitative approaches[END_REF][START_REF] Urošević | Patterns of cranial ontogeny in lacertid lizards: morphological and allometric disparity[END_REF][START_REF] Porto | Size variation, growth strategies, and the evolution of modularity in the mammalian skull[END_REF][START_REF] Giannini | Quantitative developmental data in a phylogenetic framework[END_REF]Esquérré et al., 2017). Further studies are needed perhaps confirm this claim, however.

A second and complementary approach consists of analyzing allometric patterns at the evolutionary level (among species) to test whether evolutionary changes in shape in a group could be related with variation in size (Klingenberg & Marugán-Lobón, 2013 and citation therein). This approach can highlight widespread evolutionary patterns, as is the case for the craniofacial evolutionary allometry (CREA) hypothesis in mammals, which postulates that larger mammals show a relatively longer snout combined with a relatively reduced braincase [START_REF] Cardini | Larger mammals have longer faces because of size-related constraints on skull form[END_REF][START_REF] Cardini | Why the long face? Kangaroos and wallabies follow the same 'rule' of cranial evolutionary allometry (CREA) as placentals[END_REF][START_REF] Tamagnini | Anyone with a long-face? Craniofacial Evolutionary Allometry (CREA) in a family of short-faced mammals, the Felidae[END_REF]Cardini, 2019a;[START_REF] Marcy | Australian rodents reveal conserved Cranial Evolutionary Allometry across 10 million years of murid evolution[END_REF]Section 3.1). There is much interest in comparing the patterns obtained by these two approaches (intraspecific and evolutionary), especially because it can provide information on the origin of the variation observed [START_REF] Klingenberg | Studying morphological integration and modularity at multiple levels: concepts and analysis[END_REF]. For example, a correspondence between the evolutionary level and the static level is most often interpreted as the result of neutral selection by drift [START_REF] Weaver | Were Neandertal and modern human cranial differences produced by natural selection or genetic drift?[END_REF][START_REF] Smith | The role of genetic drift in shaping modern human cranial evolution: a test using microevolutionary modeling[END_REF], whereas correspondences between the ontogenetic level and the evolutionary level may also imply differential timing of growth (Cheverud, 1982b;[START_REF] Gonzalez | Ontogenetic allometry and cranial shape diversification among human populations from South America[END_REF]. In addition, the combination of both approaches is useful, because studies looking for correlations at the evolutionary level alone can be fooled by singular evolutionary events [START_REF] Uyeda | Rethinking phylogenetic comparative methods[END_REF], and intraspecific studies alone do not inform about among-species patterns. By relating the allometric patterns at both levels, it is possible to show whether size-related shape changes observable during the ontogeny of species are the same as those detected in the morphological evolution of the group. This is important since a similarity between these two levels of variation can lend further weight to a newly detected evolutionary allometry (such as for CREA;

Cardini & Polly, 2013), especially in the case of unreplicated evolutionary events.

Cingulates represent a clade of extant placental mammals in which allometry remains poorly studied. Regarding the skull, a few studies have provided brief accounts on the evolutionary allometry within a clade such as [START_REF] Hautier | Beyond the carapace: skull shape variation and morphological systematics of long-nosed armadillos (genus Dasypus)[END_REF] and [START_REF] Feijó | Taxonomic revision of the long-nosed armadillos, Genus Dasypus Linnaeus, 1758 (Mammalia, Cingulata)[END_REF] for dasypodines and [START_REF] Abba | Systematics of hairy armadillos and the taxonomic status of the Andean hairy armadillo (Chaetophractus nationi)[END_REF] for euphractines. Our detailed study of ontogenetic and static allometry for the entire skull as well as cranial subunits in the nine-banded armadillo has provided the first in-depth investigation of cranial allometric patterns within a cingulate species (Section 3.1). To date, there has been neither a detailed analysis of cranial allometric patterns in other cingulate species, nor an analysis of cranial evolutionary allometry among cingulates that would encompass extant and fossil forms, including the giant-sized glyptodonts.

In this work, following on our previous study (Section 3.1), we first tested the hypothesis that the allometric patterns detected in Dasypus novemcinctus are similarly present in two other series of phylogenetically distant armadillo species, Zaedyus pychiy and Cabassous unicinctus/centralis. Second, we tested the existence of the same allometric pattern at the evolutionary level in a dataset incorporating almost all the extant species and a rich diversity of fossil specimens, including the large-sized glyptodonts and pampatheres. To test these hypotheses, we used 3D geometric morphometrics methods to test for allometric patterns of the whole skull (global) and of cranial subunits (local) both within and among species. The comparison of the allometric patterns obtained at various levels enabled us to highlight size-related shape changes that to be seem present both within and among cingulates species, and which represent common trends of morphological variation induced by variation in size in the group.

MATERIAL & METHODS

Intraspecific Sampling

We sampled 43 skulls of Zaedyus pichiy (Table S11), a species belonging to the Euphractinae (see Section 1.1), and 27 skulls belonging to either Cabassous unicinctus or Cabassous centralis (Table S11), two species belonging to the Tolypeutinae (see Section 1.1).

There is considerable doubt about the distinction between these two species of Cabassous which are not weakly divergent morphologically and only weakly differentiated based on molecular evidence [START_REF] Wetzel | Revision of the naked-tailed armadillos genus Cabassous McMurtrie[END_REF][START_REF] Wetzel | Taxonomy and distribution of armadillos, Dasypodidae[END_REF]Hayssen, 2014;[START_REF] Gibb | Shotgun mitogenomics provides a reference phylogenetic framework and timescale for living xenarthrans[END_REF]Supporting Information 1). The only way to differentiate them is by their geographic origin, as C. centralis has a geographic range in Central America and northwesternmost South America [START_REF] Hayssen | Cabassous centralis (Cingulata: Dasypodidae)[END_REF] whereas C. unicinctus occupies much of the remainder of northern South America east of the mountains (Hayssen, 2014a). Unfortunately, the geographic origin of each specimen was not always known. Our investigation of the shape variation in our sample of these two species revealed no clear differences based on cranial shape, and for this reason, we used both species in the same data set (for more details refer to Supporting Information 1). However, our investigation highlighted an unexpected divergence in cranial shape between Cabassous unicinctus specimens from northern the Amazon basin and Cabassous unicinctus specimens from the southern Amazon (Supporting Information 1). Consequently, we divided the Cabassous data into two sets. The first one is the largest and, containing 27 specimens including both northern and southern specimens.

We refer to this dataset as CabassousNS. The second dataset corresponds only to the northern specimens, and contains 21 specimens. We refer to this dataset as CabassousN (results for this dataset will be illustrated in supplementary data only). The material studied is stored in several museum collections, as indicated in Table S11.

Interspecific Sampling

Our sampling for the evolutionary analysis of allometry includes 27 specimens of which 6 belong to extinct species and 21 correspond to extant species (Table S12). The sample covers all extant armadillo genera and almost all species (17/21 - [START_REF] Gibb | Shotgun mitogenomics provides a reference phylogenetic framework and timescale for living xenarthrans[END_REF]. Morphotypes representing possibly distinct specific entities for species complexes are also included in the dataset for Dasypus novemcinctus (Section 3.1) and Cabassous unicinctus (Supporting Information 1). Our evolutionary sample covers a large diversity of cranial shapes in cingulates including the Santacrucian glyptodont "Metopotoxus" anceps, the Pleistocene glyptodont Glyptodon sp., the early diverging armadillo Peltephilus pumilus [START_REF] Shockey | New Early Diverging Cingulate (Xenarthra: Peltephilidae) from the Late Oligocene of Bolivia and Considerations Regarding the Origin of Crown Xenarthra[END_REF], as well as the pampathere Vassallia maxima, and the dasypodine Stegotherium tauberi. We built three datasets that represent different combinations within this total sample. The first dataset consists of all specimens with the exclusion of Proeutatus lagena, which is less well-preserved than the other specimens. This dataset maximizes the number of landmarks (nlandmark = 100) over that of species (nspecimen = 26) and is thus called Datatset-Lmax. The second dataset includes only the extant species, which are less disparate concerning their cranial shapes (nlandmark = 114; nspecimen = 21). It is thus called DatasetExt. The third dataset includes all specimens, including Proeutatus lagena, which several authors suspect to be closely related to glyptodonts and pampatheres [START_REF] Engelmann | The evolution and ecology of armadillos, sloths and vermilinguas[END_REF][START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF][START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF][START_REF] Gaudin | Cranial osteology of the pampathere Holmesina floridanus (Xenarthra: Cingulata; Blancan NALMA), including a description of an isolated petrosal bone[END_REF]. This dataset maximizes the number of taxa (nspecimen = 27) over that of landmarks (nlandmark = 90) and is called Dataset-Tmax. The results for this dataset will be illustrated in supplementary data only. The material examined in this portion of the study is stored in several museum collections, as indicated in Table S12.

Correction of taphonomic deformations

Three fossil specimens presented obvious cranial deformations that limited our landmark acquisition, and which could not be directly compensated for by missing data estimates (e.g., symmetrization requires minimally the presence of a landmark on both sides of an object). Using the software Cinema 4D (Maxon, release 23), we arbitrarily retrodeformed the cranial meshes of "Metopotoxus" anceps (YPM-VPPU 15612), Proeutatus lagena (YPM-VPPU 15613) and

Stegotherium tauberi (YPM-VPPU 15565) to reduce the deformation due to taphonomic effect. In order to keep these arbitrary corrections to a minimum, we only applied deformations when they concerned areas directly on the midline axis of the skull or when at least one of the two sides (right or left) was in place and undeformed. In the glyptodont "Metopotoxus" anceps, we corrected a slight uniform right lateral tilt of 9.33%, and we moved the left part of the skull back in line with the right part that remained in place. In Proeutatus lagena, we realigned the midline to the anterior part of the frontal bone where it was offset to the right. Then we reoriented the rostrum, which was tilted slightly to the right, to match the midline. Finally, we realigned the left posterior edge of the skull, which was slightly offset from the right part. In Stegotherium tauberi, a break separated the front part of the rostrum from the rest of the face on our specimen. A very slight shift of 0.022 cm to the right was applied to correct for this break, in accordance with the midline of the part of the face that remained in place. These few retrodeformations are all illustrated with the specimens before and after deformation in Figures S21, S22 & S23. Although not ideal, the shape variation that could be induced by the arbitrary component of these (slight) corrections have been shown to be negligible in comparison to interspecific variation of cranial shape in other groups (Gomes [START_REF] Rodrigues | Differential influences of allometry, phylogeny and environment on the rostral shape diversity of extinct South American notoungulates[END_REF]. Here, it concerned few taxa, the variations due to these deformations were relatively minor, and the high diversity of cranial shape in our interspecific sample largely exceeded these variations.

Geometric Morphometrics

Specimens for both the intraspecific and interspecific samples were scanned on X-ray microtomography imagery platforms at the American Museum of Natural History (New York, USA); the Muséum national d'Histoire naturelle (France) in Paris (AST-RX platform), the University of Montpellier (France) and the Museum für Naturkunde (ZMB) in Berlin (Germany).

Three-dimensional reconstruction and visualization of the skulls and of the virtually isolated bones were performed using stacks of digital images with MIMICS v. 21.0 software (3D Medical Image Processing Software, Materialize, Leuven, Belgium). Image stacks were improved in contrast, rotated, cropped, and reduced to 8 bits using the ImageJ software [START_REF] Schneider | NIH Image to ImageJ: 25 years of image analysis[END_REF]. Cranial shapes were quantified with a maximum of 114 anatomical landmarks (see Figure S24 for an illustration of the landmarks employed for each dataset, Table S13 for the landmark definitions, with two modifications to adapt the definitions to the interspecific datasets (#28-#29; #39-#40),

and Table S14 for landmark coordinates for all specimens) placed on the exported 3D models using AVIZO v. 9.7.0 software (Visualization Sciences Group, Burlington, MA, USA).

For the intraspecific sample, 17 landmarks were removed from the original dataset used for Dasypus novemcinctus (Section 3.1), because they could not be placed on the skulls of Zaedyus pichiy, CabassousNS and CabassousN (homologous structures were absent or not observable;

Tables S15 &S16). The remaining 114 landmarks were initially defined for the analyses concerning the Dasypus novemcinctus complex (Section 3.1; Table S13). The reduction of the landmark set was neither problematic for the analyses of the whole skull and nor for those of cranial bone subunits. None of the previously defined Operational Bone Units in the skull (OBU; see Section 3.1) included less than 4 landmarks after the reduction of the landmark dataset, thus keeping all OBUs available for analysis as explained in Section 3.1.

For the interspecific sample, only DatasetExt retained all 114 landmarks. Dataset-Lmax was composed of 100 landmarks, and Dataset-Tmax included 90 landmarks (Figure S24). For the Bone-By-Bone analyses (3B; see Section 3.1), the reduction in the number of landmarks was at times problematic, since it forced us to discard several bone units with too few landmarks (n < 4 or 5; see below). The composition of the landmark sample for each dataset and their attribution to each OBU is shown in Tables S15 &S16. Most of the missing landmarks for the Dataset-Lmax and Dataset-Tmax concerned points in the anterior part of the skull. The jugal and palatine, which had only 3 landmarks remaining in these datasets, could not be analyzed. This is also the case for the premaxillary and nasal, which each retained 4 landmarks but with some extreme points missing, precluding a comparison with other analyses (e.g., the most anterodorsal point of the internasal suture #1-Table S16). Following the methodology explained in Section 3.1, we performed a generalized Procrustes analysis [START_REF] Rohlf | Extensions of the Procrustes method for the optimal superimposition of landmarks[END_REF]) using the function gpagen in the R package geomorph version 3.1.0 [START_REF] Adams | Geomorph: Software for geometric morphometric analyses[END_REF]. Intra-individual asymmetries [START_REF] Klingenberg | Shape analysis of symmetric structures: quantifying variation among individuals and asymmetry[END_REF] were removed using the function symmetrize in the R package Morpho version 2.6 [START_REF] Schlager | Morpho and Rvcg -Shape Analysis in R: R-Packages for Geometric Morphometrics, Shape Analysis and Surface Manipulations[END_REF]. When some landmarks were missing on one side of the skull, their position was estimated using the function fixLMmirror in the Morpho R package (this represented 0.04% of the intraspecific datasets -Table S17, and 0.07% of the interspecific datasets -Table S18). Missing landmarks on the skull midline or landmarks missing on both sides were estimated in intraspecific datasets with the function estimate.missing in the R package geomorph version 3.3.1 [START_REF] Adams | Geomorph: Software for geometric morphometric analyses[END_REF] (represented 0.01% -Table S17). In the interspecific datasets, the missing midline landmarks could not be estimated because the shape of the skull is too different among specimens at the evolutionary level. These landmarks therefore had to be removed, which led to the construction of the three different datasets. The logarithm of the centroid size of the skull was used as a size variable in all analyses.

Determination of ontogenetic stages

For each intraspecific dataset within Cabassous and Zaedyus, we subdivided the sample into different age classes (ontogenetic stages) that enabled us to study allometric patterns at the ontogenetic and static levels (see Section 3.1). For Dasypus novemcinctus, we recognized three ontogenetic stagesjuvenile, subadult, and adultbased on the dental eruption stage, the level of ossification of the skull and its total length (Section 3.1). For Zaedyus and Cabassous, the datasets are too small to allow analyses at each ontogenetic stage as in Dasypus novemcinctus, but we still mention these stages in our results as useful information. Because members of the genus specimen can be found in Table S19 (see Supporting information 1 for more detail).

Phylogenetically-informed analyses

At the evolutionary level, it is necessary to consider the phylogenetic structure of the data [START_REF] Klingenberg | Evolutionary covariation in geometric morphometric data: analyzing integration, modularity, and allometry in a phylogenetic context[END_REF] because phylogeny can be a confounding variable altering the independence of the data [START_REF] Pagel | Detecting correlated evolution on phylogenies: a general method for the comparative analysis of discrete characters[END_REF]. It is therefore necessary to integrate a dated tree into our analyses to control for phylogenetic constraints. For extant species, several molecular works have already produced dated trees, and even included a Pleistocene glyptodont [START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF][START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF]. However, these did not include any other fossil taxa. We have therefore used the more complete consensus tree and branch lengths obtained in Chapter 2 (see Figure S4)

for our analyses here. Species that were not coded for Chapter 2 were duplicated with the same branch lengths as other representatives of their genus that were already present in the matrix (e.g., Dasypus). Since the three datasets had a different taxonomic composition, we adapted each baseline tree by removing taxa to be discarded while keeping the branch lengths (Figure S25) with the drop.tip function of the R ape package [START_REF] Paradis | ape 5.0: an environment for modern phylogenetics and evolutionary analyses in R[END_REF].

Allometric analyses

To quantify the covariance between cranial shape and size, we used the same approach as for the ontogenetic and static level (Section 3.1 and above). The entire skull (ES) Procrustes alignment was realized on the entire set of cranial landmarks, including both sides of the skull.

Under the Bone-By-Bone (3B) approach (see Section 3.1), the analyzed objects corresponded to the same virtually isolated bone or group of bones that we defined in the study of D. novemcinctus as Operational Bone Units (OBUs). We used the same specimens for the 3B analyses as for the ES approach. Each 3B Procrustes alignment was realized on a reduced set of landmarks corresponding to the OBU under consideration, with a slight difference in the number of landmarks compared to Section 3.1 (see Tables S15 &S16). We performed the 3B analyses only on the left side of the cranium, which was more complete in most cases. The allometric component in the shape variation of OBUs and of the entire skull was analyzed using the skull centroid size as a measure of size [START_REF] Monteiro | Multivariate regression models and geometric morphometrics: the search for causal factors in the analysis of shape[END_REF]. For intraspecific datasets, for both the ES and 3B analyses of allometry, we performed a multivariate regression of Procrustes shape coordinates [START_REF] Izenman | Multivariate regression[END_REF] on the log centroid size using the function procD.lm of the R package geomorph. For the evolutionary level, we performed a phylogenetic regression (Phylogenetic Generalized Least Squares using our baseline trees -PGLS - [START_REF] Rohlf | Comparative methods for the analysis of continuous variables: geometric interpretations[END_REF][START_REF] Klingenberg | Evolutionary covariation in geometric morphometric data: analyzing integration, modularity, and allometry in a phylogenetic context[END_REF]Adams & Collyer, 2018) for Procrustes shape variables on the log centroid size using the function procD.pgls of the R package geomorph. We also produced the same analysis without considering the phylogeny, to evaluate its effect on the regressions obtained, using the same function as for the intraspecific datasets. The same statistical approach (i.e., Procrustes ANOVA for Procrustes shape variables with permutation procedure) as the method used for Dasypus novemcinctus (Section 3.1) was used for the analysis of intraspecific datasets and evolutionary datasets. For the intraspecific datasets and for the DatasetExt, the variations were represented from the minimum to the maximum shape by vectors on deformed meshes. For the Dataset-Lmax and the Dataset-Tmax, the variations from the minimum to the maximum shape was too extreme to allow the use of mesh deformations. They were instead represented by wireframes representing the minimum and maximum shapes.

RESULTS

Allometric variations in the intraspecific samples

Allometric variations on the entire skull (ES) in Zaedyus pichiy

Ontogenetic allometry

The regression of shape on log centroid size in our ontogenetic series of Z. pichiy accounts for 7.732% of the total shape variation (p-value < 0.0002, Figure 29A; Table 7). The major cranial 125 allometric variations mainly concern a relative flattening of the cranial roof, and a slight reduction of the braincase proportions from juvenile to adult specimens. This trend is mainly shown by a relatively more ventral position of the frontal in contact with the parietal as size increases, a more medial position of the landmarks of the alisphenoid (#41-42; #45-46) and a stronger postorbital constriction (#39-40). In addition, the intersection between the most dorsal point of the annular ridge and the midline (#97), as well as the dorsal intersection between the cribriform plate and the median septum posterior to the latter (#98) show a relatively more ventral (and posterior) position, like landmarks on the frontal (#66), in larger specimens. Conversely, the contact between the parietal and the supraoccipital (#67) takes a more posterior position as the size increases, giving

the entire skull a more elongated and flattened aspect. This allometric variation is accompanied by relatively more salient nuchal crest processes posteriorly (#73-74). More anteriorly, a strong allometric variation is detected for several midline landmarks such as the contact between the maxillary and palatine (#17), between the nasal and frontal (#2) and between the premaxillary and maxillary (#5). These all move relatively forward in larger specimens. We note that the whole snout follows the same trend, but to a lesser degree, except for the triple premaxillary -nasalmaxillary contact (#3-4). This suggests a snout elongation that appears to be very unequally expressed among the landmarks in this region. Among the minor allometric variations, we can note a relatively more anterior position of the mastoid process (#89-90), a narrowing of the face at the triple contact among lacrimal-maxillary-frontal (#33-34) and a slight lateral widening of the zygomatic arches (#20-21; #49-54) when size increases.

Static allometry

The regression of shape on log centroid size in our adult specimens of Z. pichiy accounts for 9.369% of the total shape variation (p-value < 0.0066, Figure 29B; Table 7). In this species, the allometric proportion of shape variation is higher at the static level than at the ontogenetic level. However, the allometric variations are more or less the same. We can note as a difference a relative reduction of the allometric variation with respect to landmarks on the alisphenoid (#41-42; #45-46), postorbital constriction (#39-40) and zygomatic arch (#20-21; #49-54). A directional shift also affects the processes of the nuchal crests (#73-74) which are shifted posteromedially relative to other landmarks as size increases. The dorsal intersection of the annular ridge and midline (#97) no longer follows the relatively more ventral position of the frontal (#66), when size increases, but rather takes a more posterior position from the smallest to the largest specimen.

Among the other differences with the ontogenetic analysis, we also note that the most posterodorsal point of the zygomatic ridge of the squamosal (#55-56) is located relatively more anteroventrally as size increases. Overall, most of the allometric variations impacting the snout at the ontogenetic level are present at the static level.

The distribution of Zaedyus pichiy specimens in the morphospace of the regression of shape on size reveals a clear gap between the smallest and largest specimens, a pattern that is somewhat hidden by the presence of subadult specimens at the ontogenetic level (Figure 29).

Ontogenetic allometry

The regression of shape on log centroid size in our ontogenetic series of CabassousNS accounts for 6.597% of the total shape variation (p-value = 0.0471, Figure 30; Table 8) whereas it is higher for CabassousN (8.798%, p-value = 0.0131, Figure S16; Table S20). The major allometric variations concern most of the regions discussed in Zaedyus pichiy, especially at the ontogenetic level. The cranial roof is similarly impacted with a more ventral position of the frontal midline landmarks and the dorsal edge of the cribriform plate (#66, #97, #98) as size increases.

The processes of the nuchal crests extend farther posteriorly (#73-74) and the contact between the parietal and supraoccipital is in a relatively more posterior position (#67) in larger specimens. The postorbital constriction is also much more marked (#39-40) in larger specimens, but the zygomatic arches do not widen, in contrast to Zaedyus (#20-21; #49-54).

Figure 29. Ontogenetic and static allometry on the entire skull (ES) of Zaedyus pichiy. Ontogenetic stages are represented with different colors (juvenile = green; subadult = yellow; adult = red; see text for more detail). For graphical display, we used the projected regression scores of the shape data to represent shape variation related to changes in log skull centroid size [START_REF] Adams | A field comes of age: geometric morphometrics in the 21st century[END_REF]. Shape changes were visualized as vectors from the minimal shape (green) to the maximal shape (red) of the shape regression scores corresponding to the projection of the data points in shape space on to an axis in the direction of the regression vector (see [START_REF] Drake | The pace of morphological change: historical transformation of skull shape in St Bernard dogs[END_REF]. A.

Multivariate regression of skull shape on log skull centroid size at the ontogenetic level, representing 7.73% of the total shape variation. B. Same analysis, at the static level (9.37% of total shape variation) (see text).

A slight reduction of the neurocranium is indicated by the more medial position of the contact between the alisphenoid, the squamosal and the frontal (#41-42) but also with the contact between the squamosal, the parietal and the frontal (#68-69). Finally, the vectors of most snout landmarks (#1; #3-16) indicate a slight elongation of this region directed anteriorly, as size increases. In addition, some allometric variations are new compared to Zaedyus pichiy. As size increases, the tentorial process elongates more ventrally (#63). The parietal, squamosal and supraoccipital contact also shifts dorsomedially (#70-71), and the contact between the frontal and nasal (#2; #31-32) on the snout moves posteriorly, unlike most landmarks of the front of the snout that shift anteriorly. The contact between the maxillary and palatine on the midline (#17) also migrates posteriorly in larger specimens, contrary to Zaedyus pichiy. The optic foramen is located relatively more anterolateral (#64-65), and the infraorbital foramen more posteroventrally (#24-25) in larger specimens. There is no difference in the allometric patterns detected between both Cabassous datasets, except for the higher vector norm in CabassousNS.

Static allometry

We detect no significant correlation between skull shape and size at the static level for Cabassous datasets (CabassousNS, p-value = 0.2197; CabassousN, p-value = 0.0859). However, caution is required when interpreting this result because the number of individuals is relatively small in the static datasets. The different composition of the two datasets (Supporting Information 1) also seem to play a role in the difference in p-value between CabassousNS and CabassousS. For graphical display, we used the projected regression scores of the shape data to represent shape variation related to changes in log skull centroid size [START_REF] Adams | A field comes of age: geometric morphometrics in the 21st century[END_REF]. Shape changes were visualized as vectors from the minimal shape (green) to the maximal shape (red) of the shape regression scores corresponding to the projection of the data points in shape space on to an axis in the direction of the regression vector (see [START_REF] Drake | The pace of morphological change: historical transformation of skull shape in St Bernard dogs[END_REF]. Multivariate regression of skull shape on log skull centroid size at the ontogenetic level represented 6.60% of the total shape variation. 130 3.2.3.1.3. Allometric variations studied Bone By Bone (3B) in Zaedyus and Cabassous

Comparison between OBUs

In Zaedyus pichiy, we observe differences in the proportions of allometric shape variation among different OBUs both at the ontogenetic and static levels. At both levels (Figure 31), the regression of shape on size shows no statistical significance for the supraoccipital (Figure 31;

Table 7). This is not the case for other OBUs, for which at least the analyses at the ontogenetic level show a significant allometric effect.

At the ontogenetic level, the lacrimal has the lowest proportion of shape variation explained by size of all OBUs (supraoccipital excluded; Figure 31A; Table 7). The proportion of shape variation explained by size ranges between 5% and 10% for the as-os-pt-bs, petrosal, nasal, maxillary, jugal, squamosal and bo-eo OBUs (Figure 31A; Table 7). The frontal shows a slightly higher allometric proportion, at 12% (Figure 31A; Table 7). The premaxillary and parietal have an even higher allometric proportion, ranging between 15% and 20% (Figure 31A; Table 7). The OBU showing the highest proportion of variation explained by size at the ontogenetic level is the palatine, at more than 22% (Figure 31A; Table 7). At the static level, 4 OBUs in addition to the supraoccipital no longer show a significant allometric component in their shape variation (Figure 31B; Table 7)jugal, as-os-pt-bs OBU, parietal and palatine. The absence of allometric variation at the static level for the palatine and parietal is in stark contrast to the strong allometric component of their shape variation at the ontogenetic level (Figure 31). In increasing order, the squamosal, maxillary, lacrimal, petrosal and bo-eo OBU show a proportion of the variation in shape explained by size ranging between 10% and 15% (Figure 31B; Table 7). The allometric proportion of the premaxillary is comparable to that obtained at the ontogenetic level, whereas the frontal and nasal show a much higher allometric proportion, exceeding 20% (Figure 31B; Table 7).

Figure 31. Bar graphs showing the allometric proportions (R²) of each cranial unit's (OBU) total shape variation under the 3B approach (see text), at the ontogenetic (A) and static (B) levels in Zaedyus pichiy. Allometric proportions are shown with the log of skull centroid size taken as a size variable. On the virtually dislocated skull (in right lateral view), the allometric proportions are reported in corresponding colors. White bars indicate a statistically unsupported (NS) allometry for a given OBU (with a p-value > 0.05). Abbreviations of OBUs: as-os-pt-bs, alisphenoidorbitosphenoid-pterygoid-basisphenoid complex; bo-eo, basioccipital-exoccipital complex; fr, frontal; ju, jugal; lac, lacrimal; mx, maxillary; na, nasal; pa, parietal; pal, palatine; pe, petrosal; pmx, premaxillary; so, supraoccipital; sq, squamosal.

In CabassousNS, we also observe differences in the proportions of allometric shape variation between different OBUs both at the ontogenetic and static levels. At both levels (Figure 32), the regression of shape on size shows no statistical support for the lacrimal, premaxillary, boeo, nasal, supraoccipital, maxillary, parietal and palatine OBUs (Figure 32; Table 8). CabassousN differs at this point from the larger data set for the parietal which is statistically supported at the ontogenetic level (= 11.705%; Figure S27; Table S20). In CabassousNS, the frontal, squamosal and petrosal have a proportion of shape variation explained by size ranging between 5% and 10% at the ontogenetic level (Figure 32A; Table 8). The allometric proportion of the jugal is slightly higher, reaching 11.74% (Figure 32A; Table 8). The highest proportion of shape variation explained by size corresponds to the as-os-pt-bs OBU, at 19% (Figure 32A; Table 8). At the static level, only the petrosal and as-os-pt-bs OBU show a significant allometric component of their shape variation with proportions above the ontogenetic level (respectively 15.20% and 25.22%, Figure 32; Table 8). CabassousN differs at this point from the larger dataset as the jugal and nasal are also statistically supported at the 18.43% and 26.44% level, respectively (Figure S27; Table S20).

Figure 32. Bar graphs showing the allometric proportions (R²) of each cranial unit's (OBU) total shape variation under the 3B approach (see text), at the ontogenetic (A) and static (B) levels in CabassousNS. Allometric proportions are shown with the log of skull centroid size taken as size variable. On the virtually dislocated skull (in right lateral view), the allometric proportions are reported in corresponding colors. White bars indicate a statistically unsupported (NS) allometry for a given OBU (with a p-value > 0.05). Abbreviations of OBUs: as-os-pt-bs, alisphenoid-orbitosphenoidpterygoid-basisphenoid complex; bo-eo, basioccipital-exoccipital complex; fr, frontal; ju, jugal; lac, lacrimal; mx, maxillary; na, nasal; pa, parietal; pal, palatine; pe, petrosal; pmx, premaxillary; so, supraoccipital; sq, squamosal.

Allometric variation within OBUs

All descriptions of the allometric shape changes below describe the maximal shapes as compared to the minimal shapes in individual OBUs, but only those OBUs whose allometric variations were statistically significant (p-value < 0.05). Only landmarks on the left side of the skull are discussed. The results and shape changes explained by size for CabassousN at the ontogenetic level are not described below (except when different from CabassousNS), but are illustrated in supplementary data. This is also the case for the static level (see below).

Alisphenoid-Orbitosphenoid-Pterygoid-Basisphenoid complex

In Zaedyus pichiy (Figure 33), when size increases, the anterolateral edge of the alisphenoid in contact with the frontal and squamosal extends relatively more anterolaterally (#42) while the foramen ovale is more posteromedial (#60). The region bearing the sphenorbital fissure and the optic foramen is located slightly more anteromedial (#46; #65). The internal opening of the optic canal (#112) assumes a more anterolateral position as size increases, produces a reduction in the relative length of the canal. The most ventromedial point on the annular ridge lateral to posterior median septum (#114) shows the greatest allometric variation, with a more posterolateral position as size increases. At the static level, the allometric variation of this OBU is not statistically significant but the p-value is close to the significance threshold (Table 7).

Basioccipital-Exoccipital complex

In Zaedyus pichiy, at the ontogenetic and static levels (Figures 33 & 36), the allometric variation of this OBU is relatively weak. When size increases, the major variations are concentrated on the occipital condyles, with a slightly more anteromedial position of the intersection between the anteromedial edge of the occipital condyle and foramen magnum (#76)

and of the most anterolateral point of the occipital condyle (#84). The most anteroventral point of the foramen magnum is also located slightly more posterior as size increases, which, together with the variation of landmarks #75-76, makes the foramen magnum relatively smaller. In addition, the hypoglossal foramen (#82) takes a relatively more posterolateral position as size increases. The rest of the points hardly vary at all. An allometric variation for this OBU is not supported statistically for the Cabassous datasets (Tables 8 &S20).

Frontal

In Zaedyus pichiy, at the ontogenetic level and at the static level (Figures 33 & 36), when size increases, the major allometric variations mainly concern regions of the frontal close to the midline. The anterior extremity in contact with the nasal (#2; #32) shows an anteriorly directed elongation, whereas the intersection between the frontoparietal suture and the midline (#66) and the dorsal intersection of annular ridge and midline (#97) become closer to one another. These In Cabassous datasets, at the ontogenetic level (Figures 34 &S28), the directions of the allometric variations for several points differ from the observations made in Zaedyus except for the two most posterior landmarks on the midline (#66; #97), which also suggest a slight posterior narrowing of the frontal bone as size increases. As size increases, there is no elongation of the anterior extremity of the frontal (#2; #32). The anterior edge in contact with the lacrimal is situated more anterolaterally (#34; #36). The postorbital constriction is also more pronounced in larger specimens, as in Zaedyus, but it is only slightly shifted posteriorly (#40). Finally, the slight posterior narrowing of the frontal is not due to a more medial position of the posterolateral edges of the OBU (#42; #69). Instead, there is a relative lengthening in the posterolateral border of the frontal from the smallest to the largest specimens. An allometric variation for this OBU is not supported at the static level for the Cabassous datasets (Tables 8 &S20).

Lacrimal

In Zaedyus pichiy, at the ontogenetic level (Figure 33), the variation in shape due to size seem to concern most landmarks on the lacrimal to a similar extent. The anteroventral margin of the lacrimal foramen (#38) and the triple contact point of the lacrimal -maxillary -frontal (#34) are both located relatively more posterior as size increases. Conversely, the triple contact point of the maxillary -jugal -lacrimal (#48) takes a more anterior position and the intersection between the lacrimal/frontal suture and the anterior orbital edge (#36) extends anterodorsally. The position of the intersection between the anterior orbital edge and jugal/lacrimal suture (#50) seems relatively unimpacted by the increase in size. Overall, these changes suggest that the lacrimal bone becomes relatively shorter in its lateroventral part in larger specimens, and that the distance between the lacrimal foramen and the posterodorsal edge of the bone on the orbital rim increases.

At the static level (Figure 36), the increase in size is no longer accompanied by a strong change in the position of the triple contact point between maxillarylacrimalfrontal (#34). Otherwise, allometric variations at this level differ only for the intersection between the anterior orbital edge and the jugal/lacrimal suture (#50), which takes a relatively more posterior position, and for the intersection between the lacrimal/frontal suture and the anterior orbital edge (#36), which extends more anteriorly as size increases. An allometric variation for this OBU is not significantly supported for the Cabassous datasets (Tables 8 &S20).

Figure 33. Vector representation of the allometric shape changes detected for a given cranial unit (OBU) in Zaedyus, represented between its minimal (greensmaller centroid size) and maximal (redlarger centroid size) shape (see Figure 29). Results of the analysis performed at the ontogenetic level, and with the log skull centroid size taken as the size variable (see text). For each OBU, the changes are shown in three subsections organized horizontally: 1, vectors from minimal to maximal shape with minimal OBU shape; 2, same as 1) with maximal OBU shape; 3, minimal OBU shape in transparency with vectors. A) alisphenoid-orbitosphenoid-pterygoid-basisphenoid complex; A1-A2, lateral view; A3, dorsal view. B) basioccipital-exoccipital complex; B1-B2, dorsal view; B3, ventral view. C) frontal; C1-C2, lateral view; C3, ventral view. D) lacrimal; D1-D2, lateral view; D3, medial view. E) jugal; E1-E2, lateral view; E3, medial view. F) maxillary; F1-F2, lateral view; F3, medial view. G) nasal; G1-2, dorsal view; G3, ventral view. Landmark numbers and orientation arrows were added for more readability, as well as to produce an overall representation of the unpaired basioccipital. Abbreviations: A, anterior; D, dorsal; L, lateral; V, ventral.

Jugal

In Zaedyus pichiy, at the ontogenetic level (Figure 33), the major allometric variations of the jugal concern its posterior edges in contact with the squamosal (#52; #54) and an anterior landmark corresponding to its intersection with the orbital edge and lacrimal. When size increases, the dorsal (#52) and ventral (#54) contact with the squamosal move away from each other, resulting in an increase in depth of the zygomatic arch. To a lesser extent, the increase in size also results in a more posterodorsal position of the intersection between the anterior orbital edge and the jugallacrimal suture (#50). We also note that the contact with the lacrimal and maxillary (#48) is relatively more posteroventral, which reduces the relative length of the anterior extremity of the jugal. All these allometric changes suggest that the jugal becomes relatively shorter and higher in larger specimens. Finally, the intersection between the jugalmaxillary suture and the ventral edge of the zygomatic arch (#21) takes a slightly more anteroventral position as size increases. At the static level, allometric variation for this OBU is not significantly supported for this species (Table 7).

In CabassousNS, at the ontogenetic level (Figure 34), we also detect allometric variation leading to a relative enlargement of the posterior part of the jugal on the zygomatic arch, with its dorsal extremity being shifted more anteriorly and its ventral extremity shifted posteroventrally as size increases (#52; #54). It can also be noted that, as size increases, the intersection between the anterior orbital edge and the jugal/lacrimal suture (#50) and the intersection between the jugalmaxillary suture and the ventral edge of the zygomatic arch (#21) take a slightly more posterior position. In addition, the contact with the lacrimal and maxillary (#48) extends more anterodorsally, causing a slight elongation of the anterior extremity of the jugal as size increases.

At the static level, allometric variation for this OBU is nearly significant but is not supported, for CabassousNS (Table 8).

Figure 34. Vector representation of the allometric shape changes detected for a given cranial unit (OBU) in CabassousNS, represented between its minimal (greensmaller centroid size) and maximal (redlarger centroid size) shape (see Figure 29). Results of the analysis performed at the ontogenetic level, and with the log skull centroid size taken as the size variable (see text). For each OBU, the changes are shown in three subsections organized horizontally: 1, vectors from minimal to maximal shape with minimal OBU shape; 2, same as 1) with maximal OBU shape; 3, minimal OBU shape in transparency with vectors. A) alisphenoid-orbitosphenoid-pterygoid-basisphenoid complex; A1-A2, lateral view; A3, dorsal view. B) frontal; B1-B2, lateral view; B3, ventral view. C) jugal; C1-C2, lateral view; C3, medial view. D) petrosal; D1-D2, medial view; D3, lateral view. E) squamosal; E1-E2, lateral view; E3, ventral view. Landmark numbers and orientation arrows were added for more readability. Abbreviations: A, anterior; D, dorsal; L, lateral; V, ventral.

In CabassousN, at the ontogenetic and static level (Figures S28 &S29), we observe the same general allometric variations as in CabassousNS, except for the intersection between the jugal/maxillary suture and the ventral edge of zygomatic arch (#21) which assumes a more dorsal position, and for the contact with the lacrimal and maxillary (#48), which exhibits a more posteroventral position as size increases. As for Zaedyus, most of these changes suggest a relatively higher (and/or broader) and shorter jugal bone as size increases.

Maxillary

In Zaedyus pichiy, at the ontogenetic level (Figure 33), the maxillary shows an anterior elongation of the anteroventral portion that contacts the premaxillary on the palate (#5) in larger specimens, whereas its anterodorsal contacts the premaxillary and the nasal is shifted in the opposite direction (#4). One of the strongest allometric variations in this OBU corresponds to its midline contact with the palatine (#17), which takes on a more anterior position in larger specimens, similar to its ventral contact with the premaxillary (#5). The most posterior point of 8 &S20).

Figure 35. Vector representation of the allometric shape changes detected for a given cranial unit (OBU) in CabassousNS, represented between its minimal (greensmaller centroid size) and maximal (redlarger centroid size) shape (see Figure 29). Results of the analysis performed at the static level, and with the log skull centroid size taken as the size variable (see text). For each OBU, the changes are shown in three subsections organized horizontally: 1, vectors from minimal to maximal shape with minimal OBU shape; 2, same as 1) with maximal OBU shape; 3, minimal OBU shape in transparency with vectors. A) alisphenoid-orbitosphenoid-pterygoid-basisphenoid complex; A1-A2, lateral view; A3, dorsal view. B) petrosal; B1-B2, medial view; B3, lateral view. Landmark numbers and orientation arrows were added for more readability. Abbreviations: A, anterior; L, lateral; V, ventral.

Nasal

In Zaedyus pichiy, at the ontogenetic and static levels (Figures 33 & 37), the landmarks on the anterior part of the nasal (#1; #10) are relatively more anteromedial in position as size increases. The contact with the maxillary and premaxillary (#4) move much further posteriorly as size increases, which indicates that a larger portion of the nasal is in contact with the premaxillary in larger specimens. More posteriorly, the part of the nasal contacting the frontal (#2) near the midline takes a more anterior position as size increases, whereas the posterolateral edge in contact with the frontal and maxillary (#32) elongates in a posteromedial direction. The combination of these two trends indicates an elongation of the frontal process of the nasal posterolaterally as size increases and a deeper nasal process of the frontal between the nasal bones. This pattern is congruent with the results found for the frontal bone (see above).

Only CabassousN at the static level (Figure S29) shows statistically supported allometric variation for this OBU (Tables 8 &S20), although it is nearly significant at this same level in

Parietal

In Zaedyus pichiy (Figure 38), the parietal is more elongated anteroposteriorly and narrower mediolaterally (especially in its anterior part) as size increases through ontogeny (#66;

#67; #69; #71). The tentorial process varies little except for a slightly more posterior position of its ventralmost point (#63) as size increases. At the static level, the allometric variation of this OBU is not statistically supported but the p-value is close to the significance threshold (Table 7).

Only CabassousN exhibits statistically supported allometric variation over the course of ontogeny for this OBU (Tables 8 &S20). The pattern obtained (Figure S28) is similar to that of Zaedyus pichiy except that the length of the lateral part of the bone in contact with the squamosal reduces as size increases (#69; #71), and the tentorial process forms a more ventrally directed crest (#63).

It should be noted that in Dasypus novemcinctus and Cabassous spp. the tentorial process is completely formed by the parietal, whereas in Zaedyus pichiy, its anterior half is formed by the parietal and its posterior half is formed by the supraoccipital.

Petrosal

In

Premaxillary

In Zaedyus pichiy (Figure 38), the greatest ontogenetic allometric variation is concentrated on the palatal contact between the premaxillary and maxillary (#5), which extends farther anteriorly, and the triple premaxillary -maxillary -nasal contact, which extends farther posteriorly This variation in the posterior edge of the incisive foramen results in their relative enlargement in larger specimens. At the static level, when size increases, similar allometric variations are observed, except for the enlargement of the incisive foramen (#14; #16) (Figure 37). Allometric variation for this OBU is not significantly supported for the Cabassous datasets (Tables 8 &S20).

Figure 38. (continued from Figure 33). Vector representation of the allometric shape changes detected for a given cranial unit (OBU) in Zaedyus, represented between its minimal (greensmaller centroid size) and maximal (redlarger centroid size) shape (see Figure 29). Results of the analysis performed at the ontogenetic level, and with the log skull centroid size taken as the size variable (see text). For each OBU, the changes are shown in three subsections organized horizontally: 1, vectors from minimal to maximal shape with minimal OBU shape; 2, same as 1) with maximal OBU shape; 3, minimal OBU shape in transparency with vectors. H) palatine; H1-H2, ventral view; H3, dorsal view. I) parietal; I1-I2, ventral view; I3, dorsal view. J) petrosal; J1-J2, medial view; J3, lateral view. K) premaxillary; K1-K2, ventral view; K3, medial view. L) squamosal; L1-L2, lateral view; L3, ventral view. Landmark numbers and orientation arrows were added for more readability. Abbreviations: A, anterior; L, lateral; V, ventral.

Squamosal

In Zaedyus pichiy (Figure 38), the most dorsal contact between the jugal and squamosal extends farther anterolaterally (#52) whereas the ventral contact between the two bones extends farther posterolaterally (#54) when size increases through ontogeny (as observed on the jugal bone; Overall, larger specimens thus show a greater distance separating landmarks on the zygomatic arch (#52, #54) from the landmarks on the lateral wall of the braincase (#42, #62, #69), in the anterior half of the bone. This suggests more laterally protruding zygomatic arches in larger specimens, as detected in the ES analyses (see above). At the static level, the allometric variations are nearly identical but with much lower norms for the vectors (Figure 37). The phylogenetic regression of shape on log centroid size in our DatasetExt accounts for 20.66% of the total shape variation (p-value = 0.0008, Figure 39; Table 9). Dasypodines follow an allometric trend quite dissimilar from the other clades, showing a greater variation in shape with increasing size (Figure 39). From the smallest to the largest of the extant armadillo species, three trends are very strongly marked, as evidenced by high vector norms. The snout displays a strong anterior elongation with size increase, as indicated by many landmarks of the snout, including the dental row, that assume a more anterior position (#1; #3-16; #18-19; #26-29). In contrast, the intersection between the maxillopalatine suture and the midline (#17) varies only slightly. The lengthening of the snout is also accompanied by a relative reduction in its height particularly well marked by the contact between the interfrontal and the internasal sutures on the midline and the triple contact point between nasal -maxillary -frontal that assumes a more ventral position (#2;

# [START_REF]) FM<-function(M){as.matrix(dist(M))} fm<-function(M){mat<-FM(M); mat[col(mat)<row(mat)]} mEDMA<-function(A) {n<-dim(A)[END_REF][32]. The face also exhibits a mediolateral narrowing of the snout in its posterior part (#24-27;

-- - - - - - - - - -- - - - - - - - - Palatine -- - - - - - - - - -- - - - - - - - - Parietal
26 25 0.007451 0.0074505 0.05899 1.5046 0.86486 0.1963 0.003891 -0.048775

The phylogenetic regression of shape on log centroid size in our Dataset-Lmax accounts for 16.81% of the total shape variation (p-value = 0.0007, Figure 40; Table 10). Clearly, Peltephilus appears as an outlier in this analysis. Several patterns of allometric variation are consistent with that of the DatasetExt. As size increases, the snout shows a strong relative lengthening, but also a relative increase rather than a decrease in height (#2; #3-4; #6-7; #9-12; space between these points (#97-98) and the dorsal edge of the frontal (#31, #66). However, neither

Zaedyus pichiy nor Cabassous unicinctus have frontal sinuses [START_REF] Billet | The hidden anatomy of paranasal sinuses reveals biogeographically distinct morphotypes in the nine-banded armadillo (Dasypus novemcinctus)[END_REF]. Compared to the DatasetExt, the posterior processes of the nuchal crest (#73-74) extend even further posteromedioventrally and become even more prominent. For graphical display, we used the projected regression scores of the shape data to represent shape variation related to changes in log centroid size [START_REF] Adams | A field comes of age: geometric morphometrics in the 21st century[END_REF]. Shape changes were visualized as vectors from the minimal shape (green) to the maximal shape (red) of the shape regression scores corresponding to the projection of the data points in shape space on to an axis in the direction of the regression vector (see [START_REF] Drake | The pace of morphological change: historical transformation of skull shape in St Bernard dogs[END_REF]. Phylogenetic regression of skull shape on log skull centroid size of DatasetExt, represented 20.66% of the total shape variation. For graphical display, we used the projected regression scores of the shape data to represent shape variation related to changes in log centroid size [START_REF] Adams | A field comes of age: geometric morphometrics in the 21st century[END_REF]. Shape changes were visualized as vectors from the minimal shape (green) to the maximal shape (red) of the shape regression scores corresponding to the projection of the data points in shape space on to an axis in the direction of the regression vector (see [START_REF] Drake | The pace of morphological change: historical transformation of skull shape in St Bernard dogs[END_REF]. Phylogenetic regression of skull shape on log skull centroid size of Dataset-Lmax, represented 16.81% of the total shape variation.

The most medial point of the promontorium of petrosal (#87-88) is situated further lateral but also further posteriorly and thus becomes more distant from the basicranium midline in larger specimens in Dataset-Lmax. Together with other landmarks on the petrosal, this also indicates a relative reduction in the proportions of the promontorium of the petrosal. Finally, contrary to previous analyses, the sphenorbital fissure (#45-46) does not follow the general reduction in the size of the braincase, but rather shows a more posteroventral position in larger specimens.

The same dichotomy (dasypodids vs chlamyphorids) is obtained in DatasetExt and Dataset-Lmax regarding the position of species with respect to the regression line (Figure 40). As regards extinct taxa, Peltephilus is a clear outlier and seems to present a cranial shape very different from the other cingulates with regard to the size. Glyptodonts are located above the regression line, as the extant chlamyphorids. Vassallia is located below the regression line along with the dasypodids (Figure 40).

The same analysis on the Dataset-Tmax results in a slightly lower allometric proportion (R 2 = 13.62%; p-value = 0.0001 -Figure S30, Table S21) and nearly the same allometric patterns (Figure S36). It provides no further information about allometric variation. However, the position of the specimens in relation to the regression line changes strongly with the addition of Proeutatus, and no longer provides a clear distinction between the dasypodids and chlamyphorids. The chlamyphorines are located under the regression line, along with Glyptodon, Vassallia and most of the dasypodines (Figure S30).

Allometric variations studied Bone By Bone (3B) at the evolutionary level

Comparison between OBUs

In the DatasetExt, we observe differences in the proportions of allometric shape variation among different OBUs (Figure 41A). The phylogenetic regression of shape on size shows no statistical support for the nasal, lacrimal, jugal, premaxillary, parietal and as-os-pt-bs OBUs (Figure 41A; Table 9), but does reveal a significant allometric effect for the other OBUs. The squamosal and maxillary have the lowest proportion of shape variation explained by size of all OBUs (almost 10%; Figure 41A; Table 9). The petrosal and bo-eo OBUs have a proportion of shape variation explained by size ranging between 10% and 15% (Figure 41A; Table 9). The palatine and supraoccipital show a higher allometric proportion, ranging between 15% and 20%

(Figure 41A; Table 9). The OBU showing the highest proportion of variation explained by size is the frontal, at 19.75% (Figure 41A; Table 9). Without the phylogenetic correction, the regression of the shape on the size shows significant allometric variations only for the palatine, as-os-pt-bs, bo-eo and petrosal OBUs. The allometric proportions are in all cases higher without than with the phylogenetic correction (Table 9).

In the Dataset-Lmax, the premaxillary, nasal, jugal and palatine OBUs could not be analyzed due to an insufficient number of landmarks. For the other OBUs, we also observe differences in the proportions of allometric shape variation (Figure 41B; Table 10). The phylogenetic regression of shape on size shows no statistical support for allometry in the lacrimal, parietal, maxillary and squamosal (Figure 41B; Table 10). In contrast, the as-os-pt-bs, supraoccipital, frontal and petrosal OBUs have a significant proportion of shape variation explained by size, ranging between 10% and 15% (Figure 41B; Table 10). The OBU showing the highest proportion of variation explained by size is the bo-eo OBU, at 18.72% (Figure 41B; Table 10). Without the phylogenetic correction, the regression of shape on size shows significant allometric variations for all OBUs except for the lacrimal, with allometric proportions always higher than with the phylogenetic correction, except for the as-os-pt-bs OBU (Table 10). In the Dataset-Tmax, the proportion of shape variation explained by size are very similar, although a little higher, to those presented here for the Dataset-Lmax (Figure S31, Table S21).

Allometric variation within OBUs

All descriptions of the allometric shape changes below describe the minimal shapes as Abbreviations of OBUs: as-os-pt-bs, alisphenoid-orbitosphenoid-pterygoid-basisphenoid complex; bo-eo, basioccipital-exoccipital complex; fr, frontal; ju, jugal; lac, lacrimal; mx, maxillary; na, nasal; pa, parietal; pal, palatine; pe, petrosal; pmx, premaxillary; so, supraoccipital; sq, squamosal.

Alisphenoid-Orbitosphenoid-Pterygoid-Basisphenoid complex

In the DatasetExt, there is no statistically supported allometric variation for this OBU (Table 9).

In Figure 42. Vector representation of the allometric shape changes detected for a given cranial unit (OBU) in DatasetExt, represented between its minimal (greensmaller centroid size) and maximal (redlarger centroid size) shape (see Figure 29). Results of the analysis performed at the evolutionary level, and with the log skull centroid size taken as the size variable (see text). For each OBU, the changes are shown in three subsections organized horizontally: 1, vectors from minimal to maximal shape with minimal OBU shape; 2, same as 1) with maximal OBU shape; 3, minimal OBU shape in transparency with vectors. A) basioccipital-exoccipital complex; A1-A2, dorsal view; A3, ventral view. B) frontal; B1-B2, lateral view; B3, ventral view. C) maxillary; C1-C2, lateral view; C3, medial view. D) palatine; D1-D2, ventral view; D3, dorsal view. E) petrosal; E1-E2, medial view; E3, lateral view. F) squamosal; F1-F2, lateral view; F3, ventral view. G) supraoccipital; G1-G2, lateral view; G3, occipital view. Landmark numbers and orientation arrows were added for more readability as well as the overall representation of the unpaired bone (basioccipital, supraoccipital). For the facilitation of meshes deformation, we selected Cabassous rather than Dasypus or Zaedyus to represent allometric variation because this genus has a shape closer to the consensus shape across all cingulates in our analysis. Abbreviations: A, anterior; D, dorsal; L, lateral; V, ventral.

Basioccipital-Exoccipital complex

In the DatasetExt (Figure 42

Frontal

In the DatasetExt (Figure 42), from the smallest to the largest specimen, the triple contact point between the frontal -squamosal -parietal (#69) and the triple contact point between squamosal -frontal -alisphenoid (#42) take a relatively more anteromedial position. This is also the case for the dorsal intersection of annular ridge and midline (#97), which also moves ventrally.

The intersection between the frontal -parietal suture and the midline (#66) is more posteromedial Figure 43. Vector representation of the allometric shape changes detected for a given cranial unit (OBU) in Dataset-Lmax, represented between its minimal (greensmaller centroid size) and maximal (redlarger centroid size) shape (see Figure 29). Results of the analysis performed at the evolutionary level, and with the log skull centroid size taken as the size variable (see text). Each OBU is defined in three subsections organized horizontally: 1, landmarks and wireframe on an OBU of Cabassous used as a reference as in Figure 42; 2, vectors with a wireframe representing the minimal OBU shape; 3, vectors with a wireframe representing the maximal OBU shape. A1-A3, alisphenoidorbitosphenoid-pterygoid-basisphenoid complex in dorsal view. B1-B3, basioccipital-exoccipital complex in dorsal view. C1-C3, frontal in lateral view. D1-D3, petrosal in ventral view. E1-E3, supraoccipital in occipital view. Landmark numbers and orientation arrows were added for more readability as well as to provide overall representations of the unpaired bones, i.e., basioccipital, supraoccipital.

Maxillary

In the DatasetExt (Figure 42), from the smallest to the largest specimen, the triple contact point between premaxillary -maxillary -nasal (#4) assumes a more anteroventral position. The most anterior point of the alveolar margin of the dental row (#27) extends farther anteriorly as do the intersection between maxillary/palatal suture and lateral edge of palate (#19) and the most posterior point of the alveolar margin of the dental row (#29). In larger specimens, the intersection between jugal -maxillary suture and ventral edge of zygomatic arch (#21), the most dorsal point of the maxillary foramen (#23) and the triple contact point between maxillary -jugal -lacrimal (#48) are shifted posteriorly. This is also the case for the triple contact point between lacrimalmaxillary -frontal (#34), but with a slightly more ventral displacement. Overall, the combination of these allometric variations with the triple contact point between premaxillary -maxillary -nasal (#4) suggests a relative anteroposterior lengthening of the upper half of the maxillary. It also shows a relatively more posterior position of the area of the maxillary foramen and anterior root of the zygomatic (where it contacts the jugal bone), while the dental row reduces in relative length and is shifted forward. As size increased, the intersection between palatal -maxillary suture and the palate midline (#17) has a more anterodorsal position, which suggests that the maxillary contribution to the hard palate is reduced in its posteromedial part. The triple contact point between frontal -maxillary -nasal (#32) shows a more ventral position, which, when combined with the variation of landmarks #34 and #4, indicates a relative reduction of the maxillary height in larger specimens.

An allometric variation for this OBU is not significantly supported for the Dataset-Lmax and Dataset-Tmax (Tables 10 &S21).

Figure 44. (continued from Figure 43). Vector representation of the allometric shape changes detected for a given cranial unit (OBU) in Dataset-Lmax, represented between its minimal (greensmaller centroid size) and maximal (redlarger centroid size) shape (see Figure 29). Results of the analysis performed at the evolutionary level, and with the log skull centroid size taken as the size variable (see text). Each OBU is defined in three subsections organized horizontally: 1, landmarks and wireframe on an OBU of Cabassous used as a reference as in Figure 42; 2, vectors with a wireframe representing the minimal OBU shape; 3, vectors with a wireframe representing the maximal OBU shape. A1-A3, alisphenoid-orbitosphenoid-pterygoid-basisphenoid complex in lateral view. B1-B3, basioccipitalexoccipital complex in occipital view. C1-C3, frontal in ventral view. D1-D3, petrosal in lateral view. E1-E3, supraoccipital in ventral view. Landmark numbers and orientation arrows were added for more readability as well as the overall representation of the unpaired bone (basioccipital, supraoccipital).

Palatine

In the DatasetExt (Figure 42), from the smallest to the largest specimen, the intersection between palatal -maxillary suture and the palate midline (#17) is shifted laterally while the most anteroventral point of caudal palatine foramen (#44) is more medial. This indicates a relative narrowing of the palatine in larger specimens. The intersection between maxillary -palatine suture and lateral edge of palate (#19) moves anteriorly, whereas the most posterior point of the palatine midline (#30) extends more posteriorly in larger specimens. This indicates a relative anteroposterior elongation of the palatine on the midline, and an anterior shift of the lateral part of its suture with the maxillary on the palate.

An allometric variation for this OBU is not significantly supported for the Dataset-Lmax and Dataset-Tmax (Tables 10 &S21).

Petrosal

In the DatasetExt (Figure 42), the most anteroventral point of the mastoid process (#90)

shows the strongest allometric variation and extends much further posteroventrally in larger An allometric variation for this OBU is not significantly supported for the Dataset-Lmax and Dataset-Tmax (Tables 10 &S21; although it is near the significance threshold in the former).

Supraoccipital

In the DatasetExt (Figure 42), from the smallest to the largest specimen, the most posterior point of the nuchal process of the supraoccipital (#74) shows the greatest allometric variation, as it is extended much further posterodorsally than other landmarks. The point of maximum curvature

DISCUSSION

Common allometric pattern in Entire Skull (ES)

Our comparative study of allometric patterns at the ontogenetic and static levels in Zaedyus and Cabassous coupled with the analysis of evolutionary allometry across Cingulata, revealed several patterns shared with those described previously in Dasypus (Section 3.1). The strongest allometric variation over the entire skull corresponded to relative lengthening of the snout associated with a reduction in the proportions of the braincase (Table 11). This pattern was very strongly marked in Dasypus, whereas in Zaedyus and Cabassous, it appeared to be much weaker but still present. Relative lengthening of the snout and reduction of braincase proportions were also found as an allometric variation at the evolutionary level across our three datasets despite the presence of taxa with anteriorly shifted orbits on the snout, such as glyptodonts. Our study thus showed that this widespread pattern, described in the literature as craniofacial evolutionary allometry (CREA), is not only found in Dasypus (Section 3.1) but is pervasive among cingulates.

This pattern may be stronger in Dasypus, with its more dramatically elongated snout (Hautier et al., 2017; Section 3.1) but it is clearly expressed in the morphological diversity of cingulates as a whole, which suggests a deep origin for this pattern. iiiii) Enlargement between zygomatic arches and postorbital constriction iiiiii) Relative flattening of the cranial roof.

Bo-Eo: i) hypoglossal foramen located relatively more posterior; ii) relative reduction of foramen magnum (not in Cabassous ).

Frontal: i) more posterior and stronger postorbital constriction; ii) greater separation between the annular ridge and frontal roof.

Petrosal: i) more protruding mastoid process; ii) shallower fossa subarcuata (not in Dasypus ).

Squamosal: i) more protruding zygomatic arch laterally (not in Cabassous ).

Without fossils i)

Posterior snout narrowing.

Maxillary (without Cabassous ): i) reduction in height.

Palatine (without Cabassous ): i) anteroposterior elongation on the midline and mediolateral narrowing.

Only DZC i)

Widening of the zygomatic arch.

Jugal: i) shortening and increase in height.

Parietal: i) anteroposterior elongation and mediolateral narrowing.

Squamosal: i) more posterior position of the posterior root of the zygomatic arches.

Only ZC i)

More medial position of braincase anterolateral edge.

Jugal: i) more posterior position of the orbital edge.

Nasal: i) frontal process of the nasal elongated posteriorly. - ----------------------------------------------------------------------------- Several studies have shown that CREA is a global allometric pattern present in several mammalian groups [START_REF] Cardini | Larger mammals have longer faces because of size-related constraints on skull form[END_REF][START_REF] Cardini | Why the long face? Kangaroos and wallabies follow the same 'rule' of cranial evolutionary allometry (CREA) as placentals[END_REF][START_REF] Tamagnini | Anyone with a long-face? Craniofacial Evolutionary Allometry (CREA) in a family of short-faced mammals, the Felidae[END_REF]Cardini, 2019a;[START_REF] Marcy | Australian rodents reveal conserved Cranial Evolutionary Allometry across 10 million years of murid evolution[END_REF]. Cardini (2019a) even suggested that this is an allometric pattern common to all mammals and perhaps even all vertebrates. Cardini (2019a) also showed that armadillos in his sample had a relatively low craniofacial allometry compared to other mammals, even though this sample included species belonging to Dasypus.

Evolutionary

Craniofacial allometry was not the only common pattern detected on the entire skull among our cingulate species (Table 11). Allometric variation also included a postorbital constriction in larger specimens at all the levels studied in cingulates (Table 11). This allometric variation was also quite common and found in many other mammals (e.g., [START_REF] Frost | Cranial allometry, phylogeography, and systematics of large-bodied papionins (primates: Cercopithecinae) inferred from geometric morphometric analysis of landmark data. The Anatomical Record Part A: Discoveries in Molecular[END_REF][START_REF] Flores | Comparative postnatal ontogeny of the skull in the australidelphian metatherian Dasyurus albopunctatus (Marsupialia: Dasyuromorpha: Dasyuridae)[END_REF][START_REF] Segura | A quantitative approach to the cranial ontogeny of Lycalopex culpaeus (Carnivora: Canidae)[END_REF][START_REF] Moyano | Comparative cranial ontogeny of Tapirus (Mammalia: Perissodactyla: Tapiridae)[END_REF] although not in all groups (e.g., equids: [START_REF] Heck | Why the long face? Comparative shape analysis of miniature, pony, and other horse skulls reveals changes in ontogenetic growth[END_REF]. Allometry was correlated with a greater development of the temporalis muscle in large specimens of Dasyurus [START_REF] Flores | Cranial ontogeny of Caluromys philander (Didelphidae: Caluromyinae): a qualitative and quantitative approach[END_REF] and Puma concolor [START_REF] Giannini | A quantitative approach to the cranial ontogeny of the puma[END_REF] both of which also exhibited a greater postorbital constriction as size increased. This hypothesis requires further research in armadillos, since this muscle does not reach the postorbital constriction in Dasypus but it does in Euphractus [START_REF] Smith | The anatomy and function of the feeding apparatus in two armadillos (Dasypoda): anatomy is not destiny[END_REF], a closer relative of Zaedyus. We also detected a relative flattening of the cranial roof (Table 11) with larger size, which is probably associated with craniofacial allometry (e.g., [START_REF] Ferreira-Cardoso | Skull shape variation in extant pangolins (Pholidota: Manidae): allometric patterns and systematic implications[END_REF]. This flattening is accompanied by an enlarging space separating the internal landmarks on the frontal (#97, #98) from the dorsal edge of this bone (#31, #66) at the intraspecific level in Cabassous, in Dasypus, and, above all, at the evolutionary level (Table 11). This was also detected in 3B analyses focused on the frontal bone. We previously suggested that this allometric thickening of the frontal in Dasypus was linked to the development of frontal sinuses during ontogeny [START_REF] Billet | The hidden anatomy of paranasal sinuses reveals biogeographically distinct morphotypes in the nine-banded armadillo (Dasypus novemcinctus)[END_REF]Section 3.1). This hypothesis is consistent with the pattern found at the evolutionary level because the smallest cingulates such as chlamyphorines do not possess frontal sinuses [START_REF] Smith | Calyptophractus retusus (Cingulata: Dasypodidae)[END_REF]Le Verger, pers. Obs., 2020) whereas larger forms such as some dasypodines and glyptodonts have strongly developed frontal sinuses [START_REF] Fernicola | A neomorphic ossification of the nasal cartilages and the structure of paranasal sinus system of the glyptodont Neosclerocalyptus Paula Couto 1957 (Mammalia, Xenarthra)[END_REF][START_REF] Billet | The hidden anatomy of paranasal sinuses reveals biogeographically distinct morphotypes in the nine-banded armadillo (Dasypus novemcinctus)[END_REF].

Several studies have suggested a relationship between an increase in size and the presence or extension of sinuses in many mammals [START_REF] Weidenreich | The brain and its role in the phylogenetic transformation of the human skull[END_REF][START_REF] Zollikofer | New insights into mid-late Pleistocene fossil hominin paranasal sinus morphology[END_REF][START_REF] Farke | Evolution and functional morphology of the frontal sinuses in Bovidae (Mammalia: Artiodactyla), and implications for the evolution of cranial pneumaticity[END_REF][START_REF] Curtis | Repeated loss of frontal sinuses in arctoid carnivorans[END_REF][START_REF] Krentzel | Why are mammals such air-heads? Porcupines and function of the frontal sinus in mammals[END_REF][START_REF] Sharp | Cranial biomechanics, bite force and function of the endocranial sinuses in Diprotodon optatum, the largest known marsupial[END_REF][START_REF] Billet | The hidden anatomy of paranasal sinuses reveals biogeographically distinct morphotypes in the nine-banded armadillo (Dasypus novemcinctus)[END_REF][START_REF] Boscaini | Digital cranial endocasts of the extinct sloth Glossotherium robustum (Xenarthra, Mylodontidae) from the late Pleistocene of Argentina: description and comparison with the extant sloths[END_REF]2020).

Finally, we detected an elongation of the nuchal crests with increasing cranial size both within and among species (Table 11;Section 3.1). A greater protrusion of these crests in larger specimens was also an allometric pattern frequently found in other mammals at both intraspecific and evolutionary levels [START_REF] Frost | Cranial allometry, phylogeography, and systematics of large-bodied papionins (primates: Cercopithecinae) inferred from geometric morphometric analysis of landmark data. The Anatomical Record Part A: Discoveries in Molecular[END_REF][START_REF] Flores | Comparative postnatal ontogeny of the skull in the australidelphian metatherian Dasyurus albopunctatus (Marsupialia: Dasyuromorpha: Dasyuridae)[END_REF][START_REF] Moyano | Comparative cranial ontogeny of Tapirus (Mammalia: Perissodactyla: Tapiridae)[END_REF]. This region of the occiput serves as an area of insertion for several neck muscles (e.g., recti capitis dorsalis major and minor, semispinalis capitis; [START_REF] Barone | Anatomie comparée des mammifères domestiques[END_REF][START_REF] Evans | Miller's Anatomy of the Dog[END_REF], which control the flexibility of the neck for head movements [START_REF] Evans | Miller's Anatomy of the Dog[END_REF]. The stronger development of these crests in large specimens could increase the surface of insertion for these muscles to compensate for the increase in head mass. Dissections in extant Cingulata will be necessary to test this hypothesis.

In addition, we detected a relative narrowing of the snout in its posterior part in larger specimens in the evolutionary dataset including only extant species (Table 11). This pattern is relatively common in mammals (e.g., in canids: [START_REF] Drake | The pace of morphological change: historical transformation of skull shape in St Bernard dogs[END_REF][START_REF] Segura | A quantitative approach to the cranial ontogeny of Lycalopex culpaeus (Carnivora: Canidae)[END_REF]). An allometric widening of the zygomatic arches relative to the rest of the skull and a greater distance from the zygomatic arches to the postorbital constriction was also recovered in our intraspecific analyses and in the evolutionary DatasetL-max (Table 11). This allometric variation is known in several other mammals [START_REF] Cardini | Post-natal ontogeny of the mandible and ventral cranium in Marmota species (Rodentia, Sciuridae): allometry and phylogeny[END_REF][START_REF] Cardini | Why the long face? Kangaroos and wallabies follow the same 'rule' of cranial evolutionary allometry (CREA) as placentals[END_REF][START_REF] Tamagnini | Anyone with a long-face? Craniofacial Evolutionary Allometry (CREA) in a family of short-faced mammals, the Felidae[END_REF] and may be linked to the CREA pattern even though such a linkage has not yet been demonstrated. Finally, the commonly observed allometric reduction in braincase proportions in larger specimens was more strongly localized on the anterolateral edges of the braincase in our intraspecific series of Zaedyus and Cabassous (Table 11).

We also noted two allometric variations in the ES analyses that were only found at the evolutionary level, but were common to all three evolutionary datasets (Table 11). The first corresponded to a much more posterior position of the anterior edge of the orbit and anterior zygomatic arches, which seemed to accompany the snout lengthening in larger specimens (Table 11). This is congruent with the morphology of Priodontes or Vassallia, but not with that of the large-sized glyptodonts, which possess an anteriorly shifted orbit and who thus depart from this allometric trend among cingulates. The second allometric variation corresponds to a relatively more lateral position of the promontorium of the petrosal, indicating its greater separation from the midline of the basicranium in larger specimens. According to the matrix of [START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF] (character 90), large taxa (glyptodonts, pampatheres) no longer present a contact between the promontorium of the petrosal and the lateral edge of the basicranium. A patent basicochlear fissure is also present in Dasypus and Stegotherium (see [START_REF] Wible | Petrosal anatomy of the nine-banded armadillo, Dasypus novemcinctus Linnaeus, 1758 (Mammalia, Xenarthra, Dasypodidae)[END_REF]Gaudin and Lyon, 2017also in Priodontes, see [START_REF] Patterson | The ear region in xenarthrans (=Edentata, Mammalia). Part I. Cingulates[END_REF]. This is congruent with a putative negative allometry of the petrosal bone relative to skull size among placentals (Billet et al., 2015b), which further contributes to the presence of the medial cavity between the petrosal and basicranium in larger species. More research is on allometric variation of the auditory region is needed to test this hypothesis.

Allometric proportions of cranial shape variation in Cingulata

The proportions of shape variation for the entire skull explained by allometry were very unequal when comparing all the analyses. Dasypus showed the highest proportion with almost 28% at the ontogenetic level (Section 3.1). At the static level, it exhibited values closer to those of Zaedyus at both levels and Cabassous at the ontogenetic level, i.e. between 5% and 10% (Section 3.1). The allometric proportion of shape variation resulting from the evolutionary analyses were higher, approaching 20%. Compared to intraspecific values for other mammals, Cabassous and Zaedyus showed a particularly low allometric proportion of cranial shape variation, whereas Dasypus was closer to values typical for mammals [START_REF] Frost | Cranial allometry, phylogeography, and systematics of large-bodied papionins (primates: Cercopithecinae) inferred from geometric morphometric analysis of landmark data. The Anatomical Record Part A: Discoveries in Molecular[END_REF][START_REF] Hallgrímsson | Deciphering the palimpsest: studying the relationship between morphological integration and phenotypic covariation[END_REF][START_REF] Hallgrímsson | Morphometrics, 3D imaging, and craniofacial development[END_REF]. The proportions of allometric variation at the evolutionary level are particularly variable according to the group of mammals studied (although a majority shows proportions between 10% and 30% [START_REF] Cassini | Skull geometric morphometrics and paleoecology of Santacrucian (Late Early Miocene; Patagonia) native ungulates (Astrapotheria, Litopterna, and Notoungulata)[END_REF]).

As regards cranial units, the allometric proportions of shape variation for each OBU were very different among the different data sets and different levels of analysis, as was the case in our previous study of Dasypus (Section 3.1). Only the petrosal showed statistically significant supported allometric variation in all analyses and, except for Cabassous at the static level, this was also the case for the frontal. The frontal often showed strong allometric variations in previous studies at the ES level (e.g., [START_REF] Hautier | Beyond the carapace: skull shape variation and morphological systematics of long-nosed armadillos (genus Dasypus)[END_REF][START_REF] Ferreira-Cardoso | Skull shape variation in extant pangolins (Pholidota: Manidae): allometric patterns and systematic implications[END_REF]Section 3.1). To our knowledge, few studies have performed allometric analyses on virtually isolated bone units (our 3B approach), but we note, for example, that in the regionalized allometric analyses of [START_REF] Gonzalez | Ontogenetic allometry and cranial shape diversification among human populations from South America[END_REF] in humans, the face and vault showed stronger allometric variations than the basicranium.

In our analyses, it is also worth noting that the palatine and parietal, which showed strong allometry at the static level in Dasypus (Section 3.1), also exhibit a high proportion of allometric variation in Zaedyus at the ontogenetic level and, for the palatine, in the evolutionary analyses as well (in extant species only). In addition, Cabassous consistently showed a lower allometric proportion of shape variation in the ES analyses, and significant allometric variation was supported for fewer cranial units in this taxon, which suggests an lower overall level of cranial allometry.

However, the as-os-pt-bs was the OBU with the highest allometric proportions in Cabassous, and it clearly exceeded values found for this OBU in Zaedyus and Dasypus. A significant allometric variation for this OBU at the evolutionary level was only recovered in the dataset incorporating glyptodonts.

Common Allometric Pattern in Cranial Units

Through the different levels of analysis, our study allowed us to detect several allometric patterns on virtually isolated cranial units within intraspecific series in Dasypus (Section 3.1), Cabassous and Zaedyus, and among cingulate species in our evolutionary analysis. Allometric variations common to several intraspecific and evolutionary levels of analyses were found for the bo-eo, frontal, petrosal and squamosal OBUs (Table 11). This comes as no surprise, as these OBUs were often among those with the highest allometric proportions in most of our analyses (Figures 31,32 & 41;and Section 3.1). As size increased, all cingulates exhibited a more posterolateral position of the hypoglossal foramen on the basioccipital-exoccipital (bo-eo) unit, both within and among species. Similarly, the foramen magnum was reduced in size as the size of the skull increased, a tendency also known in squamates [START_REF] Monteiro | Allometry and morphological integration in the skull of Tupinambis merianae (Lacertilia: Teiidae)[END_REF]. On the frontal, the postorbital constriction was more pronounced and more posteriorly located, and a greater distance separated the annular ridge from the frontal roof dorsoventrally in larger specimens. These last two variations were also detected in part at the ES level. On the petrosal, the mastoid process (= paroccipital process of petrosal in [START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF]) elongated with increasing skull size.

The mastoid process of the petrosal in armadillos serves the site of origin for the digastric muscle involved in the mandibular movement [START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF]. A larger area of attachment may be associated with larger and stronger digastric muscles in larger specimens. At the evolutionary level, this pattern may be related to the specialized herbivory seen in the largest cingulates (pampatheres, glyptodonts) [START_REF] Vizcaíno | Functional and phylogenetic assessment of the masticatory adaptations in Cingulata (Mammalia, Xenarthra)[END_REF]. As for the nuchal crests, dissection in extant cingulates could help to better explain this pattern.

Cingulates also shared a shallower fossa subarcuata on the petrosal with increasing skull size. Because of negative allometry of the inner ear labyrinth compared with the surrounding petrosal bone, Billet et al. (2015b) have questioned whether the reduced size of the anterior semicircular canal (ASC) in large taxa could constrain the shape of the fossa subarcuata (this fossa being circumscribed by the ASC in many mammals). Our study is congruent with this idea, given that large specimens in our sample often have a shallower fossa subarcuata.

Our study also allows us to identify allometric patterns common to our intraspecific series and that are only found in the evolutionary sample that excludes fossil specimens. We detected several common allometric variations among Dasypus, Zaedyus and DatasetExt with respect to the maxillary and palatine (Table 5). With increasing skull size, the dorsoventral height of the maxillary was reduced. We also noted a relative reduction of the maxillary tooth row length at the evolutionary level and in Dasypus (Section 3.1). This allometric pattern was originally proposed in armadillos by [START_REF] Moeller | Allometrische analyse der gürteltier schädel. Ein beitrag zur phylogenie der Dasypodidae Bonaparte, 1838[END_REF]. However, the pattern does not hold in Zaedyus and Cabassous, nor at the evolutionary level when including fossils, which means that it does not represent a clear trend in the group. We also detected a general narrowing of the palatine and its elongation on the midline.

Leaving aside the evolutionary, we also detected common patterns of intraspecific allometry among Dasypus, Zaedyus and Cabassous. These concerned the jugal, the parietal and the squamosal (Table 11). The jugal became relatively shorter and deeper in larger specimens over the course of ontogeny. The parietal was more elongated anteroposteriorly and narrower mediolaterally with increasing skull size in the ontogenetic analyses. On the squamosal, the posterior root of the zygomatic arches assumed a more posterior position in larger specimens at both the ontogenetic and static level (less clear in Cabassous).

Finally, our study also allowed us to detect common allometric patterns in the jugal and nasal of Zaedyus and Cabassous (Table 11). The all edge of the jugal moved posteriorly in older, larger individuals. The frontal process of the nasal was elongated at both the ontogenetic and static levels.

Improvement and perspectives

One limitation of our analysis is the poor sampling in Cabassous compared to the other two species analyzed at both the ontogenetic and static levels. Better sampling for this taxon might potentially reveal allometric patterns that were not supported statistically in our study, especially where p-values were close to the significance threshold. The minimum sample size needed for the study of allometry is not clear in the literature [START_REF] Cobb | Hominins do not share a common postnatal facial ontogenetic shape trajectory[END_REF][START_REF] Cardini | Sample size and sampling error in geometric morphometric studies of size and shape[END_REF][START_REF] Brown | Small sample sizes in the study of ontogenetic allometry; implications for palaeobiology[END_REF], but it is certain that a larger sample size is desirable. However, improving the sampling for this taxon would require more research on the differences that exist between the northern and southern populations of Cabassous unicinctus (Supporting Information 1). In addition, improving the alpha taxonomy of the other two species would also enhance future allometric studies (Section 3.1; Supporting Information 1).

At a more inclusive taxonomic level, it would be interesting to compare the ontogenetic allometric trajectories among the different extant and extinct clades of Cingulata at the evolutionary level [START_REF] Klingenberg | Size, shape, and form: concepts of allometry in geometric morphometrics[END_REF]Esquérré et al., 2017;[START_REF] Wilson | The evolution of ontogenetic allometric trajectories in mammalian domestication[END_REF]. Clearly, our results often suggested different allometric trends, especially for dasypodids with respect to chlamyphorids, at the evolutionary level (Figures 39 & 40). In the present study, Peltephilus appears as a highly divergent specimen in terms of its relationship between shape and size in comparison with other cingulates, and future studies may want to test evolutionary allometric patterns in the group without this taxon.

Allometric analyses at the evolutionary level could also be compared to dietary habits among cingulates. Recently, the study by [START_REF] Hennekam | Morphological divergence in giant fossil dormice[END_REF] revealed that the increase in size of island giants in dormice was accompanied by novel feeding adaptations. Adding this dimension to our evolutionary analyses would be relevant because the giant fossil forms in Cingulata such as pampatheres and glyptodonts are herbivorous, as is the divergent armadillo Peltephilus [START_REF] Vizcaíno | Diet and locomotion of the armadillo Peltephilus: a new view[END_REF][START_REF] Vizcaíno | Functional and phylogenetic assessment of the masticatory adaptations in Cingulata (Mammalia, Xenarthra)[END_REF].

A last perspective relates to Procrustes superimposition and the interpretation of the shape variations obtained that cannot be unambiguously attributed to individual landmarks [START_REF] Klingenberg | How Exactly Did the Nose Get That Long? A Critical Rethinking of the Pinocchio Effect and How Shape Changes Relate to Landmarks[END_REF]. We have described the variations reconstructed for each landmark relative to the other landmarks, from which we tried to infer more general information on shape changes. A possible complementary approach would involve the use of linear distances to explore further covariation patterns in the skull of cingulates.

CHAPTER 4 Exploration of Cranial Covariation Patterns in

Cingulata

« « Quand quelqu'un cherche », dit Siddhartha, « il arrive facilement que ses yeux ne voient que ce qu'il cherche, et il est capable de ne rien trouver, de ne rien recevoir parce qu'il ne pense toujours qu'à la chose qu'il cherche, parce qu'il a un but, parce qu'il est obsédé par son but. Chercher signifie : avoir un but. Mais trouver signifie : être libre, être ouvert, ne pas avoir de but. ». ».

Hermann Hesse. 1922. Siddhartha. Translated.

" 'When someone seeks,' said Siddhartha, 'then it easily happens that his eyes see only the thing that he seeks, and he is able to find nothing, to take in nothing because he always thinks only about the thing he is seeking, because he has one goal, because he is obsessed with his goal. Seeking means: having a goal. But finding means: being free, being open, having no goal.' ".

Hermann Hesse. 1922. Siddhartha.

An exploration of the strongest covariations among cranial distances in

Cingulata ABSTRACT

Morphological integration, the trend for anatomical traits to covary, is a concept that has been intensively explored in recent decades, particularly as it relates to the skull of mammals. A detailed knowledge of morphological integration patterns represents an essential need for morphological phylogenetics, which rely on the independence of the characters analyzed. Towards that aim, it is necessary to analyze integration at several levels (static, ontogenetic, evolutionary)

and on several anatomical scales (e.g., entire skull, individual cranial bones) to gain a global understanding of the cranial covariations that can be shared within and among species. In this study, we explored cranial covariation patterns among pairs of interlandmark distances at the static and ontogenetic levels within three developmental series of phylogenetically distant extant armadillo species belonging to the genera Dasypus, Zaedyus, and Cabassous. We first described a selection of pairs of strongly correlated cranial distances shared by the three species. We showed that, apart from a strong impact of craniofacial allometry, the coordinated variations evidenced by our selection of strongly correlated cranial distances are concentrated around the anterior root of the zygomatic arch, the braincase, the mesocranium and the auditory region. Second, we tested whether the pairs selected within armadillo species are also represent correlated at the evolutionary level (i.e., among species), using a rich sample of extinct and extant cingulate species. Statistically significant evolutionary correlations were again localized to the area around the anterior root of zygomatic arch, a region particularly rich in muscular insertions for mastication and often coded as multiple independent characters in phylogenetic analyses of cingulates. The coordinated variations detected by our exploration of cranial covariation patterns within armadillo species can help to highlight groups of potentially non-independent characters in phylogenetic matrices.

INTRODUCTION

Morphological integration is the tendency of traits to covary within a morphological structure or in an entire organism [START_REF] Klingenberg | Studying morphological integration and modularity at multiple levels: concepts and analysis[END_REF]. Since its modern definition in 1958, the concept of morphological integration [START_REF] Olson | Morphological integration[END_REF] has been extensively studied in evolutionary biology, with renewed interest in the last few decades (e.g., Cheverud, 1982a;[START_REF] Wagner | Perspective: complex adaptations and the evolution of evolvability[END_REF][START_REF] Klingenberg | Morphological integration and developmental modularity[END_REF]Goswami & Polly, 2010b;[START_REF] Wagner | The road to modularity[END_REF][START_REF] Klingenberg | Evolution and development of shape: integrating quantitative approaches[END_REF][START_REF] Klingenberg | Studying morphological integration and modularity at multiple levels: concepts and analysis[END_REF]. Morphological integration, intimately connected to the concept of modularity (see Section 4.2), can be expressed at different biological levels, such as intraspecific (ontogenetic, static) and interspecific (evolutionary) levels [START_REF] Klingenberg | Studying morphological integration and modularity at multiple levels: concepts and analysis[END_REF][START_REF] Klingenberg | Size, shape, and form: concepts of allometry in geometric morphometrics[END_REF]. A promising way to gain a global understanding of morphological integration in a given clade is to analyze the covariation patterns at static and ontogenetic levels (e.g., [START_REF] Mitteroecker | Heterochrony and geometric morphometrics: a comparison of cranial growth in Pan paniscus versus Pan troglodytes[END_REF][START_REF] Bulygina | Ontogeny of facial dimorphism and patterns of individual development within one human population[END_REF][START_REF] Freidline | Ontogenetic and static allometry in the human face: contrasting Khoisan and Inuit[END_REF][START_REF] Chinga | Ontogenetic integration in two species of Schizanthus (Solanaceae): A comparison with static integration patterns[END_REF][START_REF] Goswami | EMMLi: a maximum likelihood approach to the analysis of modularity[END_REF][START_REF] Klenovšek | Modularity and cranial integration across ontogenetic stages in Martino's vole, Dinaromys bogdanovi[END_REF] and see how these align with patterns of evolutionary integration [START_REF] Klingenberg | Studying morphological integration and modularity at multiple levels: concepts and analysis[END_REF]. Several studies have explored and compared patterns of morphological integration at these three different levels in plants (e.g., [START_REF] Armbruster | Multilevel analysis of morphometric data from natural plant populations: insights into ontogenetic, genetic, and selective correlations in Dalechampia scandens[END_REF][START_REF] Armbruster | Does pollen competition reduce the cost of inbreeding?[END_REF][START_REF] Klingenberg | Developmental plasticity, morphological variation and evolvability: a multilevel analysis of morphometric integration in the shape of compound leaves[END_REF] and animals (e.g., [START_REF] Klingenberg | Morphological integration between developmental compartments in the Drosophila wing[END_REF][START_REF] Mitteroecker | Heterochrony and geometric morphometrics: a comparison of cranial growth in Pan paniscus versus Pan troglodytes[END_REF][START_REF] Monteiro | Evolutionary integration and morphological diversification in complex morphological structures: mandible shape divergence in spiny rats (Rodentia, Echimyidae)[END_REF][START_REF] Drake | Large-scale diversification of skull shape in domestic dogs: disparity and modularity[END_REF][START_REF] Urošević | Multilevel assessment of the lacertid lizard cranial modularity[END_REF].

The study of integration patterns in the vertebrate skull has drawn particular attention (e.g., [START_REF] Felice | Developmental origins of mosaic evolution in the avian cranium[END_REF][START_REF] Parsons | Conserved but flexible modularity in the zebrafish skull: implications for craniofacial evolvability[END_REF][START_REF] Watanabe | Ecomorphological diversification in squamates from conserved pattern of cranial integration[END_REF][START_REF] Bardua | Morphological evolution and modularity of the caecilian skull[END_REF][START_REF] Bardua | Evolutionary integration of the frog cranium[END_REF][START_REF] Bon | Cranial integration in the fire salamander, Salamandra salamandra (Caudata: Salamandridae)[END_REF][START_REF] Felice | Evolutionary integration and modularity in the archosaur cranium[END_REF][START_REF] Felice | Decelerated dinosaur skull evolution with the origin of birds[END_REF]. Mammals have been the target of an extensive array of studies on cranial integration and modularity, especially focused on the functional and developmental determinants of covariance (e.g., [START_REF] Bolker | Modularity in development and why it matters to evodevo[END_REF][START_REF] Klingenberg | Developmental constraints, modules, and evolvability[END_REF][START_REF] Monteiro | Evolutionary integration and morphological diversification in complex morphological structures: mandible shape divergence in spiny rats (Rodentia, Echimyidae)[END_REF][START_REF] Klingenberg | Morphological integration and developmental modularity[END_REF]Goswami & Polly, 2010b;[START_REF] Makedonska | The effect of dietary adaption on cranial morphological integration in capuchins (Order Primates, Genus Cebus)[END_REF][START_REF] Santana | Does nasal echolocation influence the modularity of the mammal skull?[END_REF][START_REF] Goswami | EMMLi: a maximum likelihood approach to the analysis of modularity[END_REF][START_REF] Heck | Why the long face? Comparative shape analysis of miniature, pony, and other horse skulls reveals changes in ontogenetic growth[END_REF][START_REF] Churchill | Asymmetry drives modularity of the skull in the common dolphin (Delphinus delphis)[END_REF]. Most of these studies generally analyzed integration and modularity at a global scale, but more rarely explore local aspects such as the covariation between two traits in a given cranial region (e.g., Cheverud, 1982a;[START_REF] Percival | Developmental constraint through negative pleiotropy in the zygomatic arch[END_REF]. Such local covariations could be analyzed directly between landmarks or among interlandmark distances (Cheverud, 1982a;[START_REF] Goswami | Cranial modularity shifts during mammalian evolution[END_REF][START_REF] Zelditch | Building developmental integration into functional systems: function-induced integration of mandibular shape[END_REF][START_REF] Goswami | EMMLi: a maximum likelihood approach to the analysis of modularity[END_REF], although misleading effects of the Procrustes superimposition on the former are possible (Cardini, 2019b). Irrespective of the method used, the characterization of covariation patterns among traits is crucial for a more comprehensive understanding of morphological variation in the skull of mammals [START_REF] Monteiro | Evolutionary integration and morphological diversification in complex morphological structures: mandible shape divergence in spiny rats (Rodentia, Echimyidae)[END_REF][START_REF] Mitteroecker | The evolutionary role of modularity and integration in the hominoid cranium[END_REF][START_REF] Porto | The evolution of modularity in the mammalian skull I: morphological integration patterns and magnitudes[END_REF][START_REF] Marroig | The evolution of modularity in the mammalian skull II: evolutionary consequences[END_REF][START_REF] Jamniczky | Modularity in the skull and cranial vasculature of laboratory mice: implications for the evolution of complex phenotypes[END_REF][START_REF] Klingenberg | Evolutionary covariation in geometric morphometric data: analyzing integration, modularity, and allometry in a phylogenetic context[END_REF]Billet et al., 2015a;[START_REF] Percival | Developmental constraint through negative pleiotropy in the zygomatic arch[END_REF]. A detailed knowledge of cranial covariation patterns also represents an essential need for morphological phylogenetic analyses [START_REF] Goswami | The macroevolutionary consequences of phenotypic integration: from development to deep time[END_REF][START_REF] Billet | Serial Homology and Correlated Characters in Morphological Phylogenetics: Modeling the Evolution of Dental Crests in Placentals[END_REF], which rely on the independence of characters during matrix construction [START_REF] Felsenstein | Maximum likelihood and minimum-steps methods for estimating evolutionary trees from data on discrete characters[END_REF][START_REF] Wilkinson | A comparison of two methods of character construction[END_REF][START_REF] Emerson | Morphological correlations in evolution: consequences for phylogenetic analysis[END_REF][START_REF] Felsenstein | Inferring phylogenies[END_REF]Goswami & Polly, 2010a;[START_REF] Guillerme | Influence of different modes of morphological character correlation on phylogenetic tree inference[END_REF]. Although this knowledge is key to building morphology-based phylogenies, collecting correlation data for every single pair of characters in a large number of taxa seems unrealistic (Goswami & Polly, 2010a, 2010b;[START_REF] Goswami | The macroevolutionary consequences of phenotypic integration: from development to deep time[END_REF]. Modularity analyses could constitute an initial step towards the incorporation of character independence models [START_REF] Goswami | The macroevolutionary consequences of phenotypic integration: from development to deep time[END_REF], but they do not provide a detailed picture of trait covariation patterns.

Xenarthra represent one of the four major clades of extant placental mammals [START_REF] Zachos | Mammalian Phylogenetics: A Short Overview of Recent Advances[END_REF]. Within it, the Cingulata include the extant armadillos and extinct glyptodonts and pampatheres [START_REF] Gaudin | Paleogene Xenarthra and the evolution of South American mammals[END_REF]. Patterns of morphological integration in the skull of cingulates are poorly known, except for a few studies on allometry (e.g., Chapter 3) and covariance structure (e.g., [START_REF] Hubbe | A case study of extant and extinct Xenarthra cranium covariance structure: implications and applications to paleontology[END_REF][START_REF] Porto | The evolution of modularity in the mammalian skull I: morphological integration patterns and magnitudes[END_REF][START_REF] Porto | Size variation, growth strategies, and the evolution of modularity in the mammalian skull[END_REF]. Previous morphology-based phylogenetic studies lack consensus regarding the relationships within Cingulata [START_REF] Engelmann | The evolution and ecology of armadillos, sloths and vermilinguas[END_REF][START_REF] Abrantes | Proposta filogenetica para os Dasypodidae (Mammalia: Cingulata)[END_REF][START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF][START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF][START_REF] Herrera | A new Eocene dasypodid with caniniforms (Mammalia, Xenarthra, Cingulata) from northwest Argentina[END_REF], with tree topologies that conflict in various ways with recent molecular results [START_REF] Delsuc | Molecular phylogenetics unveils the ancient evolutionary origins of the enigmatic fairy armadillos[END_REF][START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF][START_REF] Abba | Systematics of hairy armadillos and the taxonomic status of the Andean hairy armadillo (Chaetophractus nationi)[END_REF][START_REF] Gibb | Shotgun mitogenomics provides a reference phylogenetic framework and timescale for living xenarthrans[END_REF][START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF].

In this study, we present a novel approach to explore cranial covariation patterns at the ontogenetic and static levels, using three growth series from phylogenetically distant extant armadillo species, and at the evolutionary level, using a large extant and extinct diversity of armadillos and their kin. Our two-step approach consists of intraspecific analyses of covariation between interlandmark distances (1) followed by the testing of these covariations at the evolutionary level (2). To our knowledge, this represents the first in-depth (though non-exhaustive) exploration of the strongest cranial covariations present on the mammalian skull at different levels.

The comparison of the patterns found within each of the three species in our sample enables us to highlight shared intraspecific covariation patterns and test if these were also expressed during the morphological evolution of the group, particularly in its most diversified family (i.e., Chlamyphoridae). Based on a landmark sample partly corresponding to traits used in cladistic matrices, our aim is to further explore cranial covariation patterns to provide important information about the degree of independence of these traits before their potential implications for phylogenetic matrices can be evaluated.

MATERIAL AND METHODS

Biological sample

We sampled 118 skulls corresponding to four extant species belonging to three out of four extant clades recognized within the order Cingulata (see below). The material studied is a recomposition of the specimens used in Chapter 3 (see Table S22 for a complete list of specimensfor Dasypus novemcinctus, we selected only the southern morphotype (SM) to ensure that we remain at an intraspecific level). Our sample includes four species, with two species gathered into the same series. Each series is divided into a dataset for the ontogenetic level (juvenile to adultsee Chapter 3 for ontogenetic determination) and for the static level (adult stages only): Dasypus novemcinctus. (nontogenetic = 48, nstatic = 33; Southern morphotype, [START_REF] Huchon | Armadillos exhibit less genetic polymorphism in North America than in South America: nuclear and mitochondrial data confirm a founder effect in Dasypus novemcinctus (Xenarthra)[END_REF][START_REF] Gibb | Shotgun mitogenomics provides a reference phylogenetic framework and timescale for living xenarthrans[END_REF][START_REF] Billet | The hidden anatomy of paranasal sinuses reveals biogeographically distinct morphotypes in the nine-banded armadillo (Dasypus novemcinctus)[END_REF][START_REF] Hautier | Beyond the carapace: skull shape variation and morphological systematics of long-nosed armadillos (genus Dasypus)[END_REF][START_REF] Feijó | Taxonomic revision of the long-nosed armadillos, Genus Dasypus Linnaeus, 1758 (Mammalia, Cingulata)[END_REF][START_REF] Feijó | Phylogeny and molecular species delimitation of long-nosed armadillos (Dasypus: Cingulata) supports morphology-based taxonomy[END_REF][START_REF] Arteaga | Conservation Genetics, Demographic History, and Climatic Distribution of the Nine-Banded Armadillo (Dasypus novemcinctus): An Analysis of Its Mitochondrial Lineages[END_REF]; Zaedyus pichiy (nontogenetic = 43, nstatic = 23); Cabassous unicinctus and Cabassous centralis (see below).

Our sample of Cabassous contains specimens identified as Cabassous unicinctus (n = 15) and Cabassous centralis (n = 4) based on geographical data, and several specimens that could not be unambiguously attributed to one of these two species (n = 8), which are weakly divergent morphologically and only weakly differentiated on a molecular basis (Hayssen, 2014;[START_REF] Gibb | Shotgun mitogenomics provides a reference phylogenetic framework and timescale for living xenarthrans[END_REF]; Supporting Information 1) as explained in Section 3. were improved in contrast, rotated, cropped, and reduced to 8 bits to facilitate the 3D specimen acquisition using the ImageJ software [START_REF] Schneider | NIH Image to ImageJ: 25 years of image analysis[END_REF]. Three-dimensional reconstruction and visualization of the skulls were performed using modified stacks of digital images with MIMICS v. 21.0 software (3D Medical Image Processing Software, Materialize, Leuven, Belgium). Cranial shapes were quantified with the 114 anatomical landmarks used in Section 3.2 and placed on the exported 3D models using AVIZO v. 9.7.0 software (Visualization Sciences Group, Burlington, MA, USA). The same corrections as in Section 3.2 have been made in this section regarding the consideration of asymmetry. Analyses at the evolutionary level have been performed on the Dataset-Lmax, which is described in Section 3.2.

Size standardization

Size can significantly affect the analysis of covariation patterns among linear measurements, especially at the ontogenetic level. We used the log shape ratio approach to isolate the shape and size components from our set of linear measurements [START_REF] Mosimann | Size allometry: size and shape variables with characterizations of the lognormal and generalized gamma distributions[END_REF][START_REF]Morphometrics with R[END_REF][START_REF]Log-shape ratios, Procrustes superimposition, elliptic Fourier analysis: three worked examples in R. Virtual Morphology and Evolutionary Morphometrics in the new millennium[END_REF]. First, the set of interlandmark distances was calculated for each specimen and the geometric mean of all these measurements was used to define its size (geosize; Claude, 2008), using the following equation:

𝑔𝑒𝑜𝑠𝑖𝑧𝑒 = √∏ 𝐷𝑖 𝑁 𝑖=1 𝑁
The geometric mean of a specimen thus corresponds to the Nth root of the product of all the distances (D) of a specimen where N is defined by the number of possible distances for a given set of landmarks (= n) such that 𝑁 = 𝑛(𝑛-1)

2

. Unfortunately, for large datasets, the product of the set of distances reaches numbers far too high for classical computers to compute their root. Therefore, the order of the equation was changed in the following manner as initially proposed by Claude ( 2008):

𝑔𝑒𝑜𝑠𝑖𝑧𝑒 = ∏ √𝐷𝑖 𝑁 𝑁 𝑖=1
The overall calculation is the same, but the sequence changes so that the size of N no longer becomes an obstacle to the computation of the geometric mean. For the computation of the log shape ratios, we then divided each interlandmark distance (Dx) by the geometric mean (Gy) of the specimen (Claude, 2008)the logarithm of this ratio (log (Dx/Gy)) was then used in subsequent analyses.

Selection of pairs of correlated standardized distances

We explored the existence of significant correlations between pairs of standardized interlandmark distances (computed as log shape ratios and named S-distances hereafter) in each dataset of Dasypus, Zaedyus and Cabassous, in order to detect the strongest correlations. For each data set (n = 114 landmarks), the number N of interlandmark S-distances obtained was equivalent to 6441, which means more than 20 million of pairs of distances (= 𝑁(𝑁-1)

2

). First, we produced matrices of interlandmark distances for each specimen and we selected only one half of the skull (left side) to reduce the number of variables. After standardization with the log shape ratio (see above), we used the following criteria and levels of thresholding for statistical parameters to select the strongest correlations among the large number of pairs of S-distances in each dataset. First, we excluded pairs of S-distances with shared landmarks because their correlation can be partly induced by the variation of only one of their three defining landmarks, and thus due not only to a coordinated variation of several landmarks. Second, for each dataset, we calculated the correlation coefficient r for each remaining pair of S-distances (log (Dx/Gy)) and we arbitrarily selected the pairs of S-distances with |r| > 0.71 (i.e., square of the correlation coefficient (R²) > 0.5). This thresholding enabled us to achieve a compromise between the need to reduce of the number of pairs to be analyzed, and the desire to explore a wide spectrum of the strongest covariations. Third, we performed analyses of standardized major axis regression (= SMA; [START_REF] Warton | Common slope tests for bivariate errors-in-variables models[END_REF][START_REF] Warton | Bivariate line-fitting methods for allometry[END_REF][START_REF] Warton | smatr 3-an R package for estimation and inference about allometric lines[END_REF] on these selected pairs, thus assuming the absence of an independent variable. We selected only the pairs of S-distances whose correlation was significantly statistically supported (p-value < 0.05). At the end of this selection process, the SMA regressions of each supported pair of S-distances were compared among the three species, and only shared correlations were retained for description (i.e., correlation supported in Dasypus, Zaedyus and at least one dataset for Cabassous = DZC comparison). We also retained for the description the correlations only shared by the more closely related Zaedyus and Cabassous (at least one dataset) (= ZC comparison). We used this rationale because our aim was to retain only intraspecific correlations shared among species, which was more interesting for phylogenetic purposes (see

General Discussion & Conclusion

). Among these, we discarded pairs that included S-distances that were closely parallel or overlapping, because they may not signal a coordinated change in shape (e.g., pairs related to skull lengthening; Figure S34) and were thus not deemed most informative for the purposes of our study. Pairs with contrasting signal among species (e.g., positive vs negative correlation) were also not retained for description because they do not induce the same anatomical variation. We also discarded pairs that signaled an increase in the length of the snout relative to a decrease in the proportions of the neurocranium, as it is a pattern corresponding to the craniofacial allometry already well-known in mammals and now in cingulates as well (Cardini, 2019a; Chapter 3; Figure S34). Finally, because many linear S-distances were in part parallel and overlapping, several selected pairs were redundant, i.e. they highlighted the same anatomical information in terms of cranial covariation. In such cases, only one pair was then chosen for description, and the redundant pairs were summarized in Table 12 and listed in Tables S23-S26. The correlation among the pairs of S-distances selected for description was subsequently scrutinized among the corresponding raw distances (R-distances) in order to evaluate the allometric or isometric nature of the covariation (since the standardization of S-distances affects the values of the slopes)2 . These analyses were performed at the ontogenetic and static levels.

Finally, we analyzed the selected pairs with the same analyses at the evolutionary level, considering both S-distances and R-distances. The R script used is available in Supporting information 5.

RESULTS

The total number of pairs of correlated S-distances above our threshold criteria is shown in Figure S44 for each species at the ontogenetic and static level.

Selected pairs of correlated S-distances and R-distances common to all three species (DZC) Ontogenetic level

According to our selection criteria, 1558 pairs of correlated S-distances on the skull are common to all three species (Table S27). The set of pairs signaling a skull lengthening or craniofacial allometry correspond to 98% of these pairs (Figure S34; Table S27). Among the remaining selected pairs (= 38, Table S23), several carry the same kind of anatomical information (see below) and all essentially involve the braincase while the face lacks any of these selected pairs. After carefully checking for redundancy among pairs, most of the anatomical information carried by the 38 selected pairs can be tentatively summarized by the 3 pairs presented in Figure 45 and Tables 12 & 13 and briefly described below (similar pairs at other levels or the number of redundant pairs are listed in Table 12).

The pair n°1 shows a coordinated variation between the S-distance from the triple contact alisphenoid -squamosal -frontal (#42) to the intersection between the frontoparietal suture and the midline (#66), and the S-distance between the triple contact frontal -parietal -squamosal (#69)

and the most dorsal point of the annular ridge (#97) (Figure 45). The scrutiny of the correlation between the corresponding R-distances suggests a more rapid horizontal (#69-97) than dorsoventral (#42-66) growth of the front of the braincase in Zaedyus and Cabassous, whereas the opposite is the case in Dasypus (Table 14). Overall, it suggests a coordinated variation of the oblique height of the anterior part of the braincase with its subhorizontal dimensions, terminating at the annular ridge dorsoanteriorly. Several other pairs of S-distances express similar covariation in the dorsorostral part of the braincase (Table 12, Table S23). This coordinated variation is also supported by other pairs found at the ontogenetic and static levels in the ZC analyses below (Table 12, Table S23). Each distance pair is numbered in relation to Table 13 and the colors distinguish the different pairs. Covarying distances ending with bars are isometric. Pairs in which one of the two distances has arrows pointing towards the landmarks are allometric, the distance with arrows being the one increasing the fastest (see Table 14). Scale = 1 cm.

Table 12. Summary of the anatomical information provided by the selected pairs at the ontogenetic and static level for DZC and ZC (Tables 13 &14) and their concordance with the evolutionary level (Table 15) (see text). Numbered pairs are described in the text. Pairs not described but presenting similar information are indicated by an asterisk (*) and are detailed in Tables S27-S30. Abbreviations: Allom., allomrtic; intrasp., intraspecific level; Isom., isometric; onto., ontogenetic. Faster growth of the mesocranium than of the ventral part of the braincase.

Dasypus

- ------------------------ 14). Several other pairs express similar covariation in the analysis of S-distances, almost always involving the dorsal and ventral edges of the annular ridge (Table 12, Table S23). Overall, it suggests that the dorsal part of the annular ridge moves away from the occiput (tentorial process) at a quicker pace than the ventral part of the annular ridge in chlamyphorids. This coordinated variation is also supported by two pairs at the DZC static level (Table 12, Tables S23 -S24).

The pair n°3 shows a coordinated variation between the most anterodorsal point of the optic foramen (#65) and the most ventral point of the external aperture of cochlear canaliculus (#92) and the most anteromedial point of the foramen acusticum inferius (#106) with the most dorsal point of the internal posterior aperture of the optic canal (#112). Scrutiny of the correlation between the corresponding R-distances suggests a faster growth of the distance linking the internal posterior aperture of the optic canal to the petrosal than of the distance linking the same bone with the anterior external opening of the same canal (Figure 45; Table 14 potential isometry in Dasypus).

An examination of the extreme specimens of each species reveals that, when the two S-distances grow relative to the geometric mean of the skull, the posterior internal opening of the optic canal takes a more anterior and lateral position than its external opening and the overall course of the optic canal reorients slightly more transversely (Figure S36). In other words, this suggests that as the optic canal becomes more distant from the basicranium, reduces its length and assumes a more transverse orientation (Figure S36). This coordinated variation is supported by several selected pairs in this analysis, but also at the DZC static level and at the ZC ontogenetic and static levels for in which other adjacent landmarks of the optical canal may also be involved (e.g., n°46sphenorbital fissure; Table 12, Tables S23-S26).

Static level

According to our selection criteria, 1670 pairs of correlated S-distances on the skull are common to all three species at the static level (Table S28). When excluding pairs corresponding to skull lengthening, craniofacial allometry and poorly informative variation (= 99% of pairs; see Material & Methods), there remain only nine selected pairs (Table S24). These pairs essentially involve the anterior part of the zygomatic arches, the ventral part of the orbitotemporal region, and the auditory region. Four correspond to anatomical variations already discussed at the ontogenetic level regarding the optic canal and the middle and caudal crania fossae (Table 12, Tables S23 &S24). For the remaining five pairs, most of the anatomical information they carry can be summarized by the two pairs presented in Figure 46 and Tables 12 & 13 and discussed below.

The pair n°4 shows coordinated variation between the S-distance from the anteroventral margin of the lacrimal foramen (#38) to the most posterolateral point of the jugular foramen (#80)

and the S-distance between the intersection between anterior orbital edge and jugal/lacrimal suture (#50) and the most ventral point of the external aperture of the cochlear canaliculus (#92). Scrutiny of the correlation between the corresponding R-distances suggests a more rapid growth of the distance connected to the jugal-lacrimal suture than of the distance connected to the more dorsal lacrimal foramen, especially in Dasypus and Zaedyus, whereas in Cabassous this coordinated variation is very close to isometry (Figure 46, Table 14). Overall, it suggests a faster growth of the distance connected to the more ventral part of the anterior orbital edge compared to its more dorsal part in a direction opposite the auditory region in Dasypus and Zaedyus. Three other pairs express similar covariation with S-distances (Table 12, Table S24). In complementary fashion, the pair n°5

shows a coordinated variation between the S-distance from the landmark #50 to the most anterior point of the fenestra vestibuli (#94) and the S-distance linking the intersection between jugal/maxillary suture and anteroventral base of the zygomatic arch (#21) and the most anterior point of the epitympanic wing of the petrosal (#108). Scrutiny of the correlation between the corresponding R-distances suggests a more rapid growth of the distance connected to the anteroventral base of the zygomatic arch in comparison to that connected to its anterodorsal margin (lacrimal-jugal suture) especially in Zaedyus and Cabassous (Table 14).

Taken together, the pairs 4 and 5 therefore suggest, at least in Zaedyus, a more rapid increase of the distances connected to the ventral parts of the anterior root of the zygomatic arch and orbital edge, as compared to those connected to their respective dorsal parts, in a direction opposite the auditory region. To better understand this, we checked the relative positions of the relevant landmarks in extreme specimens for this covariation (Figures S37 -S38). For both pairs, the points in the auditory region move very slightly in relation to each other in all three species (Figure S37 -S38), which suggests that it is the variation of the landmarks in front of the zygomatic arch which may drive these correlations. For pair n°4, the more ventral landmark on the anterior root of the zygomatic arch is shifted relatively more anteriorly than the more dorsal one in specimens with maximal values of S-distances (Figure S37). For pair n°5, the more ventral landmark seems to be shifted more ventrally in Dasypus and Zaedyus, but not Cabassous (Figure S38). This coordinated variation is also supported by other pairs found at the static levels in the ZC analyses below (Table 12, Table S26). 13 and the colors distinguish the different pairs. Covarying distances ending with bars are isometric. Pairs in which one of the two distances has arrows pointing towards the landmarks are allometric, the distance with arrows being the one increasing the fastest (see Table 14). Scale = 1 cm.

Selected pairs of correlated S-distances and R-distances common to Zaedyus and

Cabassous (ZC) Ontogenetic level

According to our threshold criteria, 197 pairs of correlated S-distances on the skull are common to the two species (Table S27). When excluding pairs corresponding to skull lengthening, craniofacial allometry and poorly informative variation (= 48% of pairs), the remaining selected pairs number 103 (Table S25). Most of these pairs concern the orbitotemporal region and connect the posterior half of the snout, the anterior part of the zygomatic arch and several regions of the braincase. Of these, 85 are redundant with anatomical variation presented for DZC. For the other pairs, most of the anatomical information they carry can be summarized by the four covariations presented in Figure 47 and Tables 12 &13.

Pair n°6 shows coordinated variation between the S-distance from the intersection between maxillary/palatine suture and lateral edge of palate (#19) and the triple contact point between the supraoccipital/exoccipital/petrosal (#78) and the S-distance between the most posterior point of the alveolar margin of the tooth row (#29) and the most anteroventral point of mastoid process (#90). Scrutiny of the correlation between the corresponding R-distances suggests that the mesocranium (portion of the skull base between the palate and ear region; [START_REF] Wible | The eutherian mammal Maelestes gobiensis from the Late Cretaceous of Mongolia and the phylogeny of Cretaceous Eutheria[END_REF] grows at a faster pace than the ventral part of the braincase in Zaedyus, whereas Cabassous exhibits isometric growth (Table 14). Two other pairs express similar S-distance covariation (Table 12, Table S25). This coordinated variation of these S-distances is far from being statistically supported in Dasypus, but with R-distances the trend is similar to Zaedyus (Tables 12 &14).

Pair n°7 shows coordinated variation between the S-distance from the intersection between jugal/maxillary suture and ventral edge of zygomatic arch (#21) and the dorsal intersection of annular ridge and midline (#97) and the S-distance between the triple contact point between maxillary/jugal/lacrimal (#48) with the dorsal intersection between cribriform plate and median septum posterior to the latter (#98). Scrutiny of the correlation between the corresponding Rdistances suggests isometric growth of the cranium in the dorsomedial-ventrolateral direction at 197 the level of the anterior edge of the orbit, and more posteriorly at the level of the midlength of the orbit and most ventral point of the zygomatic arch (Table 14; but possibly allometric in CabassousNS). In other words, this pair suggests coordinated isometric growth for distances linking the zygomatic arch and cranial roof in the vicinity of the orbit. This coordinated variation is significantly supported but with a poor correlation between S-distances in Dasypus (Table 13), which also exhibits an isometric relation of R-distances (Table 14). Each distance pair is numbered in relation to Table 13 and the colors distinguish the different pairs. Covarying distances ending with bars are isometric. Pairs in which one of the two distances has arrows pointing towards the landmarks are allometric, the distance with arrows being the one increasing the fastest (see Table 14). Scale = 1 cm.

Pair n°8 shows coordinated variation between the S-distance from the most anteroventral point of the foramen ovale (#60) and the intersection between frontal/parietal suture and the midline (#66) and the S-distance between landmark #97 and the most dorsal point of the internal posterior aperture of the optic canal (#112). Scrutiny of the correlation between the corresponding R-distances suggests a faster growth of the anterior part of the braincase height just posterior to the orbit than its height at the level of the foramen ovale posteriorly (Table 14; but not in CabassousN). Three other pairs express similar covariation among S-distances (Table 12, Table S25). It is also well-supported in Dasypus, with a moderate fit to the regression line (Table 13).

With R-distances, Dasypus shows an opposite allometric trend to that of Cabassous and Zaedyus (Table 14). A complementary pattern is provided by pair n°9, which shows coordinated variation between the S-distance from the most anterior point of the fenestra vestibuli (#94) and landmark #97 and the S-distance between landmark #66 and the most ventromedial point on the annular ridge lateral to posterior median septum (#114). Scrutiny of the correlation between the corresponding R-distances suggests a faster growth of the height of the braincase just posterior to the olfactory bulbs than the oblique diameter of the braincase from the annular ridge to the auditory region (Table 14). This coordinated variation is significantly supported but with a poor correlation between S-distances in Dasypus, which shows the same allometric trend with R-distances (Tables 13 &14). The two pairs described above, and their associated pairs suggest a faster growth in height of the anterior part of the braincase compared to the rest of the braincase in Cabassous and

Zaedyus. Nine other pairs express similar covariation with S-distances (Table 12, Table S25).

Many coordinated variations concern this anatomical region and show the same information at the static level in ZC analysis (= 28 pairs are concerned, Table 12).

Static level

According to our threshold criteria, 403 pairs of correlated S-distances on the skull are common to the two species (Table S28). When excluding pairs corresponding to skull lengthening, craniofacial allometry and poorly informative variation (= 79% of pairs), the remaining selected pairs number 82. Most of the covarying linear S-distances concern the posterior edge of the palatal region and connect the posterior half of the snout, the anterior part of the zygomatic arch, the orbitotemporal region and several regions of the braincase. Of these, 69 are redundant with anatomical variation presented for DZC and for the ontogenetic level of ZC. For the other pairs, most of the anatomical information they carry can be summarized by the three covariations presented in Figure 48 and Tables 12 &13. 13 and the colors distinguish the different pairs. Covarying distances ending with bars are isometric. Pairs in which one of the two distances has arrows pointing towards the landmarks are allometric, the distance with arrows being the one increasing the fastest (see Table 14). Scale = 1 cm.

Pair n°10 shows coordinated variation between the S-distance from the intersection between maxillary/palatine suture and lateral edge of palate (#19) and the intersection between jugal/maxillary suture and ventral edge of zygomatic arch (#21) and the S-distance between the intersection between palatine/maxillary suture and the palate midline (#17) and the triple contact point between maxillary/jugal/lacrimal (#48). Scrutiny of the correlation between the corresponding R-distances suggests a more rapid growth in width between the posterolateral edge of the palate and the ventral base of the zygomatic arch than between the central part of the palate and the anterodorsal edge of the zygomatic arch (Figure 48, Table 14). This is particularly true for Zaedyus, less so for Cabassous which is closer to isometry for this selected pair with R-Distances.

Four other pairs express similar S-distance covariation (Table 12, Table S26). This allometric variation is not significant in Dasypus (Table 13).

Pair n°11 shows coordinated variation between the S-distance from the landmark #19 and the most anteroventral point of the foramen ovale (#60) and the S-distance between the most posterior point of the alveolar margin of the tooth row (#29) and the most ventral point of the external aperture of cochlear canaliculus (#92). Scrutiny of the correlation between the corresponding R-distances suggests a more rapid growth of the mesocranium (length and/or height of the entopterygoid process) than of the distance linking the basicranium to the posterior edge of the palate (Figure 48). Five other pairs express similar covariation with S-distances (Table 12, Table S26). This allometric variation is complementary to the pair n°6 found at the ZC ontogenetic level (Table 12; Figure 48). This allometric variation approaches but is not significant in Dasypus and shows isometry with R-distances (Tables 13 &14).

Pair n°12 shows coordinated variation between the S-distance from the landmark #19 and the most dorsal point of the maxillary foramen (#23) and the S-distance between the most posterior median point of the palatine (#30) and the anteroventral margin of the lacrimal foramen (#38).

Scrutiny of the correlation between the corresponding R-distances suggests a much faster growth of the region between the posterolateral edge of the palate and the maxillary foramen than of the larger and more dorsal area contained between the anterior edge of the orbit and the posteromedial edge of the palate (Table 14). Another pair shows similar covariation with S-distances (Table 12, Table S26). This allometric variation is significantly supported but with a poor correlation between S-distances in Dasypus, and R-distances shows the same allometric variation as in Cabassous and Zaedyus (Tables 13 &14).

Testing the selected pairs of correlated distances at the evolutionary level

The analysis at the evolutionary level allowed us to test whether the pairs of correlated Sdistances selected at the intraspecific level were also correlated at the evolutionary level among cingulates (Table 15, Figure 49 & Figure S39). Pairs n°1, 8 and 12 are below the threshold criterions used at the intraspecific levels, and there is no statistically supported correlation for pair n°9 (Table 15). All other pairs are strongly supported at this level. In addition to the slopes provided by the R-distances, the distribution of species in plots of S-distances is described to see if it can provide additional information on the variation of these distances at the evolutionary level.

The R-distances for pair n°1 show a more rapid growth of the oblique height of front of the braincase than its subhorizontal dimensions as observed in Dasypus (Table 15). The distribution of species in the morphospace shows low S-distances for glyptodonts, Vassallia and euphractines, whereas Peltephilus, dasypodines, and some tolypeutines and chlamyphorines show the highest Sdistances (Figure 49). The allometric variation observed for the R-distances suggests that the oblique height of the anterior part of the braincase is relatively larger compared to its subhorizontal dimensions in larger taxa.

The R-distances for pair n°2 show isometrically coordinated variation of the dorsal part of the vault with that of the oblique ventral axis of the middle and caudal cranial fossae (Table 15).

The distribution of the species with S-distances does not show any particular pattern except for Glyptodon, which possesses a relatively small braincase anteroposteriorly compared to other cingulates (Figure 49).

The R-distances for pair n°3 show isometrically coordinated variation of the distance linking the internal posterior aperture of the optic canal to the petrosal with the distance linking the same bone with the anterior external opening of the same canal (Table 15). The distribution of species with S-distances shows that euphractines, Peltephilus and some tolypeutines have the highest values and thus an optic canal relatively distant from the basicranium, whereas some dasypodines and glyptodonts have the lowest S-distances (Figure 49).

The R-distances for pair n°4 show an isometrically coordinated variation of the distance connected to the jugal-lacrimal suture with the distance connected to the more dorsal lacrimal foramen as obtained above in Cabassous at the static level (Table 15). The distribution of species in the morphospace seem to closely parallel size proportions among cingulates, with chlamyphorines and dasypodines showing the lowest S-distances, and large fossil taxa having the highest S-distances (Figure 49). This indicates that large taxa have an anterior root of the zygomatic arch relatively more distant from the basicranium than small taxa.

The R-distances for pair n°5 show a more rapid growth of the distance connected to the anteroventral base of the zygomatic arch (jugal/maxillary suture) in comparison to that connected to its anterodorsal margin (lacrimal-jugal suture) as observed at the intraspecific level (Table 15).

The distribution of species in the morphospace shows that large species have the highest Sdistances, and dasypodines the smallest (Figure 49). This indicates that large species have an anterior root of the zygomatic arch relatively more distant from the petrosal than dasypodines. The allometric variation observed for the R-distances suggests, in turn, that the distance (#21-108) connected to the anteroventral base of the zygomatic arch is relatively larger compared to distance #50-94 in larger taxa. This difference is clearly visible among the species with the shortest Sdistances (dasypodines -Figure 49) and those with the highest (the glyptodonts -Figure 49) (Figure 50). In large species, such as glyptodonts, the anteroventral base of their zygomatic arch is shifted more ventrally, with a long descending process of the maxillary and a slightly more dorsal position of the most anterior point of the epitympanic wing of the petrosal (#108), which may, at least partly, explain the observed allometric pattern.

The R-distances for pair n°6 show that the distance on the mesocranium (i.e., #19-78) increases at a faster pace than that on the ventral part of the braincase (Table 15). The distribution of species in the morphospace shows a relatively clear distinction between the dasypodines presenting the highest S-distances and Peltephilus, the tolypeutine Priodontes, and the chlamyphorines characterized by the lowest S-distances (Figure 49). This indicates that dasypodines have a relatively elongated palatal region posterior to the tooth row. The allometric variation observed for the R-distances suggests, in turn, that the distance focused on the mesocranium (i.e., #19-78) is relatively larger compared to the distance on the ventral part of the braincase (i.e., #29-90) in larger taxa.

Table 15. Summary statistics of the standard major axis regression (SMA) for the pairs of correlated log(R-distances) and S-distances selected for description at the evolutionary level (with Dataset-Lmax). Each distance is indicated by the landmarks that define it. The lower and upper limit of the slope are estimated with the construction of a confidence interval of 95%. The R 2 and the P-value for R-distances are indicated but not discussed. The R-distances for pair n°7 show isometric growth between the distances linking the zygomatic arch and cranial roof in the vicinity of the orbit, as observed at the intraspecific level (Table 15). The distribution of species in the morphospace does not reveal major differences among the clades, except that the lowest values are found in some dasypodines and the highest values are found in glyptodonts and Vassalia (Figure 49).

The R-distances for pair n°8 show a slower growth in height of the anterior part of the braincase just posterior to the orbit than its height posteriorly, at the level of the foramen ovale as observed in Dasypus but in contrast to the pattern in Cabassous and Zaedyus (Table 15). The distribution of species in the morphospace shows that chlamyphorines and some tolypeutines and dasypodines have the highest S-distances, and thus a relatively high braincase, whereas euphractines, Vassallia and glyptodonts have the lowest S-distances (Figure 49). Glyptodon stands out with a particularly low #97-112 S-distance, and thus a very low anterior height of the braincase.

The allometric variation observed for the R-distances suggests, in turn, that the anterior height of the braincase (#97-112) is relatively smaller compared to the more posterior height (#60-66) in large taxa. Glyptodon deviates from this trend towards even smaller proportions for the anterior height of the braincase. 13. Covarying distances ending with bars are isometric. Pairs in which one of the two distances has arrows pointing towards the landmarks are allometric, the distance with arrows being the one increasing the fastest (see Table 15). Scale = 1 cm.

The R-distances for pair n°10 show a more rapid growth in width between the posterolateral edge of the palate and the ventral base of the zygomatic arch than between the more central part of the palate and the anterodorsal edge of the zygomatic arch, as observed at the intraspecific level (Table 15). The distribution of species in the morphospace reveal much higher S-distances in glyptodonts, Vassallia and chlamyphorines (Figure 49), which have a relatively large area between their palate and anterior root of zygomatic arch. The allometric variation observed for the R-distances suggests, in turn, that the width between the posterolateral edge of the palate and the ventral base of the zygomatic arch is relatively larger compared to the width between the more central part of the palate and the anterodorsal edge of the zygomatic arch in larger taxa (Figure 51). However, chalmyphorines show values close to those of glyptodonts which also suggests a strong phylogenetic signal (Figure 49).

The R-distances for pair n°11 show a more rapid anteroposterior growth of the mesocranium than of the distance linking the basicranium to the posterior edge of the palate, as observed for Cabassous and Zaedyus at the intraspecific level (Table 15). The distribution of species in the morphospace is similar to that of pair n°6 (see above) (Table 15). Likewise, the allometric variation observed for the R-distances suggests, in turn, that the distance focused on the mesocranium (#29-92) is relatively larger compared to the distance from the palate to the basicranium in larger taxa, which is similar to the condition in pair n°6.

Finally, the R-distances for pair n°12 show a much faster growth of the distance between the posterolateral edge of the palate and the maxillary foramen than of the distance between the anterior edge of the orbit and the posteromedial edge of the palate, as observed at the intraspecific level (Table 15, Figure 51). The distribution of species in the morphospace shows a clustering of dasypodines, Peltephilus and most tolypeutines at low values of S-distances, whereas the highest S-distances are found in glyptodonts, Vassallia, chlamyphorines and euphractines, which therefore have a relatively large area between their posterior palate and their orbit and maxillary foramen (Figure 49). This is in part reminiscent with the variation seen in pair n°10 (see above). The allometric variation observed for the R-distances suggests, in turn, that the distance between the posterolateral edge of the palate and the maxillary foramen is relatively larger compared to the distance between the anterior edge of the orbit and the posteromedial edge of the palate in larger taxa, as shown in Figure 51. 15). Scale = 1 cm.

DISCUSSION

Methodological considerations

The exceedingly large amount of data resulting from the exploration of correlations among interlandmark distances led us to define threshold criteria in the selection process of correlated Sdistance pairs. Our study was thus non-exhaustive and focused on the strongest correlations, using threshold values that revealed readily detectable, widespread and strong cranial covariations within Cingulata. Future studies may want to lower these thresholds in order to uncover a larger proportion of correlations among cranial distances in the group. In the future, this approach could probably be automated with higher computing power, which would make it possible to process data more rapidly and cover as many pairs as possible. They might also take into account the effect of the phylogeny using phylogenetic comparative methods when searching for covariations at the evolutionary level [START_REF] Klingenberg | Evolutionary covariation in geometric morphometric data: analyzing integration, modularity, and allometry in a phylogenetic context[END_REF]; see also a comment on this method and our approach in the introduction of Section 3.2).

In addition, other avenues of research to explore morphological integration in detail could include the use of methods of geometric morphometrics such as Partial Least Squares (2Block -PLS; e.g., [START_REF] Bookstein | Cranial integration in Homo: singular warps analysis of the midsagittal plane in ontogeny and evolution[END_REF][START_REF] Klingenberg | Developmental integration in a complex morphological structure: how distinct are the modules in the mouse mandible?[END_REF][START_REF] Monteiro | Evolutionary integration and morphological diversification in complex morphological structures: mandible shape divergence in spiny rats (Rodentia, Echimyidae)[END_REF][START_REF] Klingenberg | Evolutionary covariation in geometric morphometric data: analyzing integration, modularity, and allometry in a phylogenetic context[END_REF][START_REF] Barbeito-Andrés | Prenatal development of skull and brain in a mouse model of growth restriction[END_REF], which could be valuable in understanding the shape changes linked to a covariation when two covarying blocks have been pre-identified.

This approach would be particularly relevant to shed light on the anatomical covariations indicated by our selected pairs. In several cases, such as for pair n°12, the interpretation of the anatomical changes causing the two distances to covary remains difficult. For a PLS analysis of pair n°12, one could try various constructions of two blocks of landmarks spanning over the anterior root of the zygomatic arch and the posterior edges of the palate to understand further the covariation detected, both within and among species.

Shared cranial covariations in cingulates

Our exploratory approach revealed that extant species of armadillos in our sample share a variety of intraspecific, strongly correlated intracranial distances, most of which were also significantly supported at the evolutionary level. Most of these correlations have an allometric component and some are partially consistent with our results on cranial allometry. For example, pair n°10 (Figures 48 & 51) involves a strong mediolateral enlargement of the ventral part of the temporal fossa in larger specimens, which is partially consistent with the greater separation between the zygomatic arches and postorbital constriction in larger specimens in our exploration of cranial allometry (Chapter 3). Almost all the pairs of correlated distances selected for description here locate exclusively in the posterior half of the cranium, whereas statistically supported pairs with at least one distance on the anterior part of the face (landmarks 1-16) all relate to craniofacial allometry (Chapter 3); i.e., they always involve one distance on the face and one on the neurocranium. In other words, there was no intrafacial pair of correlated S-distances detected above our selection criteria. A possible explanation for this result is that craniofacial allometry could constrain the morphological variation of the whole face so strongly (e.g., [START_REF] Cardini | Larger mammals have longer faces because of size-related constraints on skull form[END_REF][START_REF] Ledevin | Patterns and constraints of craniofacial variation in Colobine monkeys: disentangling the effects of phylogeny, allometry and diet[END_REF][START_REF] Monson | Patterns and magnitudes of craniofacial covariation in extant cercopithecids[END_REF] that it reduces the possibility of having other strong covariation patterns on the face [START_REF] Cardini | Larger mammals have longer faces because of size-related constraints on skull form[END_REF]. We can also assume that the whole face can present strong covariations controlled by the diet/function (see below). An alternative or complementary explanation is given by Cheverud (1982a) who revealed that the facial units he detected on the skull of rhesus macaque are not genetically independent but complementary, contrary to neurocranial units, which are more independent. This relationship of genetic dependence in the face could further explain why a single strong covariation pattern (craniofacial allometry) is obtained for facial pairs, whereas the regions of the neurocranium were more susceptible to vary and covary in different combinations and directions due to their relative genetic independence. In addition, bones of the face are impacted by developmental processes, such as neural crest migration, neural crest patterning, facial outgrowth and fusion, earlier than bones of the neurocranium in ontogeny (i.e., during prenatal growth; [START_REF] Hallgrímsson | Deciphering the palimpsest: studying the relationship between morphological integration and phenotypic covariation[END_REF], possibly because they ossify first [START_REF] Hautier | Skeletal ossification and sequence heterochrony in xenarthran evolution[END_REF]. It is possible that patterns of covariation due to early developmental processes on the face are expressed in young armadillos, but are subsequently hidden in more mature specimens by the superimposition of other overarching patterns such as craniofacial allometry. This hypothesis could be verified in armadillos with an analysis of prenatal specimens. Most importantly, it is also possible that pairs of correlated distances on the face could be found just below the threshold criteria in our sample. Therefore, whether there is an underrepresentation of pairs of covarying distances on the face in armadillos should be carefully examined with lower threshold criteria.

Based on our selection criteria, our study described twelve selected pairs of correlated distances at the intraspecific level, that are shared among three distantly related species of armadillos (Table 12). When tested at the evolutionary level, only one of these pairs (pair n°9) no longer presents a statistically supported correlation between distances (Table 15). This pair corresponds to a covariation shared only at the ontogenetic level among our three series (and only weakly so in Dasypus), thus suggesting a common ontogenetic origin behind this pattern [START_REF] Bookstein | Cranial integration in Homo: singular warps analysis of the midsagittal plane in ontogeny and evolution[END_REF][START_REF] Klingenberg | Studying morphological integration and modularity at multiple levels: concepts and analysis[END_REF]. It is possible that this pattern is expressed at the intraspecific level in all cingulate species, but this hypothesis could only be confirmed by comparing intraspecific series for more species. The strong statistical support for the remaining eleven pairs at both the intraspecific and evolutionary levels highlight more pervasive covariation patterns in cingulates. However, among these eleven pairs, seven do not show similar trends (e.g., isometry vs allometry) within and among species (Table 12). The stability of the four remaining pairs, which each showed comparable covariation trends at the intraspecific and evolutionary levels (Table 1), highlights the pervasiveness of these covariations in cingulates.

Our aim was to search for common covariation patterns among cingulates to address the issue of dependence among cranial traits at a later stage. Therefore, the four selected pairs (n°5,7, showing the same covariations in all cingulates at all levels (Table 12)

are of great interest in this regard. These pairs mainly cover the region of the zygomatic arch, the orbital region, the auditory region and the posterior part of the palate ( Table 12,Figures 50 & 51).

Although this requires further analysis, several of these pairs (n°5, 10, 12) seem to suggest a relatively fast growth of distances linked to the anteroventral area of the zygomatic arch (including the maxillary foramen) as size increases (Table 12). This region often undergoes strong allometric variation in mammals (e.g., [START_REF] Cardini | Larger mammals have longer faces because of size-related constraints on skull form[END_REF][START_REF] Ferreira-Cardoso | Skull shape variation in extant pangolins (Pholidota: Manidae): allometric patterns and systematic implications[END_REF]. More broadly, the concentration of most of these pairs in the zygomatic, posterior palatal and mesocranial regions also echoes the zygomatic-pterygoid module initially identified in carnivores [START_REF] Goswami | Cranial modularity shifts during mammalian evolution[END_REF].

This region constitutes a source of phylogenetic characters within cingulates (e.g., characters 84 -86 in [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF] as well as the posterior part of the palate (e.g., characters 56 -59 in

In view of these results, it is a complex matter to clearly assign one or more origins for these covariation patterns. These regions are impacted by several developmental processes that overlap during the life of an organism [START_REF] Hallgrímsson | Deciphering the palimpsest: studying the relationship between morphological integration and phenotypic covariation[END_REF]. The anterior root of the zygomatic arch is part of the masticatory apparatus and interacts with the musculature in connection with the jaw, particularly during development [START_REF] Hallgrímsson | Deciphering the palimpsest: studying the relationship between morphological integration and phenotypic covariation[END_REF]. In armadillos, few studies have dealt with the development of the cranial musculature. The few existing ones show the attachment of the m. masseter on the ventromedial surface of the zygomatic arch in embryos [START_REF] Edgeworth | On the development of the cranial muscles of Tatusia and Manis[END_REF] and a larger area of insertion in adults on the ventral part of the zygomatic arch (especially the anterior root) of the m. nasolabialis (Figure 52) and m. masseter 52) in Dasypus and Euphractus [START_REF] Smith | The anatomy and function of the feeding apparatus in two armadillos (Dasypoda): anatomy is not destiny[END_REF]. Dissection of a Dasypus skull in a study in progress also shows the strong interaction between the m. nasolabialis and masseter with the anterior root of the zygomatic arch (Hautier et al., in prep -Figure 52). In any case, we can hypothesize an association between our covariation patterns in this region and the insertion surfaces of the masticatory muscles. A putatively increasing muscle mass in this region as size increases could explain modifications in the shape of the ventromedial surface of the zygomatic arch, as muscles and bones have been shown to often covary (e.g., [START_REF] Cornette | The shrew tamed by Wolff's law: Do functional constraints shape the skull through muscle and bone covariation?[END_REF][START_REF] Fabre | Do muscles constrain skull shape evolution in Strepsirrhines?[END_REF]. Further research is of course needed to test this hypothesis.

(Figure
The strong integration between the distances of pairs n°5, 7, 10 & 12 could then be partly functional if related to muscle ontogeny and function because "it is intuitive that changes in such systems [i.e., associations between parts interacting in some functional contexte.g., upper and lower jaws], and the coordination among parts within them, are likely to have significant fitness consequences" (Klingenberg, 2014: pp. 4). Some studies argue for a correspondence between developmental and functional integration [START_REF] Cheverud | Quantitative genetics and developmental constraints on evolution by selection[END_REF][START_REF] Wagner | Perspective: complex adaptations and the evolution of evolvability[END_REF], although if such a correspondence exists, testing it is difficult if not impossible [START_REF] Klingenberg | Studying morphological integration and modularity at multiple levels: concepts and analysis[END_REF]. In our case, the potential functional and/or developmental integration for pairs n°5, 7, 10 & 12 is also evolutionary, attesting to a conservation of covariation patterns in all cingulates.

In a phylogenetic context, our study makes it possible to identify patterns preserved at different levels of the evolutionary history of Cingulata and thus to target potentially nonindependent morphological characters, which should be avoided in phylogenetic analyses [START_REF] Emerson | Morphological correlations in evolution: consequences for phylogenetic analysis[END_REF][START_REF] Felsenstein | Inferring phylogenies[END_REF]Goswami & Polly, 2010a;Guillerme & Brazeau, 212 2018). Our work clearly identifies integration patterns common to cingulates and forms a first basis for dealing with these aspects. For instance, as mentioned above, several of these pairs suggest a relatively rapid growth of distances linked to the anteroventral area of the zygomatic arch (including maxillary foramen) as size increases. This calls to mind the presences of a descending process of the zygomatic arch known in glyptodonts to form a large ventrally directed apophysis (character 86 - [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF][START_REF] Scott | Mammalia of the Santa Cruz beds. I. Edentata[END_REF] (see General Discussion & Conclusion). In addition, pampatheres also have a large process in the anterior part of the zygomatic arch [START_REF] Gaudin | Cranial osteology of the pampathere Holmesina floridanus (Xenarthra: Cingulata; Blancan NALMA), including a description of an isolated petrosal bone[END_REF] while Euphractus exhibits a smaller boss [START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF]. This descending process is also found in sloths, in which its broad development provides a large insertion surface for masticatory muscles (m.

masseter superficialis & m. masseter profundus [START_REF] Naples | Form and function of the masticatory musculature in the tree sloths, Bradypus and Choloepus[END_REF]. It is possible that the same muscle configuration was present in glyptodonts (see [START_REF] Gillette | Glyptodonts of North America[END_REF], Figure 96), suggesting that these covariation patterns common to all cingulates are also common to all xenarthrans. As noted above, dissections of extant xenarthrans are now needed to investigate these questions further and test for a link between the development of the descending process, muscle mass, mastication patterns and cranial size.

The novel approach used in this study to search for integration patterns present at various levels of morphological variation in cingulates allowed to highlighted novel cranial covariations within the group. It opens new avenues for research on cranial covariations in the group and their relation to muscular anatomy, cranial development and allometry, as well as their implications for phylogenetic matrices (see Section 5). In order to deepen our knowledge of cranial integration in cingulates, we can also complement the present study on local covariations (pairs of correlated distances) with broader analyses of global covariation pattern (see next sections).

Cranial modularity in Cingulata

ABSTRACT

The assumption of a regionalization of morphological integration in the skull has been extensively tested in mammals, giving rise to a plethora of modular hypotheses. Most studies use confirmatory approaches that require the definition of potential modules prior to testing, while exploratory approaches tend to address this problem instead by searching for the most likely modular model in the data. We propose to use one of these exploratory approaches to determine the most probable modular pattern in cingulates, which represent one of the few large mammalian groups unexplored for this question. We performed an approach using Euclidean Distance Matrix Analysis (EDMA) to identify potential patterns of cranial modularity in the three phylogenetically distant armadillo genera Cabassous, Zaedyus and Dasypus at the ontogenetic and static levels.

This approach is complementary to our previous analyses of cranial integration and allows us to test whether there is a regionalization of the latter common to all three species and thus potentially to all cingulates. Our results show that the most probable modular pattern with our approach corresponds to an anteroposterior partitioning of the skull (for the ontogenetic and static level) into three modules in Zaedyus and Cabassous: face, orbit-neurocranium, and vault-basicranium.

Dasypus shows an additional module corresponding to a parceling of the face module. After a brief discussion of the known modular patterns in mammals, we suggest that the additional module in Dasypus is potentially due to extreme snout elongation in this genus.

Le Verger K, Ferreira-Cardoso F, Gerber S, Hautier L, Delsuc F, Amson E, Ladevèze S, Bardin J, Billet G. Article In Preparation.

INTRODUCTION

Modularity is a concept derived from morphological integration which stipulates that organisms or structures can be divided into strongly integrated sets of traits, i.e., modules, that present a relatively weak integration between them [START_REF] Klingenberg | Studying morphological integration and modularity at multiple levels: concepts and analysis[END_REF]. This assumption is based on the idea that there are functional or developmental anatomical regions (e.g., the facial region)

that are more integrated within themselves than with the rest of a structure (i.e., the rest of the skull) [START_REF] Olson | Morphological integration[END_REF][START_REF] Cheverud | Morphological integration in the saddle-back tamarin (Saguinus fuscicollis) cranium[END_REF][START_REF] Hallgrímsson | Craniofacial variability and modularity in macaques and mice[END_REF][START_REF] Hallgrímsson | Evolution of covariance in the mammalian skull[END_REF][START_REF] Willmore | Effects of developmental and functional interactions on mouse cranial variability through late ontogeny[END_REF]. In recent decades, many studies have tested hypotheses of modularity in vertebrates (e.g., [START_REF] Felice | Developmental origins of mosaic evolution in the avian cranium[END_REF][START_REF] Parsons | Conserved but flexible modularity in the zebrafish skull: implications for craniofacial evolvability[END_REF][START_REF] Watanabe | Ecomorphological diversification in squamates from conserved pattern of cranial integration[END_REF][START_REF] Bardua | Morphological evolution and modularity of the caecilian skull[END_REF][START_REF] Bardua | Evolutionary integration of the frog cranium[END_REF][START_REF] Bon | Cranial integration in the fire salamander, Salamandra salamandra (Caudata: Salamandridae)[END_REF][START_REF] Felice | Evolutionary integration and modularity in the archosaur cranium[END_REF][START_REF] Felice | Decelerated dinosaur skull evolution with the origin of birds[END_REF], especially in mammals, in which these concepts and methods have been initiated (e.g., [START_REF] Bolker | Modularity in development and why it matters to evodevo[END_REF][START_REF] Klingenberg | Developmental constraints, modules, and evolvability[END_REF][START_REF] Monteiro | Evolutionary integration and morphological diversification in complex morphological structures: mandible shape divergence in spiny rats (Rodentia, Echimyidae)[END_REF][START_REF] Klingenberg | Morphological integration and developmental modularity[END_REF]Goswami & Polly, 2010b;[START_REF] Makedonska | The effect of dietary adaption on cranial morphological integration in capuchins (Order Primates, Genus Cebus)[END_REF][START_REF] Santana | Does nasal echolocation influence the modularity of the mammal skull?[END_REF][START_REF] Goswami | EMMLi: a maximum likelihood approach to the analysis of modularity[END_REF][START_REF] Heck | Why the long face? Comparative shape analysis of miniature, pony, and other horse skulls reveals changes in ontogenetic growth[END_REF][START_REF] Churchill | Asymmetry drives modularity of the skull in the common dolphin (Delphinus delphis)[END_REF]. This has produced a multitude of modular hypotheses.

A large majority of past studies used a priori hypotheses of modules to test whether integration is stronger within these modules than between them. For example, one of the most frequently tested hypotheses corresponds to the two-modules face/neurocranium hypothesis which is particularly well-supported by developmental arguments (e.g., [START_REF] Urošević | Multilevel assessment of the lacertid lizard cranial modularity[END_REF]. This confirmatory approach has gained weight recently with the development of methods to compare the supports for different modular models (e.g., [START_REF] Goswami | EMMLi: a maximum likelihood approach to the analysis of modularity[END_REF]. However, this approach requires the formulation of modular hypotheses prior to testing, whereas an organism could be constituted of any combination of modules organized hierarchically [START_REF] Hallgrímsson | Deciphering the palimpsest: studying the relationship between morphological integration and phenotypic covariation[END_REF]. Therefore, the confirmatory approach only tests a reduced number of modular models among the many possible ones. Exploratory approaches tend to reduce this problem, since they do not require a priori hypotheses, but seek the most probable modular pattern in the data (e.g., [START_REF] Suzuki | Modularity of a leaf moth-wing pattern and a versatile characteristic of the wing-pattern ground plan[END_REF][START_REF] Parr | Cranial shape and the modularity of hybridization in dingoes and dogs; hybridization does not spell the end for native morphology[END_REF]. Among these approaches, a method developed by Cheverud (1982a) makes it possible to explore the most probable modular pattern based on linear distances [START_REF] Goswami | Cranial modularity shifts during mammalian evolution[END_REF][START_REF] Zelditch | Building developmental integration into functional systems: function-induced integration of mandibular shape[END_REF]. It is the only method of this kind that does not use Procrustes superimposition. This is important, since this superimposition used in geometric morphometrics may spuriously alter the degree of morphological integration among landmarks and affect the exploration of modularity (Cardini, 2019b;[START_REF] Goswami | High-density morphometric analysis of shape and integration: the good, the bad, and the not-really-a-problem[END_REF][START_REF] Cardini | Less tautology, more biology? A comment on "high-density" morphometrics[END_REF].

Cranial modularity in Xenarthra is unexplored since, to our knowledge, there exists no analysis searching for modular patterns in the skull of any xenarthran species. Some studies analyzed cranial covariance structures among the Cingulata, but without specifically testing for the existence of cranial modules within the group (e.g., [START_REF] Hubbe | A case study of extant and extinct Xenarthra cranium covariance structure: implications and applications to paleontology[END_REF][START_REF] Porto | The evolution of modularity in the mammalian skull I: morphological integration patterns and magnitudes[END_REF][START_REF] Porto | Size variation, growth strategies, and the evolution of modularity in the mammalian skull[END_REF]. In the context of this PhD dissertation, the exploration of cranial modularity within cingulates represents a complementary approach to our previous analyses on cranial integration and enables us to test whether there is a regionalization of the latter.

In this section, we use the exploratory approach of Cheverud (1982a) based on an Euclidean Distance Matrix Analysis (EDMA) to identify potential patterns of cranial modularity. We perform this analysis at the static and ontogenetic levels, following [START_REF] Klingenberg | Studying morphological integration and modularity at multiple levels: concepts and analysis[END_REF], in the three developmental series of Cabassous, Zaedyus and Dasypus used in previous sections of this thesis.

In order to test whether the modular patterns obtained are common to all three species, and thus potentially to all cingulates. This study provides new elements that can improve understanding of the structure of cranial integration in cingulates, and allows comparisons to patterns known in other mammals.

MATERIAL & METHODS

Biological sample

The selected sampling corresponds exactly to that of Section 4.1 for Dasypus, Zaedyus and Cabassous (2 datasets), for both the ontogenetic and static levels. Please refer to Section 4.1 for more details.

Geometric morphometrics

As for sampling, the acquisition of 3D models and landmarks as well as the corrections applied to them are identical to those described in the Section 4.1. Please refer to this previous section for more details.

Analyses of modularity

We analyzed cranial modularity for each of the datasets mentioned above for Dasypus, Zaedyus and Cabassous. We favored an approach using interlandmark linear distances to maintain consistency with the detailed analysis of the strongest covariations (Section 4.1). Despite their great potential for modularity studies [START_REF] Goswami | EMMLi: a maximum likelihood approach to the analysis of modularity[END_REF][START_REF] Goswami | High-density morphometric analysis of shape and integration: the good, the bad, and the not-really-a-problem[END_REF], 3D geometric morphometric approaches were not used here for consistency's sake and to avoid transformation effects on raw data such as Procrustes superimposition, which may cause artifacts in the intensity of a correlation (Cardini, 2019b;[START_REF] Cardini | Less tautology, more biology? A comment on "high-density" morphometrics[END_REF] or may affect the landmark variance (e.g., [START_REF] Richtsmeier | The promise of geometric morphometrics[END_REF]; but see also Goswami & Polly, 2010b). We performed an Euclidean Distance Matrix Analysis (EDMA) to detect modular pattern of the skull in the four intraspecific datasets. This method uses interlandmark distance matrices and compares each of the distances to the average of all distances of a set of objects (here all skulls of one species) in order to construct a calculation of mean shape (see details in [START_REF] Lele | Euclidean distance matrix analysis: A coordinate-free approach for comparing biological shapes using landmark data[END_REF]. Once this mean configuration was obtained, we computed the variance-covariance matrix [START_REF]Morphometrics with R[END_REF]. At this stage, some landmarks that were too close in 3D space could produce distances that were too small and induced missing data in the mean shape [START_REF] Lele | Euclidean distance matrix analysis: A coordinate-free approach for comparing biological shapes using landmark data[END_REF][START_REF]Morphometrics with R[END_REF]. Such landmarks (n=8) were removed from the analysis bringing our total landmark number to 106 (see Figure S40 for an illustration of the landmarks removed in the modular search). We constructed an interlandmark distance correlation matrix and then used the eigenvalues and eigenvectors from a principal component analysis (PCA) to obtain the interlandmark distance loadings (only those of the components with positive eigenvalues) which were then used as coordinates (Cheverud, 1982a). We then performed a hierarchical clustering using the Ward method (see [START_REF] Ward | Hierarchical grouping to optimize an objective function[END_REF][START_REF] Murtagh | Ward's hierarchical agglomerative clustering method: which algorithms implement Ward's criterion?[END_REF]. The graphical visualization of a dendrogram alone does not allow the definition of a preferred number of clusters without a priori information [START_REF] Tibshirani | Estimating the number of clusters in a data set via the gap statistic[END_REF]. Many approaches have been proposed to estimate the number of clusters [START_REF] Gordon | Classication[END_REF], and we opted here for a three-step approach. First, we used the gap statistic (= Gapk) on the distance loadings to evaluate the quality of a clustering measure in comparison with an appropriate null reference distribution of the data [START_REF] Tibshirani | Estimating the number of clusters in a data set via the gap statistic[END_REF]. This index was measured for each cluster number hypothesis (= K) which we increased arbitrarily up to 20, because the number of relevant modules retrieved for mammals never exceeded this number (e.g., [START_REF] Churchill | Asymmetry drives modularity of the skull in the common dolphin (Delphinus delphis)[END_REF].

This estimates the cluster optimal number, which is graphically translated by a slope break. More precisely, this optimal number is the K value for which the logarithm of the pooled within-cluster sum of squares around the cluster means (= log(Wk)) becomes much lower than its reference curve [START_REF] Tibshirani | Estimating the number of clusters in a data set via the gap statistic[END_REF]. Second, the robustness of the K value was tested using a clustering method based on parameterized finite Gaussian mixture models [START_REF] Scrucca | mclust 5: clustering, classification and density estimation using Gaussian finite mixture models[END_REF]. For this, we imposed the number of mixture components as a function of the K value obtained with the gap statistic. The analysis then assigned each landmark to a module (e.g., [START_REF] Terray | Modularity of the neck in birds (Aves)[END_REF]. If the K is stable, then the allocation agrees with the distance tree obtained with the Ward clustering method. Third, once the number of clusters was fixed, we evaluated their stability by resampling the data using bootstraps (see [START_REF] Hennig | Cluster-wise assessment of cluster stability[END_REF]. This step enabled us to estimate the average similarities between the original cluster and the clusters produced by resampling. We arbitrarily considered a cluster to be well-supported when it yielded bootstrap values greater than 80%. The analysis was performed at the ontogenetic and static levels. The R script is incorporated in the same script for Section 4.1 which is available in Supporting Information 5.

RESULTS

Number of modules

The statistically stable module number determined with the EDMA varies among the three species but not among levels and datasets within each species (Figures 53,S41). In Dasypus novemcinctus, the slope break for Gapk corresponded to four modules (K = 4), while three modules were detected for Zaedyus pichiy and for the Cabassous datasets (K = 3) (Figures 53,S41). D.

novemcinctus also differed from the other two species with a second slope break at K = 8 (Figure 53). However, the eight modules obtained were not statistically supported by bootstrapping, although a face/neurocranium modular pattern was statistically supported (Figures S42 -S45).

The four modules hypothesis of D. novemcinctus and the three modules of the two other species were consistent with the trees obtained with Mclust and were all statistically supported by bootstrapping (Figures S42 -S45, Table S29), with the sole exception of D. novemcinctus, which has a bootstrap of 78% for its third module (orbitotemporal region) at both ontogenetic and static levels (Figures S42 -S45). Figure 54 summarizes the distribution of landmarks in each module among all species and datasets.

Figure 54. Top: mapping of the modules obtained for each species in dorsal and lateral view (only CabassousNS is represented, see Figure S59 for CabassousN) at the ontogenetic, and static levels. Phylogenetic relationships between the three species are indicated based on molecular and morphological studies [START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF], Delsuc et al., 2016, Gibb et al., 2016-colors follow Mitchell et al., 2016). Bottom: concatenation of the distribution of each landmark in each module between the three species as a percentage represented by diagrams (considering both Cabassous datasets) is provided, mapped onto a skull of Dasypus novemcinctus in dorsal view. The number of every landmark that is shared by several modules is indicated. In red, face/anterior-face module; in purple, mid-face module; in green, orbitneurocranium module; in blue, vault-basicranium module. Scale = 1 cm.

Most landmarks are consistently found in the same modules among the three species (Table S30), with the least stable landmarks corresponding to the areas of contact between modules, such as the contact between the frontal and nasal bones, the most posterior part of the snout and the region connecting the first half of the neurocranium to the posterior part of the orbitotemporal region (Figure 54; Table S30).

The static level differs from the ontogenetic level in D. novemcinctus by a larger posterodorsal extension of the orbit-neurocranium module similar to that retrieved in Z. pichiy and Cabassous datasets at the ontogenetic level (Figure 54; Figures S44, S45 & S46). This module thus becomes the largest at this level in this species, and covers all of the anterior half of the neurocranium. In Zaedyus pichiy, the vault-basicranium module is no longer present on the zygomatic arches and is replaced there by the orbit-neurocranium module, which then completely encompasses these structures (landmarks #51 & #52) (Figure 54; Figure S45). For Cabassous, the two datasets exhibit the same modular distribution at the static level, with only a few changes compared to the ontogenetic level (Figure 54; Figures S45 &S46). There is no asymmetry of modules at this level. The posterior extension of the orbit-neurocranium module is weaker at the static level in CabassousN than in the ontogenetic level, with the transfer of the landmark connecting the parietal, supraoccipital and squamosal (landmarks #70 & #71) from the orbitneurocranium module to the vault-basicranium module (Figure 54; Figure S46). The summarized distribution of landmarks among the three species at the static level shows that the least stable landmarks correspond to the contact between the nasal and frontal and the contact between orbitneurocranium and vault-basicranium modules, which is largely similar to the patterns observed at the ontogenetic level (Figure 54, Table S46).

DISCUSSION

Cranial modularity hypotheses have flourished in the literature over the last thirty years.

Studies either tested several a priori hypotheses of modularity on the basis of functional or developmental arguments (e.g., [START_REF] Hallgrímsson | Craniofacial variability and modularity in macaques and mice[END_REF][START_REF] Willmore | Effects of developmental and functional interactions on mouse cranial variability through late ontogeny[END_REF] or searched for modular patterns without a priori assumptions (Cheverud, 1982a;[START_REF] Goswami | Cranial modularity shifts during mammalian evolution[END_REF][START_REF] Zelditch | Building developmental integration into functional systems: function-induced integration of mandibular shape[END_REF]. Mammals have been the subject of these investigations without a priori assumptions, with more attention paid to primates, rodents, and carnivorans (see [START_REF] Klingenberg | Cranial integration and modularity: insights into evolution and development from morphometric data[END_REF]. The most commonly supported patterns range from 2 modules (face/neurocranium -Drake & Klingenberg, 2010) to about 10 modules distributed across the skull (e.g., [START_REF] Parr | Cranial shape and the modularity of hybridization in dingoes and dogs; hybridization does not spell the end for native morphology[END_REF][START_REF] Churchill | Asymmetry drives modularity of the skull in the common dolphin (Delphinus delphis)[END_REF]. Using interlandmark distances, we detected 3 anteroposteriorly distributed modules both at ontogenetic and static levels in Cabassous and Zaedyus (face, orbit-neurocranium and vaultbasicranium), with Dasypus showing an additional parcellation of the face module into an anteriorface module and a mid-face module. The anteroposterior distribution of modularity in these taxa stands out regarding previously supported hypotheses, which most often suppose a division of the placental skull into six modules distributed in various directions (e.g., [START_REF] Cheverud | Morphological integration in the saddle-back tamarin (Saguinus fuscicollis) cranium[END_REF][START_REF] Goswami | Cranial modularity shifts during mammalian evolution[END_REF][START_REF] Goswami | EMMLi: a maximum likelihood approach to the analysis of modularity[END_REF]. However, our results also strongly support a major division into two larger modules corresponding to the face/neurocranium complex (i.e, first two branches of the distance tree -Figures S44 &S45). The addition of a third, or even a fourth module, corresponds closely to several empirical hypotheses of the distribution of integration in mammalian skulls (Cheverud, 1982a;[START_REF] Hallgrímsson | Evolution of covariance in the mammalian skull[END_REF], that recognize the rostrum, neurocranium and basicranium as separate modules (e.g., [START_REF] Castillo | Skull ontogeny and modularity in two species of Lagenorhynchus: Morphological and ecological implications[END_REF], although the neurocranium and basicranium are each partly separated within our two posterior modules (orbitneurocranium and vault-basicranium modules). This partition gives us a first global view on the distribution of morphological integration on the skull of three cingulate species and highlights above all the particularity of Dasypus compared to the two others, with its two modules on the face.

Long-nosed armadillos (Dasypus) exhibit a strong craniofacial allometry [START_REF] Hautier | Beyond the carapace: skull shape variation and morphological systematics of long-nosed armadillos (genus Dasypus)[END_REF]Section 3.1), which is also supported by the high proportion of selected pairs of correlated S-distances that were related to this pattern at the ontogenetic level (Section 4.1). Our previous results on cranial allometry have also suggested a weaker craniofacial allometry in Cabassous and Zaedyus compared to Dasypus (Section 3.2). We therefore hypothesize that the additional module in Dasypus is due to a stronger craniofacial allometry. It is already well known that size is a powerful integrating factor and could affect modular distribution especially at the ontogenetic level [START_REF] Mitteroecker | The conceptual and statistical relationship between modularity and morphological integration[END_REF][START_REF] Klingenberg | Cranial integration and modularity: insights into evolution and development from morphometric data[END_REF][START_REF] Porto | Size variation, growth strategies, and the evolution of modularity in the mammalian skull[END_REF]. It would be interesting to test this hypothesis further in different ontogenetic stages in long-nosed armadillos as the number of modules may also vary during ontogeny (e.g., [START_REF] Zelditch | Developmental regulation of variability[END_REF][START_REF] Hallgrímsson | Deciphering the palimpsest: studying the relationship between morphological integration and phenotypic covariation[END_REF][START_REF] Gonzalez | Ontogenetic allometry and cranial shape diversification among human populations from South America[END_REF][START_REF] Klenovšek | Skull modularity of the European ground squirrel Spermophilus citellus (Linnaeus, 1766)[END_REF][START_REF] Klenovšek | Modularity and cranial integration across ontogenetic stages in Martino's vole, Dinaromys bogdanovi[END_REF]. However, at the static level, the distribution of modules barely changes relative to the ontogenetic level and the two modules on the face are still supported in Dasypus. This stability of modular architectures throughout ontogeny is consistent with the results of a previous study on Japanese macaques [START_REF] Goswami | EMMLi: a maximum likelihood approach to the analysis of modularity[END_REF] and other primates [START_REF] Ackermann | Ontogenetic integration in the hominoid face[END_REF].

The difference in facial patterns observed between Dasypus and the other two armadillo species in our sample could be the result of other developmental factors as well, in addition to a stronger craniofacial allometry. For instance, potential explanations can be explored in the proliferation rates and patterns of cells and chondrocytes of the face and sphenoethmoidal synchondrosis, which show differences between taxa of different snout shapes (Smith et al., 2017;[START_REF] Camacho | Differential cellular proliferation underlies heterochronic generation of cranial diversity in phyllostomid bats[END_REF]. These are only lines of reasoning, but it is clear that a good way to further explore these differences lies in the study of these developmental processes which remains understudied in armadillos [START_REF] Loughry | Research on armadillos: a review and prospectus[END_REF]. In any case, the existence of two modules on the face in Dasypus, with an anterior face module and a mid-face module, is consistent with the results of several studies on modularity which highlight a strong relationship between naso-frontal landmarks and landmarks in a molar-palate area. These studies have shown that the naso-frontal landmarks and the molar landmarks may constitute an individual module (Cheverud, 1982a;[START_REF] Goswami | Cranial modularity shifts during mammalian evolution[END_REF][START_REF] Parr | Cranial shape and the modularity of hybridization in dingoes and dogs; hybridization does not spell the end for native morphology[END_REF][START_REF] Churchill | Asymmetry drives modularity of the skull in the common dolphin (Delphinus delphis)[END_REF], which would closely resemble our midface module in Dasypus.

A next step for this work would be to compare our modular hypothesis to existing mammalian modular models using a confirmatory approach (e.g., [START_REF] Goswami | EMMLi: a maximum likelihood approach to the analysis of modularity[END_REF].

The addition of such an analysis will allow us to further evaluate the robustness of our modular hypotheses and draw comparisons between cingulates, the most diverse group of Xenarthra, and other mammals.

INTRODUCTION

Morphological variation is a complex phenomenon affecting the shape of an organism in multiple directions. Quantification of morphological variation can be performed using several complementary approaches ranging from the analysis of shape of an anatomical object such as the skull [START_REF] Klingenberg | Evolutionary covariation in geometric morphometric data: analyzing integration, modularity, and allometry in a phylogenetic context[END_REF] to the scrutiny of the relationship between two shape variables (e.g., Cheverud, 1982a), the correlation of shape with an external factor (e.g., diet, geographical distribution - [START_REF] Nogueira | Morphological correlates of bite force and diet in the skull and mandible of phyllostomid bats[END_REF][START_REF] Cáceres | Ecogeographical variation in skull shape of capuchin monkeys[END_REF] or with a variable such as size, for investigating allometry [START_REF] Klingenberg | Size, shape, and form: concepts of allometry in geometric morphometrics[END_REF]. 3D geometric morphometrics is a muchused method that allows quantification of morphological differences between objects using landmark coordinates [START_REF] Adams | Geometric morphometrics: ten years of progress following the 'revolution[END_REF][START_REF] Zelditch | Geometric morphometrics for biologists: a primer[END_REF]. Compared to linear distances, it offers the advantage of quantifying more components of shape variation, especially by enabling the use of three-dimensional data.

Several studies have quantified shape variation in cingulates using linear distances on the skull (or mandible) within [START_REF] Squarcia | Morfología craneana de Chaetophractus villosus (Desmarest, 1804) (Mammalia, Dasypodidae)[END_REF]Squarcia & Casanave, 1999;Squarcia et al., 1999;[START_REF] Squarcia | Osteología Craneana del Armadillo Chaetophractus villosus (Mammalia, Xenarthra, Dasypodidae)[END_REF][START_REF] Squarcia | Sexual dimorphism in the mandible of the armadillo Chaetophractus villosus (Desmarest, 1804) (Dasypodidae) from northern Patagonia, Argentina[END_REF] or among armadillo species [START_REF] Squarcia | The hypertrophy of the tympanic bulla in three species of dasypodids (Mammalia, Xenarthra) from Argentina[END_REF][START_REF] Sidorkewicj | Morphology of the middle ear in three species of armadillos (Dasypodidae, Xenarthra) from Argentina[END_REF], 2013;[START_REF] Hubbe | A case study of extant and extinct Xenarthra cranium covariance structure: implications and applications to paleontology[END_REF]. Shape variation in the group has also been addressed with linear distances on postcranial material [START_REF] Vizcaíno | Un índice de aptitud fosorial para armadillos (Xenarthra, Cingulata) fósiles sudamericanos[END_REF][START_REF] Vizcaíno | Ulnar dimensions and fossoriality in armadillos and other South American mammals[END_REF][START_REF] Vizcaíno | Structure and function in armadillo limbs (Mammalia: Xenarthra: Dasypodidae)[END_REF][START_REF] Vizcaíno | Limb reconstruction of Eutatus seguini (Mammalia: Xenarthra: Dasypodidae). Paleobiological implications[END_REF][START_REF] Vizcaíno | The armadillos (Mammalia, Xenarthra, Dasypodidae) of the Santa Cruz formation (early-middle Miocene): An approach to their paleobiology[END_REF][START_REF] De Esteban Trivigno | Body mass estimation in Xenarthra: A predictive equation suitable for all quadrupedal terrestrial placentals?[END_REF][START_REF] Galliari | Evolution of the axial skeleton in armadillos (Mammalia, Dasypodidae)[END_REF] and even on the shape of cells [START_REF] Polini | Morphological and morphometrical study of the blood leukocytes from Chaetophractus villosus (Mammalia, Dasypodidae)[END_REF][START_REF] Codón | Ultrastructure and morphometry of ovarian follicles in the armadillo Chaetophractus villosus (Mammalia, Dasypodidae)[END_REF][START_REF] Sousa | Morphology, morphometry and ultrastructure of captive six-banded armadillo (Euphractus sexcinctus) sperm[END_REF].

The first analyses of geometric morphometrics (GMM) on armadillos used twodimensional landmarks to characterize morphological variation of skull by comparing the patterns of a few extant and fossil specimens (Vizcaíno & Bargo, 1998;Vizcaíno et al., 1998;[START_REF] De Iuliis | Variation in skull morphology and mastication in the fossil giant armadillos Pampatherium spp. and allied genera (Mammalia: Xenarthra: Pampatheriidae), with comments on their systematics and distribution[END_REF]Vizcaíno & De Iuliis, 2003;[START_REF] Vizcaíno | Functional and phylogenetic assessment of the masticatory adaptations in Cingulata (Mammalia, Xenarthra)[END_REF]. More recently, 2D GMM was used to analyze morphological variation of the postcranial material [START_REF] Oliver | Vertebral bending mechanics and xenarthrous morphology in the nine-banded armadillo (Dasypus novemcinctus)[END_REF][START_REF] Acuña | A geometric morphometric study of sex differences in the scapula, humerus and ulna of Chaetophractus villosus (Xenarthra, Dasypodidae)[END_REF] or cranial (or mandibular) variation in relation to different factors such as geography, environment or diet [START_REF] Serrano-Fochs | Finite element analysis of the Cingulata jaw: an ecomorphological approach to armadillo's diets[END_REF][START_REF] Magnus | The environment is a major driver of shape and size variation in widespread extant xenarthrans[END_REF].

A more powerful way to characterize shape variation involves the use of 3-dimensional landmarks [START_REF] Rohlf | A revolution morphometrics[END_REF]. In cingulates, 3D GMM studies were performed either on postcranial material [START_REF] Milne | A 3D geometric morphometric analysis of digging ability in the extant and fossil cingulate humerus[END_REF][START_REF] Milne | Scaling of form and function in the xenarthran femur: a 100-fold increase in body mass is mitigated by repositioning of the third trochanter[END_REF]Milne et al., 2012), cranial shape within a clade [START_REF] Abba | Systematics of hairy armadillos and the taxonomic status of the Andean hairy armadillo (Chaetophractus nationi)[END_REF]Feijó & Cordeira-Estrela, 2016;[START_REF] Hautier | Beyond the carapace: skull shape variation and morphological systematics of long-nosed armadillos (genus Dasypus)[END_REF][START_REF] Feijó | Taxonomic revision of the long-nosed armadillos, Genus Dasypus Linnaeus, 1758 (Mammalia, Cingulata)[END_REF][START_REF] Feijó | Phenotypic variability and environmental tolerance shed light on nine-banded armadillo Nearctic invasion[END_REF]Section 3.1) or on selected cranial regions (e.g., inner ear; Billet et al., 2015a;[START_REF] Coutier | Orientation of the lateral semicircular canal in Xenarthra and its links with head posture and phylogeny[END_REF]. To our knowledge, no analysis of the shape of the cingulate skull using 3-dimensional landmarks has been performed on the whole diversity of the group.

In this PhD dissertation, we first explored the variations in cranial shape correlated with size in cingulates (Chapter 3). We then tried to detect the strongest covariations between interlandmark distances (SubChapter 4.1) and, finally, we explored for the first time cranial modular patterns (SubChapter 4.2). However, an analysis of 3-dimensional shape variation among cingulate species is missing. This type of analysis can provide a useful overview of variational patterns in the group, as well as clues on potential covariations at the evolutionary level. Here, we investigate this variation using 3D GMM on the skull of multiple cingulate species, and employing a Principal Component Analysis [START_REF] Jolicoeur | Size and shape variation in the painted turtle. A principal component analysis[END_REF] to analyse shape variation. This method enables coverage of a large proportion of the shape variation in order to identify potential covariation patterns, because a strong covariance between traits could be correlated with differences in shape variance [START_REF] Young | Function, ontogeny and canalization of shape variance in the primate scapula[END_REF]. We apply this method on seven evolutionary datasets incorporating a large diversity of extant and fossil cingulates. We analyze shape variation both for the entire skull, but also for the modules detected in the previous section. We briefly describe the main variations obtained from these datasets and discuss these results in the general discussion and conclusion of this PhD dissertation, as it provides avenues for future research on the group.

Material & Methods

Biological sample

Our sampling for this study was split into seven evolutionary datasets with an aim at incorporating alternatively a maximum number of taxa or a maximum number of landmarks.

Among these datasets, three correspond to those used for the analysis of allometry at the evolutionary level (see Section 3.2): DatasetExt, Dataset-Lmax and Dataset-Tmax. A fourth dataset was added to incorporate a maximum number of glyptodonts (referred to as dataset-G hereafter), which lowered the number of landmarks (ntaxa = 29; nlandmark = 60 -Tables S31 &S32). Three additional datasets were created to analyze the morphological variation within the three modules (referred to as Dataset-M-face; Dataset-M-orbit-neurocranium; Dataset-M-vault-basicranium) delineated in the preceding section (Section 4.2). Only stable landmarks have been preserved in the composition of these module datasets (see Section 4.2). The taxonomic composition for each dataset is given in Table S31. The taxa added with respect to Section 3.2 are Propalaehoplophorus minus, Eucinepeltus complicatus and "Cochlops" debilis (see Chapter 1), which are all Santacrucian glyptodonts.

Correction of taphonomic deformations

As for some specimens in Section 3.2, we applied a retrodeformation on the "Cochlops" debilis specimen. We followed the same method rigorously. We corrected a slight uniform ventral displacement of skull height on the left lateral region of the skull, to match the right lateral part of the skull that is undistorted. This correction is shown in Figure S47.

Geometric morphometrics

The acquisition of 3D models and landmarks, as well as the corrections made to them, follow the methodology described in Section 4.1. Please refer to this section for more details.

The landmark composition for each dataset is given in Table S32. For Propalaehoplophorus minus, Eucinepeltus complicatus and "Cochlops" debilis, the landmark coordinates are available in Table S33, and details about their missing and symmetrized landmark, are given in Table S34.

Phylogenetic considerations

To investigate whether the morphometric data contains a phylogenetic signal, we used the multivariate Kmult-statistic, which estimates the phylogenetic signal present in the symmetrized Procrustes coordinates for each dataset [START_REF] Adams | A generalized K statistic for estimating phylogenetic signal from shape and other high dimensional multivariate data[END_REF]. This was calculated using the function physignal of the R geomorph package [START_REF] Adams | Geomorph: Software for geometric morphometric analyses[END_REF], with 10,000 permutations to determine the significance. A Kmult close to 1 means that the taxa are phenotypically similar, as expected under Brownian motion [START_REF] Adams | A generalized K statistic for estimating phylogenetic signal from shape and other high dimensional multivariate data[END_REF]. A Kmult greater than 1 means that the taxa are phenotypically more similar than expected by the model, and a Kmult less than 1 means that the taxa are phenotypically less similar than expected by Brownian motion [START_REF] Adams | A generalized K statistic for estimating phylogenetic signal from shape and other high dimensional multivariate data[END_REF]. The value of the phylogenetic signal served here as an indication of the possible phylogenetic patterning of the data. It was complemented by the representation of the phylogenetic tree used in the Section 3.2 in the morphospace (i.e., baseline cladogram used in previous chaptersee below and Figure S4). This same tree was used for the computation of the Kmult statistics. We adapted each baseline tree by removing taxa to be discarded while keeping the branch lengths (refer to Material & Methods -Section 3.2).

Because our goal was to analyze the overall cranial shape variation, we kept all aspects responsible for the shape changes in our analyses. Therefore, no correction was made regarding the effect of phylogeny or allometry. This approach was also favored because this kind of correction in general shape analyses is still strongly debated in the literature (e.g., [START_REF] Klingenberg | Size, shape, and form: concepts of allometry in geometric morphometrics[END_REF][START_REF] Uyeda | Rethinking phylogenetic comparative methods[END_REF].

Shape variation

To investigate major shape variations in the datasets we used a principal component analysis (PCA) [START_REF] Jolliffe | Graphical representation of data using principal components[END_REF] using the gm.prcomp function of the geomorph R package [START_REF] Adams | Geomorph: Software for geometric morphometric analyses[END_REF]. For each dataset, the corresponding phylogenetic tree was incorporated into the morphospace to illustrate possible phylogenetic relationships. We decided to present only the variations contained in the first two axes (generally representing more than 50% of the total variance). These shape variations were illustrated by vectors representing the minimum and maximum shape of each axis. Using the distance matrix from the principal component scores, we performed neighbor-joining tree estimations [START_REF] Saitou | The neighbor-joining method: a new method for reconstructing phylogenetic trees[END_REF] of the total variance, using the function nj in the ape R package v. 5.3 (Paradis & Schliep, 2019). This phenetic analysis considers the overall dissimilarities between all the specimens and makes comparisons between them to build a tree that summarizes overall morphological distances among specimens.

Results

For each dataset, we describe here the main variations of the minimum to maximum shapes observed on the two main axes of PCA. Then we report on the proximity of clusters (i.e., clade and fossil taxa) in the morphological space on these first two axes, which is complemented by the Neighbor Joining tree.

Only extant species

For the DatasetExt, the first two axes of the PCA account for 73.86% of the total variance (Figure 55). Kmult is low (= 0.17072; p-value = 0.0001) which means that the taxa are phenotypically significantly less similar than expected with Brownian motion, assuming a high level of homoplasy. The first axis accounts for almost half of the total variance (60.62%). From the minimal shape (most negative value) to the maximal shape (most positive value) along this axis, we observe that: i) almost all landmarks move away from the center of the braincase showing a relative increase in the proportions of neurocranium also affecting part of the face (Figure 55); and, ii) the snout is shortened with an increase in its height (#2; #3-4; #31-32) and width (#31-32) accompanied by a strong reduction of tooth row length from its posterior edge (#28-29) and an anterior elongation of the palatine (#18-19). The shape variation along this first axis distinguishes most chlamyphorids (except for the large-sized tolypeutine Priodontes) from the long-nosed dasypodids, which plot at negative values. For the second axis (explaining 13.24% of total variance), the anterior part of the snout shows a dorsoventral and mediolateral enlargement at positive values (#2; #3-4; #9-12; #31-32). The premaxillary is elongated anteroposteriorly especially at its posterior ventral end (#5-7). The dental row is also relatively more elongated anteriorly (#26-29) and the posterior part of the palate is less ventrally positioned (#18-19; #28-29; #30). The orbit is strongly displaced anteroventrally position (#35-40; #47-50). The parietal extends more anteriorly (#66-67). The orbitotemporal region narrows mediolaterally (#41-42; #45-46; #64-65; #111-112). The posterior part of the zygomatic arch and the anterior part of the basicranium take a more posteromedial position while the rest of the basicranium takes a more posterior position (Figure 55). Finally, the tentorial process is displaced further anteriorly (#63)

and the nuchal crests extend more ventrolaterally (#73-74). These shape changes are driven largely by Priodontes, which plots at high PC2 values, as opposed to chlamyphorines at negative values.

All dasypodids, euphractines and other tolypeutines are clustered at median values.

On the PC1-2 morphospace, a slight overlap is detected between the tolypeutines and the euphractines (Figure 55). In contrast, the Neighbor Joining (NJ) tree (computed on 100% of the variance) shows a closer resemblance between chlamyphorines and euphractines (Figure 55).

Dasypodines are well differentiated from other armadillos on the NJ tree, as are most tolypeutines (Figure 55). Peltephilus are more or less all grouped around the same values (Figure 56).

For the second axis (explaining 16.88% of total variance) (dataset-Tmax = 37.75%;

dataset-G = 57.38%), the variation corresponds mainly to the reduction of the relative proportions of the braincase towards positive values. We also note a relative mediolateral widening of the anterodorsal part of the snout (#3-4; #9-10; #31-32). The shape variation along this second axis appears to be highly allometric. It distinguishes small taxa such as chlamyphorines (most negative values) from large taxa (most positive values) such as glyptodonts, Vassallia, Priodontes and a large proportion of dasypodines (Figure 56).

On the Neighbor Joining tree, chlamyphorines are nested within euphractines (Figure 56,

Figures S48 & S49

Intramodular Morphological variation

For the dataset-M-face, the first two axes of the PCA account for 82.72% of the total variance (Figure 57). Kmult is low (= 0.54089; p-value = 0.0001) which means that the taxa are phenotypically significantly less similar than expected with Brownian motion, assuming a high level of homoplasy. The first axis accounts for more than three-fifths of the total variance (64.37%). From the minimum shape (most negative value) to the maximum shape (most positive value) along this axis (Figure 57), the face module shows a relative shortening posteriorly due to the anterior shift of the posterior extremity of the dental row (#26-27). The anterior part of the module shows a relative broadening of the premaxillary in several directions. Ventrally, the anterior processes of the premaxillary (#11-12) take a more posterolateral and more ventral position. Dorsally, the most anterior point of the internasal is located relatively more anteriorly (#1) while the rest of the landmarks defining the anterolateral extremities of the nasal shows a strong mediolateral relative widening (#3-4; #9-10). Overall, the anterior part of the module also shows a strong relative increase in height (#3-4; #8-14). Finally, the incisive foramina (#13-16)

and the anterior end of the premaxillary on the midline (#8) migrate much further posteriorly. This shape is found in dasypodines, which plot exclusively at low PC1 values. Glyptodonts, Vassalia

and Peltephilus plot at positive values and thus rather exhibit the opposite shape pattern, while tolypeutines, euphractines and chlamyphorines are found at more intermediate values.

For the second axis (explaining 18.35% of total variance), from the minimum shape (most negative value) to the maximum shape (most positive value) along this axis (Figure 57), the anterior edge of the dental row (#26-27) takes a relatively more anterodorsal and lateral position.

The triple contact point between premaxillary -maxillary -nasal (#3-4) is located much more posterodorsal, but also relatively more medial, while the most anterior point of the premaxillarynasal suture (#9-10) moves anteroventrally and medially. Combined, these relative variations show a strong elongation of the dorsal part of the premaxillary. The variation of these landmarks also indicates a relative mediolateral narrowing of the front of the snout. When combined with the most anterodorsal point of the internasal suture (#1) and the most anterior points of the ventral part of the premaxillary (#8; #9-10# [START_REF]col="blue",lty=3) abline[END_REF][12], it also creates a slight shift in the orientation of the narial aperture anteroventrally. Finally, the anterior margin of the incisive foramina migrates anteriorly (#13-14). This shape variation distinguishes glyptodonts, corresponding to the lowest values of PC2, from euphractines, which show the highest values of PC2 (Figure 57). The other taxa are found at more intermediate values.

The NJ tree shows a good discrimination of dasypodines based on the shape of this module (Figure 57). In contrast, the distribution of the other extant clades shows less congruence with the systematics of the group (Figure 57). Fossil specimens are found closer to a subset of euphractines defined by Euphractus and Chaetophractus (Figure 57). We also note that chlamyphorines are closely linked to Tolypeutes in this tree (Figure 57). For the dataset-M-orbit-neurocranium, the first two axes of the PCA account for 68.24%

of the total variance (Figure 58). Kmult is low (= 0.19177; p-value = 0.0001) which means that the taxa are phenotypically significantly less similar than expected with Brownian motion, assuming a high level of homoplasy. The first axis accounts for more than half of the total variance (53.11%).

From the minimum shape (most negative value) to the maximum shape (most positive value) along this axis (Figure 58 For the second axis (explaining 15.13% of total variance), from the minimum shape (most negative value) to the maximum shape (most positive value; Figure 58), the orbit-neurocranium module shows a slightly more posteroventral relative position of the posterior edge of the dental row (#28-29) while the most posterior point of the median palatine suture (#30) moves anteriorly.

The internal landmark close to the cribriform plate (#111-114) take a more anteroventral and lateral position. Overall, without describing the vectors of every single landmark on this module, the deformation towards positive values on PC2 produces an anteroposterior shortening and a mediolateral widening of the module. We also note that the proportions of the orbit are reduced Figure 58. Principal Component Analysis on the Dataset-M-orbit-neurocranium with a neighbor-joining tree estimation for the total variance. Morphological shape changes on each axis are represented from the minimal (green) to the maximal (red) value of each axis. Landmarks discussed in the text are numbered for more readability. A skull of Dasypus novemcinctus in ventral and lateral views is added to illustrate the module in each view. Scale = 1cm.

This shape mostly corresponds to chlamyphorines and euphractines, which possess the highest values on PC2 while glyptodonts, Vassallia and Priodontes express the lowest values. This axis seems highly allometric, with a strong distinction between small and large taxa.

As for the face module, the NJ tree for the orbitotemporal/neurocranium module results in strong discrimination of dasypodines (Figure 58). In contrast, the distribution of the other extant clades shows a lesser congruence with the systematics of the group (Figure 58). Glyptodonts and Vassallia are found close to Euphractus and Tolypeutes (Figure 58). We also note that chlamyphorines most closely resemble Chaetophractus and Zaedyus (Figure 58).

For the dataset-M-vault-basicranium, the first two axes of the PCA account for 56.88% of the total variance (Figure 59). Kmult is low (= 0.23742; p-value = 0.0001) which means that the taxa are phenotypically significantly less similar than expected with Brownian motion, assuming a high level of homoplasy. The first axis accounts for more than a third of the total variance (38.42%). From the minimum shape (most negative value) to the maximum shape (most positive value) (Figure 59), the vault-basicranium module varies primarily in the vault area. This variation includes a relative increase in the height of the entire module, especially in the posterior part of the vault (#55-56; #67; #70-74; 99-100). A relative decrease in width of this entire module is also visible (#55-58; #70-71; #73-74). In addition, the most posterodorsal point of the zygomatic ridge of the squamosal (#55-56) is relatively more posterodorsal and medial, and is separated by an increased distance from the most dorsal point of the external acoustic meatus on the squamosal (#57-58) that shows a more posteroventral and more medial position. This suggests a strong increase in height between these two structures. This shape mostly corresponds to glyptodonts, but also to euphractines and some tolypeutines. They have the highest values on this axis, while the negative values correspond to dasypodines. Contrary to the other two modules, the relative position of taxa in the morphospace shows many overlaps, and therefore a less clear distinction of clusters (Figure 59). The NJ tree shows a good discrimination of dasypodines, which are closely linked to Vassallia (Figure 59).

Glyptodonts are found closer to euphractines and Peltephilus is found closer to tolypeutines (Figure 59).

As indicated in the Introduction, these results will be discussed along other results of the PhD in the General Discussion & Conclusion that follows.

GENERAL DISCUSSION & CONCLUSION

« La variation phénotypique est la matière première de la sélection naturelle, mais un siècle après Darwin, c'est un sujet presque inconnu ».

Leigh Van Valen, 1974, Translated. "Phenotypic variation is the raw material for natural selection, yet a century after Darwin, it is an almost unknown subject". Leigh Van Valen, 1974.

General Discussion and Conclusion

Limitation of taxonomic data and sampling

A robust systematic framework and detailed knowledge of the taxonomic diversity generally constitute prerequisites for a multitude of biological analyses of a biological clade (e.g., [START_REF] Tschopp | A specimen-level phylogenetic analysis and taxonomic revision of Diplodocidae (Dinosauria, Sauropoda)[END_REF]. In studies on morphological integration (Chapters 3 & 4), one needs a clear definition of the species sampled for analyses at the static and ontogenetic levels [START_REF] Klingenberg | Studying morphological integration and modularity at multiple levels: concepts and analysis[END_REF]. However, as we have observed in our study, the systematics of extant cingulates is often far from clear, and remains the subject of much debate in three of the four extant clades, despite their low diversity, of roughly 21 widely recognized living species (see Chapter 1).

The dasypodines (long-nosed armadillos) have been extensively investigated in recent years, and are grouped into seven extant species belonging to the single genus Dasypus in the latest taxonomic reports (see Section 1). Recent morphological and molecular studies suggest increasing the number of recognized species, and perhaps the number of genera as well (e.g., [START_REF] Castro | Reassessment of the hairy long-nosed armadillo "Dasypus" pilosus (Xenarthra, Dasypodidae) and revalidation of the genus Cryptophractus Fitzinger[END_REF]Feijó & Cordeira-Estrela, 2016;[START_REF] Billet | The hidden anatomy of paranasal sinuses reveals biogeographically distinct morphotypes in the nine-banded armadillo (Dasypus novemcinctus)[END_REF][START_REF] Hautier | Beyond the carapace: skull shape variation and morphological systematics of long-nosed armadillos (genus Dasypus)[END_REF][START_REF] Feijó | Taxonomic revision of the long-nosed armadillos, Genus Dasypus Linnaeus, 1758 (Mammalia, Cingulata)[END_REF].

The nine-banded armadillo (i.e., D. novemcinctus) was probably the most intensively investigated species in recent years. Nine-banded armadillos have a very wide Panamerican geographical distribution [START_REF] Mcbee | Dasypus novemcinctus[END_REF] and might actually represent a complex of two to four distinct species supported by both molecular [START_REF] Huchon | Armadillos exhibit less genetic polymorphism in North America than in South America: nuclear and mitochondrial data confirm a founder effect in Dasypus novemcinctus (Xenarthra)[END_REF][START_REF] Gibb | Shotgun mitogenomics provides a reference phylogenetic framework and timescale for living xenarthrans[END_REF][START_REF] Feijó | Taxonomic revision of the long-nosed armadillos, Genus Dasypus Linnaeus, 1758 (Mammalia, Cingulata)[END_REF][START_REF] Feijó | Phylogeny and molecular species delimitation of long-nosed armadillos (Dasypus: Cingulata) supports morphology-based taxonomy[END_REF][START_REF] Arteaga | Conservation Genetics, Demographic History, and Climatic Distribution of the Nine-Banded Armadillo (Dasypus novemcinctus): An Analysis of Its Mitochondrial Lineages[END_REF] and morphological evidence [START_REF] Hautier | Beyond the carapace: skull shape variation and morphological systematics of long-nosed armadillos (genus Dasypus)[END_REF][START_REF] Billet | The hidden anatomy of paranasal sinuses reveals biogeographically distinct morphotypes in the nine-banded armadillo (Dasypus novemcinctus)[END_REF].

Our study of cranial allometry in nine-banded armadillos (Section 3.1) showed similar allometric patterns in a dataset gathering three of the four potential species, as well as within the best-sampled of the four potential species, i.e., the Southern Morphotype. In the rest of our analyses including D. novemcinctus, we considered only this best-sampled potential species, to ensure that our sample did not cover more than one species when performing analyses at the static and ontogenetic level.

However, we then incorporated all four potential species in the analyses at the evolutionary level.

Although we were cautious in taking into account as much as possible the potentially changing species delimitation, a unified framework for the systematics of long-nosed armadillos remains desirable for this kind of study.

The euphractines are a less diverse clade than the dasypodines, containing 5 species of armadillos according to the latest taxonomic reports (Chapter 1). Recently, the species Chaetophractus nationi was challenged based on morphological and molecular arguments, and merged with the species Chaetophractus vellerosus (e.g., [START_REF] Abba | Systematics of hairy armadillos and the taxonomic status of the Andean hairy armadillo (Chaetophractus nationi)[END_REF][START_REF] Gibb | Shotgun mitogenomics provides a reference phylogenetic framework and timescale for living xenarthrans[END_REF].

The validity of the latter is also debated in relation to its relationship with Zaedyus pichiy, (Supporting Information 1; [START_REF] Wetzel | Taxonomy and distribution of armadillos, Dasypodidae[END_REF][START_REF] Superina | Zaedyus pichiy (Cingulata: Dasypodidae)[END_REF][START_REF] Abba | Systematics of hairy armadillos and the taxonomic status of the Andean hairy armadillo (Chaetophractus nationi)[END_REF][START_REF] Carlini | Chaetophractus vellerosus (Cingulata: Dasypodidae)[END_REF]. This taxonomic uncertainty with respect to these two species is also highlighted by molecular analyses [START_REF] Gibb | Shotgun mitogenomics provides a reference phylogenetic framework and timescale for living xenarthrans[END_REF][START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF]. For our analyses at the static and ontogenetic level, we restricted our sample to the species Zaedyus pichiy because it is the most represented abundantly euphractine in museum collections, though our sample is still plagued by a large amount of missing information attached to specimens (e.g., location, sex...). Our investigation of cranial shape diversity in our sample of Zaedyus pichiy revealed a partitioning of the sample into two clusters (Supporting Information 1). When analyzing allometric variations in adult specimens (Section 3.2), we also observed a partitioning into two clusters, one small and one large. However, the clusters in the two analyses do not completely coincide (see Figure 60 below).

Although we hypothesize that the gap observed in the allometric analysis (Figure 60 below and Section 3.2) corresponds, at least partly, to a difference in size between females and males (sex data almost absent for our specimensonly three females were positively identified, and these represented minimal body sizes within gp2 -Figure 60, Supporting Information 1). This would be consistent with what is known about sexual dimorphism in this species [START_REF] Sidorkewicj | Morphological characterization and sex-related differences of the mandible of the armadillos Chaetophractus vellerosus and Zaedyus pichiy (Xenarthra, Dasypodidae), with consideration of dietary aspects[END_REF][START_REF] Superina | Zaedyus pichiy (Cingulata: Dasypodidae)[END_REF]. On the other hand, the division into two clusters in the analysis of cranial shape diversity (gp1 & gp2, see Supporting Information 1) could reflect the distinction between the two known subspecies, Zaedyus pichiy pichiy Desmarest, 1804 and Zaedyus pichiy caurinus [START_REF] Thomas | Size differences in the little "pichi" armadillos[END_REF], which also differ in size [START_REF] Frechkop | Etude systematique et zoogéographique des Dasypodidés conserves a l'lnstitut[END_REF]Squarcia & Casanave 1999;[START_REF] Superina | Zaedyus pichiy (Cingulata: Dasypodidae)[END_REF]. However, the geographic distributions of the two subspecies are disputed [START_REF] Wetzel | Order cingulata[END_REF][START_REF] Sidorkewicj | Morphological characterization and sex-related differences of the mandible of the armadillos Chaetophractus vellerosus and Zaedyus pichiy (Xenarthra, Dasypodidae), with consideration of dietary aspects[END_REF][START_REF] Superina | Zaedyus pichiy (Cingulata: Dasypodidae)[END_REF], and the recent diagnosis of the species [START_REF] Superina | Zaedyus pichiy (Cingulata: Dasypodidae)[END_REF] no longer mentions a difference in their geographic ranges. This is consistent with the distribution of our groups in the PCA in Supporting Information 1, which did not derive from distinct geographical areas. Unfortunately, no study has jointly quantified the morphological variation in Zaedyus pichiy regarding size, sex, subspecies, and geographical distribution. Such a study is desirable to clarify morphological variations within the species, although the frequent lack of information attached to museum specimens remains an obstacle for any allometric study. The Tolypeutinae contains 6 currently recognized extant species (Chapter 1). Several taxonomic issues have been raised recently within the genus Cabassous. The first issue corresponds to the very weak molecular and morphological distinction between Cabassous unicinctus and Cabassous centralis [START_REF] Hayssen | Cabassous centralis (Cingulata: Dasypodidae)[END_REF]Hayssen, 2014;[START_REF] Gibb | Shotgun mitogenomics provides a reference phylogenetic framework and timescale for living xenarthrans[END_REF], which calls into question the validity of these two species that are otherwise only distinguished on a geographical criterion. The second issue corresponds to the definition of the species Cabassous unicinctus, as revealed in our study of cranial shape diversity. This species showed an unexpectedly strong morphological distinction between specimens of Cabassous unicinctus from northern Brazil and those from southern Brazil (Supporting Information 1). Their geographical distribution could coincide with the two subspecies known for this species, Cabassous unicinctus squamicaudis Lund, 1845 which occurs north of the Amazon, and Cabassous unicinctus unicinctus Linnaeus, 1758, occuring south of the Amazon. These two subsets differed in cranial shape much more strongly from one another than specimens of Cabassous centralis differed from specimens of Cabassous unicinctus from northern Brazil (Supporting Information 1). For these reasons, we constructed two different datasets in Cabassous for our analyses at the static and ontogenetic levels, and we performed each analysis separately on the two datasets. However, as for Dasypus, a clarification of the systematics within the genus Cabassous is urgently needed.

In this PhD dissertation, we were able to analyze a wide diversity of extant and fossil cingulate taxa. However, as explained in the previous paragraphs, the persistence of uncertainties concerning the definition of extant species constituted a limiting factor, which we tried to overcome by using several datasets. It is highly probable that these issues occur for other extant cingulate species, beyond the three that were targeted for our intraspecific analyses. Our study clearly reveals that in-depth morphological and molecular accounts of extant armadillo species are urgently needed. As regards analyses at the evolutionary level, the morphological divergence was particularly strong between the extinct and early diverging genus Peltephilus and other cingulates (Sections 3.2 & 4.1). A clear morphological gap often separated dasypodines from other clades as well (Sections 3.2). Future workers on cranial integration in the group may wish to analyze these morphologically divergent groups separately because they may differ in their patterns of covariation as well. Despite these divergences, our analyses at the evolutionary level recovered covariation patterns similar to those found at the intraspecific level, which suggests that these patterns are pervasive in cingulates.

Potential implications of internal anatomy and morphological integration on morphological matrices in cingulates

In this PhD Dissertation, we explored the internal anatomy and the morphological integration of the cingulate skull with an aim of examining their potential implications for morphological matrices and phylogenetic relationships in the group. We discuss here our results in relation to the largest morphology-based matrix on the Cingulata, that produced by [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF]abbreviated GW hereafter). We focus on some craniodental characters in this matrix and in the revised version published by [START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF]abbreviated B hereafter). Greater attention is paid to the matrix of [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF] because the modifications made by [START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF] were not accompanied by a detailed justification. For this discussion, we have added the following taxa to the matrix: Calyptophractus and all glyptodonts of our sample except Propalaehoplophorus (see Chapter 2 for coding). Potential evolutionary scenarios (reconstructed using parsimony with DELTRANS optimization) for the characters discussed are mapped below on the baseline cladogram used for Chapter 2 (see Figure S4). See Figures S50-S55 for plates illustrating the skulls of the cingulate taxa in our analysis in various views.

The results of our study of the internal cranial anatomy are difficult to compare with previous matrices, because no endocranial features were included in previous matrices. In addition, the few studies discussing the implication of internal structures for the phylogeny of Cingulata do not explicitly propose any characters to be included in phylogenetic matrices (e.g., [START_REF] Fernicola | A neomorphic ossification of the nasal cartilages and the structure of paranasal sinus system of the glyptodont Neosclerocalyptus Paula Couto 1957 (Mammalia, Xenarthra)[END_REF]Tambusso & Fariña, 2015a, 2015b). However, it is possible to evaluate the implications of our observations on the GW characters that deal with the external openings of the internal structures we have analyzed. Seven GW characters are relevant in this regard.

Character 71 from [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF] (GW71) coded the relationship between the sphenopalatine foramen and caudal palatine foramen (Figure 61). In a way, this character thus codes the relationship between the sphenopalatine canal and the palatine canal at the level of their opening in the temporal fossa. Its coding indicates a clear confluence between the two foramina in most cingulates, except for Stegotherium, in which they are clearly separated. For several extant taxai.e., Dasypus, Chaetophractus, Priodontes and Tolypeutesthis character is coded as polymorphic in [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF]. In our study (i.e., Chapter 2), we analyzed the confluence between the two canals well before their opening in the temporal fossa (see character 4 -Chapter 2). A complete fusion of the two canals may distinguish chlamyphorines and glyptodonts from other cingulates (Chapter 2). Scoring this internal fusion may prove more phylogenetically informative (i.e., a posteriori of the phylogenetic analyses) than the seemingly more variable fusion of their external openings.

GW78 deals with the absence/presence of the anterior opening of the posttemporal canal.

Our study of the course of the orbitotemporal canal on the internal lateral wall of the braincase in cingulates indicated that all cingulates in our sample except for Priodontes had an orbitotemporal canal (or groove) (Chapter 2). Chlamyphorus and Vassallia were coded "absent" for the anterior opening of this canal in [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF]Figure 61). Our study suggests that this canal and its anterior opening are not absent in the above-mentioned taxa and that its absence may only represent an autapomorphy of the giant armadillo Priodontes. In such a case, this character would become uninformative.

Four GW characters correspond to variation in the numerous foramina often present on the cranial roof or close to the posterior root of the zygomatic arch in cingulates (foramina of different origins, see below). Our study showed a high variability for most of these foramina and calls for further investigation (Chapter 2). The character GW94 describes the presence or absence of multiple foramina on the dorsal surface of the frontal bone and suggests a similarity among Peltephilus, extant euphractines, tolypeutines (excluding Tolypeutes), chlamyphorines, Proeutatus, Vassallia and some glyptodonts (Figure 61). Our study shows that some of these foramina are derived from branches of the frontal diploic vein canal (Chapter 2), whose presence remains dubious in pampatheres and glyptodonts (Chapter 2). However, some of these frontal foramina have been observed in these groups [START_REF] Gaudin | Phylogenetic relationships among sloths (Mammalia, Xenarthra, Tardigrada): the craniodental evidence[END_REF][START_REF] Gaudin | Cranial osteology of the pampathere Holmesina floridanus (Xenarthra: Cingulata; Blancan NALMA), including a description of an isolated petrosal bone[END_REF]. The high variability in their number and the doubts expressed about their presence in Vassallia and glyptodonts suggest that this character be abandoned until a better knowledge of these structures is gained. The same applies to characters GW95 and GW97, but this time in relation to the posttemporal and orbitotemporal canals (Figure 61). Character GW95 describes a presence of foramen in the posterolateral region of the frontal in dasypodines (with a polymorphism in Dasypus), Prozaedyus, extant euphractines, Cabassous, Calyptophractus and the crown group including Proeutatus, Vassallia and glyptodonts (excluding Glyptodon) (Figure 61). GW 97 describes the presence of more than 5 foramina in the temporal fossa on the parietal, which are present in all cingulates, except for Chlamyphorus, dasypodines and Peltephilus, and which are polymorphic in Tolypeutes and Prozaedyus (Figure 61). A joint revision of characters GW94, GW95 and GW97 is needed and might also focus on the varying density of rami temporales observed in our study (Chapter 2).

Finally, GW120 describes the presence or absence of the suprameatal foramen and accompanying accessory foramina (Figure 61). The presence/absence or number of multiple accessory foramina in this region can be variable within the same species (Chapter 2). Our examination of the internal canals has shown that these accessory foramina may correspond to ramifications originating from the posttemporal canal (and sometimes from the orbitotemporal canal), the canal for the capsuloparietal emissary vein or the region of confluence between these canals (Chapter 2). To make this distinction, we need not just endocranial data from skulls, but actual anatomical information on the vasculature housed in these canals. As for GW94, a better knowledge of the variability and homology of these structures is required. In addition, GW120 is highly polymorphic within cingulate species and its scoring also varies much within clades except for chlamyphorines (Figure 61).

GW111 describes the presence or absence of the foramen transverse canal (Figure 61). This character was weakly informative as it only showed a resemblance between Stegotherium and Chlamyphorus (foramen absentdefined as a primitive state in [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF]. Our investigation of the internal course of the transverse canal revealed that the Tolypeutes specimen in our sample did not possess this canal, which is therefore either absent in this taxon or polymorphic. More importantly, we showed that the orientation of the main branch of the transverse canal suggests a resemblance between Proeutatus, the pampatheres and the glyptodonts, with a loss of the canal in Pleistocene glyptodonts. This phylogenetically informative variation could be combined within a single composite character with the variation encoded by GW111 in future analyses (see Chapter 2).

Figure 61. Evolutionary scenarios for some characters of [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF]GW) and [START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF][START_REF] Sidlauskas | Continuous and arrested morphological diversification in sister clades of characiform fishes: a phylomorphospace approach[END_REF] mentioned in this Discussion (mapped on the baseline cladogram of Chapter 2). The coding follows [START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF], except for the added taxa Calyptophractus, "Metopotoxus", Eucinepeltus, "Cochlops" and Glyptodon, whose scores are available in Chapter 2. Branches with dots of different colors indicate polymorphism.

The second part of our work explored cranial integration patterns in relation to size with GMM methods (Chapter 3) or based on correlation among linear distances (Chapter 4), at the intraspecific and evolutionary levels. We were able to detect several allometric trends (Figure 62)

and cranial covariations (Figure 63) that appear to be widespread in cingulates. Of course, none of these approaches is exhaustive, and we are surely far from having unearthed all the interesting cranial covariations in the group, which must be numerous and very complex. Nevertheless, these represent complementary approaches for an exploration of covariation patterns and their relation to morphological characters.

Considering the morphological characters present in the GW matrix, relatively few can be unambiguously connected to the strongest and most widespread covariations we found. However, there are still some aspects to be discussed in this regard, including potential implications and ways of improving some characters.

First, several GW characters quantify the variation of selective cranial distances relative to greatest skull length, which may in fact present an allometric component. For example, one could postulate that the allometric elongation of the snout and masticatory apparatus in large specimens (craniofacial allometry; CREA) detected at all levels of our analyses (Figure 62) could affect in some way the variation scored by GW36 and GW37 (Figure 64). For character 36, [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF] describes the relative length of the rostrum starting posteriorly from the orbital rim. This character discriminates the posterior position of the orbit in dasypodines and the anteriorly shifted orbit of glyptodonts (Figure 64). In addition, it also shows a lower elongation of the snout relative to the orbit in Calyptophractus and Vassallia (Figure 64). The anteriorly shifted position of the orbit in glyptodonts contrasts with the allometric patterns we detected at the intraspecific levels or at the evolutionary level on extant species only, which rather showed a posteriorly shifted or stable position of the orbit, except for the evolutionary analysis including fossils (Chapter 3). Smaller species such as chlamyphorines also show a relatively anterior orbit position in contrast to larger forms such as certain dasypodines and Priodontes. At first glance, the scoring of GW36 thus seems to be incongruent with the allometric elongation of the snout found at most levels in our study and not much affected by the CREA. However, this character would be better scored with continuous data (see below) in order to better check for a possible allometric component in its variation. Unlike the pre-orbital length, the masticatory apparatus is extremely enlarged in glyptodonts which is congruent with our results and the CREA. GW37 describes the length of the nasal relative to the skull length. In our study, the variation of the landmark located on the nasal midline suggested an allometric shortening of the nasal in several, but not all, analyses (instraspecific Zaedyus, static Dasypus, and evolutionary analyses). The scoring of GW37 evidences no clear allometric trend as well (Figure 64), except that glyptodonts have short nasals ending posteriorly at the front of the anteriorly shifted orbits [START_REF] Fernicola | A neomorphic ossification of the nasal cartilages and the structure of paranasal sinus system of the glyptodont Neosclerocalyptus Paula Couto 1957 (Mammalia, Xenarthra)[END_REF]. As for GW36, it would be interesting to examine more the variation of this character with quantitative data (see below).

Our study also detected an allometric widening of the distance between the zygomatic arch and the postorbital constriction, creating a relatively larger temporal fenestra in large specimens (Figure 62). This allometry could influence the variation scored in GW61, which describes the maximum skull width at the zygomatic arches in relation to the greatest skull length (Figure 64).

However, the scoring of GW61 only shows a resemblance between the Dasypodinae and the tolypeutines Priodontes and Tolypeutes, coded as having a transversely narrow inter-zygomatic region with all other armadillos considered wide. Thus, the binary scoring used for this character does not reflect the allometric pattern detected for these structures in our study.

Our exploration also revealed a stronger postorbital constriction as the size increases at the intraspecific and evolutionary levels in cingulates (Figure 62). This allometric pattern could affect GW62 which describes the relative width of the interorbital area compared to the greatest skull length (Figure 64). The postorbital constriction and the interorbital area may be fully confounded or very close in some taxa (e.g., Dasypussee Figures S50-S55), which is why we suspect a possible relationship between our allometric pattern and this character. GW62 exhibits substantial homoplasy on our baseline cladogram and is polymorphic in several clades and species (Figure 64). Its distribution on the tree seems to be partly consistent with our results, with several large taxa presenting a strong postorbital constriction (glyptodonts, pampatheres; and Priodontes when compared to other tolypeutines).

The variation of several of the characters discussed above may be, at least partly, impacted by allometry and would thus necessitate a revision. However, their scoring corresponds to the discretization of a ratio between two distances (i.e., one length on GSL) which hides part of their variation and may partly obscure an allometric component. Alternative coding strategies may need to be used to assess more effectively their variation and to avoid an allometric signal (see Section

5.3).

Figure 64. Evolutionary scenarios for some characters of [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF]GW) and [START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF][START_REF] Sidlauskas | Continuous and arrested morphological diversification in sister clades of characiform fishes: a phylomorphospace approach[END_REF] mentioned in this Discussion (mapped on the baseline cladogram of Chapter 2). The coding follows [START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF], except for the added taxa Calyptophractus, "Metopotoxus", Eucinepeltus, "Cochlops" and Glyptodon, whose scores are available in Chapter 2. Branches with dots of different colors indicate polymorphism.

In accordance with the widespread craniofacial allometry in mammals, our study also shows a reduction in braincase proportions as size increases (Figure 62). GW91 describes the shape of the braincase with a focus on the parietal (Figure 64). The scoring of GW91 suggests a resemblance between euphractines, Prozaedyus, chlamyphorines and glyptodonts, with a dorsoventrally compressed braincase that would distinguish them from other cingulates (Figure 64). Although this binary scoring does not reflect clearly the allometric flattening of the braincase shown in our study (small-sized chlamyphorines scored as flat), it is likely that the latter plays a role in the variation scored for this character. Large-sized glyptodonts are indeed found to have a flattened braincase (Figures S50-S55).

One of the strongest allometric patterns detected at all levels corresponds to more prominent nuchal crest processes as size increases (Figure 62). GW100 describes the shape of these crests in dorsal view, which are W-shaped in cingulates, as shown in our study. This represents a possible synapomorphy for Cingulata (Figure 64). GW163 describes differences in the posterior thickening of the nuchal crests which occur within cingulates. The scoring of GW163 suggests a resemblance between Stegotherium, Priodontes and Peltephilus, with posteriorly thickened dorsal bosses that would distinguish them from other cingulates (Figure 64). This scoring does not reflect the allometric pattern found in our study. The large-sized glyptodonts and pampatheres are not scored as having posteriorly thickened dorsal bosses, yet they present prominent nuchal crests (Figures S50-S55). The link between this character and our detected allometric pattern is obviously not direct, however it would be relevant to measure the correlation between the presence of these rugosities and the development of nuchal crests. As with previous characters, an alternative coding strategy could be used to accurately assess the variation of this character and avoid an allometric signal (see Section 5.3). As demonstrated in our study, allometric pattern analysis over the entire skull (ES approach) can mask more regionalized patterns of allometry (Chapter 3). Our analyses of allometry on cranial units (3B approach) also revealed several common patterns among cingulates (Figure 62), two of which may have potential implications on GW characters.

Our 3B approach revealed an allometric reduction in the proportions of the foramen magnum as size increases (Figure 62). GW159 describes the width of the foramen magnum in relation to the width of the occiput (Figure 65). It suggests a resemblance between Dasypus and Tolypeutes as taxa with a relatively broad foramen magnum in opposition to the other cingulates (Figure 65). As for several other characters mentioned above, although the scoring of this binary character is not strongly congruent with our allometric pattern, allometry may still play a role in the variation that was scored. For this reason, alternative character constructions should be explored in the future (see Section 5.3).

Our 3B approach of cranial allometry also revealed a more salient development of the mastoid process (= paroccipital process of the petrosal in [START_REF] Wible | On the cranial osteology of the yellow armadillo Euphractus sexcintus (Dasypodidae, Xenarthra, Placentalia)[END_REF] as size increases (Figure 62). GW134 describes the direction of the greatest width of the mastoid process and suggests a resemblance between Peltephilus, Prozaedyus, euphractines and chlamyphorines that have a process that is broader mediolaterally than anteroposteriorly (Figure 65). Only one landmark was placed on the mastoid process in our study (see Section 3.1), which did not permit examination of whether the allometric protrusion of this process could be accompanied by changes in the direction of its greatest width.

To a lesser extent, the selected pairs of correlated distances also highlight covariation patterns that need to be considered when revising phylogenetic matrices. The reduced number of selected pairs supported both at the intraspecific and evolutionary levels mainly concern the orbitotemporal region containing the anterior root of the zygomatic arch, the orbit, and the posterior part of the palate (Figure 63).

Pair n°5 suggests faster growth of the distance from the anterior root of the zygomatic arch (most ventral contact between the zygomatic process of the maxillary and the jugal) to the petrosal than of the distance from the petrosal to a more dorsal point on the anterior edge of the orbit. This may be due to a more ventral position of the zygomatic processes of the maxillary and the jugal in larger specimens (see Section 4.1). This aspect can be compared with the variation described by at least two characters of the GW matrix.

GW 85 describes the anterior depth (height) of the jugal (Figure 65). It suggests a resemblance between Tolypeutes, Zaedyus and Dasypus which present a uniform depth, as opposed to Prozaedyus, Euphractus, the chlamyphorines, Proeutatus and glyptodonts (except Eucinepeltus -Figure 65) presenting a maximum depth in the anterior half of the bone, and to the other cingulates that show a maximal depth posteriorly (Figure 65). The scoring of this character cannot be directly compared to the information brought by pair n°5 but it is possible that the trend towards a more ventral position of the maxillary-jugal suture in large specimens may affect it to some extent. In addition, we were also able to note that a relatively higher jugal bone is found in larger individuals in the three species analyzed at the ontogenetic and static levels (Chapter 3). It was unclear, however, whether the jugal bone was higher anteriorly than posteriorly in large specimens, and this trend was not supported at the evolutionary level. Therefore, more research would be needed on the allometric patterns in this region (see Section 5.3) to determine if a revision of GW85 is necessary.

GW86 describes the variation of the ventral process on the anterior root of the zygomatic arch (Figure 65). It shows that glyptodonts possess a distinctive descending ventral process of the zygomatic arch [START_REF] Scott | Mammalia of the Santa Cruz beds. I. Edentata[END_REF] that is more marked than in other cingulates (Figures S50-S55). This is strongly reminiscent of the information provided by the pair n°5 (see above and Section 4.1)

with a potentially more ventral landmark #21 in larger specimens. This suggests that the variation of this character may be influenced by an allometric pattern indicated by pair n°5 (Section 4.1), but which was not clearly detected by our GMM studies on cranial allometry (Section 3.2). Only a slightly more ventral position for this landmark was detected in intraspecific series (weak in Zaedyus but stronger in Dasypus) and at the evolutionary level incorporating fossil taxa (i.e., Dataset-Lmax). In this case, like in many others, more research is needed before a revision of this character is undertaken despite the particularly extreme morphology of glyptodonts (see Section

5.3).

Finally, the pair n°12 suggests a faster growth of the distance between the posterolateral margin of the palate and the maxillary foramen than of the more dorsal distance between the anterior edge of the orbit and the posteromedial margin of the palate (Figure 63). This covariation therefore could signal an anterolateral shift of the position of the maxillary foramen with respect to the palatal edge when this area is growing, but the exact anatomical changes behind this covariation remains obscure and more research is needed (see below). Characters whose variations could be potentially related to this pattern include GW63 & B51, which both describe different aspects of the location of the maxillary foramen (Figure 65). GW63 describes the visibility of the foramen in lateral view. It suggests a resemblance between dasypodines and tolypeutines (with a polymorphism in Tolypeutes) which exhibit a visible foramen in lateral view (Figure 65). B51

describes the connection between this foramen and the caudal palatine foramen. The two foramina are in the same groove in Stegotherium, Priodontes and Cabassous (Figure 65). Curiously, the taxa gathered by these two characters correspond to taxa with a strong reduction in the height of the dental alveoli, an aspect for which we question the allometric component (see Chapter 2).

Overall, potential links between GW characters and the pairs of correlated distances selected in our work are extremely difficult to establish, more than for the results of our studies on cranial allometry. A complementary analytical method to overcome these difficulties would be to analyze the covariation between two anatomical regions each composed of several landmarks. This is a strategy that is widely used with the 2-Blocks Partial Least Squares (PLS & PGLS -Bookstein et al., 2003;[START_REF] Klingenberg | Developmental integration in a complex morphological structure: how distinct are the modules in the mouse mandible?[END_REF][START_REF] Monteiro | Evolutionary integration and morphological diversification in complex morphological structures: mandible shape divergence in spiny rats (Rodentia, Echimyidae)[END_REF][START_REF] Klingenberg | Evolutionary covariation in geometric morphometric data: analyzing integration, modularity, and allometry in a phylogenetic context[END_REF]. However, this method requires the a priori definition of the two regions to be analyzed.

Our study now allows us to highlight these potential regions (see Section 5.3).

In summary, only a small proportion of the GW and B characters were found to have a potential link with the allometric and covariation patterns obtained in our study (20 GW characters and one additional character of B). However, this small proportion should be considered in relation to the composition of our landmark set and the definition of the characters which cannot easily compared with one another in many cases. Of the 163 GW characters, 123 could not be addressed by our analyses of cranial allometry and covariations because they cannot be represented by landmarks and because a substantial number concern the mandible (not included in our study;

Figure 66, Table 16). We have discussed above several characters (n = 13 GW characters) whose variation may have ties to patterns of allometry and covariation highlighted in our study.

Additional GW characters may also be related to patterns that were supported only at the intraspecific levels (Figure 66, Table 16) and were not discussed because they were not found at the evolutionary level, or vice versa. This is, for example, the case for GW39, which describes the presence or absence of a well-defined notch on the anteroventral edge of the premaxillary. The shape of this structure was allometric in Dasypus and Zaedyus (Section 3.2). This is also the case, at the evolutionary level for GW121 which describes the contact between the petrosal and the basicranial axis, which was found to be allometric at the evolutionary level but not at the intraspecific level (Section 3.2). These aspects also warrant further research. [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF] on morphological variation especially when they were performed on the modules obtained in Section 4.2. A good example concerns the second axis of the PCA performed on the vaultbasicranium module with the posterodorsal part of the module showing a relative increase in height of the vault (#67; #72-74; #86; #99-100) while the lateral part of the module corresponding to the squamosal (#55-58; #70-71) showed a much more ventral position (Section 4.3). These cooccurring shape changes on PC2 may signal a coordinated variation which could impact several GW characters (e.g., 90; 91; 99; 100). However, this pattern was only analyzed with PCA and at the evolutionary level, which does not allow us to conclude whether it really represents a covariation. Analyses focused on this region at the intraspecific level would be required to test if such a covariation is present within species. Nevertheless, three-dimensional analysis of shape diversity using PCA may represent a complementary way to detect potentially covariant regions.

In conclusion, based on our investigation of GW and B characters, we observe that links between the detected patterns of integration and the scored phylogenetic characters are hard to establish. This is mainly because the comparison between the detected pattern of integration and the definition of the GW or B characters was not straightforward in many cases, due to differing methods (e.g., continuous vs discrete characters) and/or scope (e.g., landmarks not covering all the variation scored with a naked eye for a character). Most of the potential implications on GW and B characters are related to allometric patterns highlighted in Chapter 3 rather than with pairs of correlated distances from Section 4.1, probably because the interpretation of the former is less complex. Nevertheless, covariation patterns are not restricted to allometry, and even though allometry is more easily related to morphological characters than pairs of correlated distances, both need to be taken into account in morphological phylogenetics, which appears difficult with traditional coding strategies. Other approaches are thus needed to improve our understanding of the relationship between detected covariation patterns and phylogenetic characters, and thereby improve our character constructions.

Complexity of morphological variation, limitations, and prospects

Advances in analytical methods and techniques have highlighted our gross lack of sizable gaps remaining in our knowledge of morphological variation in general [START_REF] Hallgrímsson | Variation: a central concept in biology[END_REF]. This is partly explained by the extreme complexity of this phenomenon, which has determinants that can be multiple and interconnected, acting at all levels of the biological hierarchy [START_REF] Hallgrímsson | Variation: a central concept in biology[END_REF]. This complexity impacts all morphological studies, and in particular the studies on morphological integration and modularity which have become a major topic in evolutionary biology in recent years [START_REF] Wagner | Perspective: complex adaptations and the evolution of evolvability[END_REF][START_REF] Klingenberg | Morphological integration and developmental modularity[END_REF]Goswami & Polly, 2010b;[START_REF] Wagner | The road to modularity[END_REF][START_REF] Klingenberg | Evolution and development of shape: integrating quantitative approaches[END_REF]. The complexity and integrated nature of morphological variation certainly represents one of the major constraints for morphological phylogenetics because the latter require independence between the characters analyzed [START_REF] Felsenstein | Maximum likelihood and minimum-steps methods for estimating evolutionary trees from data on discrete characters[END_REF][START_REF] Kluge | A concern for evidence and a phylogenetic hypothesis of relationships among Epicrates (Boidae, Serpentes)[END_REF][START_REF] Emerson | Morphological correlations in evolution: consequences for phylogenetic analysis[END_REF][START_REF] O'keefe | Inferring and testing hypotheses of cladistic character dependence by using character compatibility[END_REF][START_REF] Lewis | A likelihood approach to estimating phylogeny from discrete morphological character data[END_REF][START_REF] Felsenstein | Inferring phylogenies[END_REF]. Our poor knowledge of patterns of covariation and of their complexity has potentially led authors to involuntarily leave this issue aside when scoring characters. This has led to calls for improvements in our approaches and methods relative to the issue of correlated characters [START_REF] Dávalos | Integrating incomplete fossils by isolating conflicting signal in saturated and non-independent morphological characters[END_REF][START_REF] Goswami | The macroevolutionary consequences of phenotypic integration: from development to deep time[END_REF]Billet et al., 2015;[START_REF] Billet | Serial Homology and Correlated Characters in Morphological Phylogenetics: Modeling the Evolution of Dental Crests in Placentals[END_REF].

To this end, we have adopted an exploratory approach, so as not to limit the very wide field of possible morphological variations to be discovered, and to take paths that are still poorly known [START_REF] Yanai | A hypothetical is a liability[END_REF]. This exploratory approach was complemented by a confirmatory approach that tested at the evolutionary level the hypotheses generated from our results at the intraspecific level, as in the case of pairs of correlated distances (Section 4.1).

Our exploratory approach extended to several biological levels (static, ontogenetic, and evolutionary) to find widespread patterns in the group (limiting the effect of ontogeny with the static level or of phylogeny with the intraspecific levelssee [START_REF] Klingenberg | Studying morphological integration and modularity at multiple levels: concepts and analysis[END_REF]. We also looked at different scales of variation on the skull, from global (entire skull) to more local patterns (cranial subunits, pairs of distances). These different levels of analysis could be complex to interpret, especially since the approaches also varied. In the case of a strong and pervasive patterns such as those often induced by allometry, we opted for a geometric morphometrics method with a

Procrustes superimposition. This superimposition can, however, be problematic for a broader approach to covariations among landmarks, e.g., without depending on factors such as size (Cardini, 2019b[START_REF] Cardini | Less tautology, more biology? A comment on "high-density" morphometrics[END_REF][START_REF] Klingenberg | How Exactly Did the Nose Get That Long? A Critical Rethinking of the Pinocchio Effect and How Shape Changes Relate to Landmarks[END_REF]. Therefore, we opted for the analysis of covariations among distances, although this approach also presents a high degree of complexity and the constraint of dealing with a gigantic amount of data. The relationship between distances and 3D coordinates (i.e., landmarks) remains exceedingly difficult and unclear [START_REF] Hubbe | A case study of extant and extinct Xenarthra cranium covariance structure: implications and applications to paleontology[END_REF] limiting our interpretations. This limitation is also one of the major impediments to the exploratory approach. By taking new paths, we had very few comparable studies in the literature on which to rely. We tried to interpret some of our covariation patterns on the basis of well-known general patterns, e.g., craniofacial allometry or developmental and functional hypotheses, but we often found ourselves limited by the lack of comparable data. Nevertheless, our exploratory approach allowed us to treat a very large amount of data and generate many new hypotheses on integration patterns within the cingulate skull. We are hopeful that this will pave the way for future studies to test our hypotheses further and to extend our patchy knowledge of morphological integration with the use of other exploratory approaches.

As regards the GW characters whose variation may be partly linked to size (see above), several ways forward may exist. If several characters score evolutionary changes all related to size variation, then they are necessarily partly dependent, which is problematic for phylogenetic analyses [START_REF] Felsenstein | Maximum likelihood and minimum-steps methods for estimating evolutionary trees from data on discrete characters[END_REF][START_REF] Kluge | A concern for evidence and a phylogenetic hypothesis of relationships among Epicrates (Boidae, Serpentes)[END_REF][START_REF] Emerson | Morphological correlations in evolution: consequences for phylogenetic analysis[END_REF][START_REF] O'keefe | Inferring and testing hypotheses of cladistic character dependence by using character compatibility[END_REF][START_REF] Lewis | A likelihood approach to estimating phylogeny from discrete morphological character data[END_REF][START_REF] Felsenstein | Inferring phylogenies[END_REF]. One strategy would be to simply remove these characters from phylogenetic analysis. This strategy would appear as unsatisfactory as it could lead to a loss of phylogenetic information, since a phylogenetic signal may still be contained in the variation of characters with an allometric component. The GW 36, 37, 61, and 62 characters discussed above correspond to discretized continuous characters. Numerous studies criticize the unsatisfactory nature of this type of trait, notably because of the loss of information linked to discretization, which reflects less well the morphological variation but also the subjective aspect of the definition of the intervals [START_REF] Hillis | Signal, noise, and reliability in molecular phylogenetic analyses[END_REF][START_REF] Yang | On the best evolutionary rate for phylogenetic analysis[END_REF][START_REF] Donoghue | Homoplasy and developmental constraint: a model and an example from plants[END_REF][START_REF] Wiens | Character analysis in morphological phylogenetics: problems and solutions[END_REF][START_REF] Parins-Fukuchi | Use of continuous traits can improve morphological phylogenetics[END_REF]. In addition, several authors argue that most morphological variation is basically continuous [START_REF] Thiele | The holy grail of the perfect character: the cladistic treatment of morphometric data[END_REF][START_REF] Rae | The logical basis for the use of continuous characters in phylogenetic systematics[END_REF][START_REF] Wiens | Character analysis in morphological phylogenetics: problems and solutions[END_REF][START_REF] Parins-Fukuchi | Use of continuous traits can improve morphological phylogenetics[END_REF]. A better strategy would be to treat these traits in a continuous manner [START_REF] Wiens | Character analysis in morphological phylogenetics: problems and solutions[END_REF][START_REF] Parins-Fukuchi | Use of continuous traits can improve morphological phylogenetics[END_REF] and then assess their relationship with allometry. This would greatly facilitate assessment by making it clearer to compare with only continuous variables (see below).

If two characters are covarying, one strategy could be to combine them in a single character as proposed by [START_REF] Wilkinson | A comparison of two methods of character construction[END_REF] in his composite coding strategy (Figure 67). Although the relationship between GW characters and the detected patterns of integration remains to be clarified in many cases, this strategy can represent a promising way forward relative to the issue of character independence for phylogenies (see a different example on discrete characters in [START_REF] Billet | Serial Homology and Correlated Characters in Morphological Phylogenetics: Modeling the Evolution of Dental Crests in Placentals[END_REF]; and see a concrete example below on continuous variables).

Figure 67. Rationale of the composite coding strategy [START_REF] Wilkinson | A comparison of two methods of character construction[END_REF] in the case of highly correlated continuous characters.

Our study also gives rise to other ideas of character construction and scoring regarding the evolutionary history of cingulates. The covariation patterns detected at certain levels appear as potentially discriminating elements within cingulates. For example, a well-established consensus in the literature lies in the distinction between dasypodids (containing Dasypus) and chlamyphorids (containing Cabassous and Zaedyus). We detected in various cases covariation patterns common to Cabassous and Zaedyus but absent in Dasypus, such as the relative lengthening of the frontal process of the nasal when the size increases at the intraspecific level (Section 3.2). Further investigation in other cingulates could confirm that this covariation itself is potentially a synapomorphy of chlamyphorids, which could thus be coded as a character.

In a different way, patterns common to all three species at the intraspecific level may also be present in other cingulates and might deliver phylogenetic information as well. In this case, coding strategies could follow the suggestion to code the allometric trajectories that potentially represent biological traits under selection [START_REF] Weber | Selection on wing allometry in Drosophila melanogaster[END_REF][START_REF] Frankino | Natural selection and developmental constraints in the evolution of allometries[END_REF][START_REF] Adams | Ontogenetic convergence and evolution of foot morphology in European cave salamanders (Family: Plethodontidae)[END_REF][START_REF] Wilson | Diversity trends and their ontogenetic basis: an exploration of allometric disparity in rodents[END_REF][START_REF] Klingenberg | Evolution and development of shape: integrating quantitative approaches[END_REF][START_REF] Urošević | Patterns of cranial ontogeny in lacertid lizards: morphological and allometric disparity[END_REF][START_REF] Porto | Size variation, growth strategies, and the evolution of modularity in the mammalian skull[END_REF][START_REF] Giannini | Quantitative developmental data in a phylogenetic framework[END_REF]. This could be done, for instance, for the relative shortening and increase in height of the jugal when size increases, detected at the intraspecific level in Dasypus, Zaedyus and Cabassous (Section 3.2). Coding the slopes of differing trajectories could thus add new characters to matrices on cingulates.

The relationship between the intra-and interspecific level can also potentially provide ideas for new coding strategies. In the case of two highly correlated traits at the two levels, the regressions could have rather similar slopes. This is what we observe in the case of pair n°5 for example (Figure 68A; and see Section 4.1). In the case of pair n°5, a quantification of the orthogonal distance of taxa from the regression line may provide phylogenetic information that could be scored as a continuous character (Strategy C1 -Figure 68B). This would represent the position of species relative to the regression line. For instance, the lower position of most euphractines (red dots; Figure 68B) relative to the line indicate that they tend to have lower values for the distance #21-108 relative to the common trend in cingulates, which could constitute interesting phylogenetic information. Similarly, one may also want to code as a continuous character the position of the taxa along the regression line once fitted (Strategy C2). It could for example distinguish the dasypodines, which have low values for these distances relative to the skull size when compared to other cingulates (Figure 68B). Ideally, these strategies could be used only if the resulting traits are not correlated with other traits and not allometric. Further investigation in this direction could be conducted based on our results but the position of taxa on regression plots suggests that it might be a promising avenue for alternative coding to incorporate the impact of covariation patterns. Finally, the covariation patterns derived from correlated distance pairs as well as PCAs allow the targeting of potentially highly covariant regions, e.g., anterior edge of orbit and ventral part of anterior root of zygomatic arches), once these regions have been identified, one way to further investigate patterns of covariation would be to conduct analyses such as 2-blocks partial least squares to improve our understanding of the 3-dimensional covariation of two regions (e.g., [START_REF] Bookstein | Cranial integration in Homo: singular warps analysis of the midsagittal plane in ontogeny and evolution[END_REF][START_REF] Klingenberg | Developmental integration in a complex morphological structure: how distinct are the modules in the mouse mandible?[END_REF][START_REF] Monteiro | Evolutionary integration and morphological diversification in complex morphological structures: mandible shape divergence in spiny rats (Rodentia, Echimyidae)[END_REF][START_REF] Klingenberg | Evolutionary covariation in geometric morphometric data: analyzing integration, modularity, and allometry in a phylogenetic context[END_REF]. These analyses require an a priori division into two blocks which was not possible before our study, but which could now be utilized based on the results of our study.

Beyond their phylogenetic implications, our multilevel analyses of patterns of cranial integration in cingulates may pave the way for further studies aiming at a better understanding patterns and processes of morphological covariation. In the light of our results, it would be possible to analyze more concretely the development of cranial units during ontogeny in cingulates,

particularly at the prenatal level. This would be particularly relevant in the case of the development of the zygomatic arch, which appears to be developed at the prenatal level in glyptodonts [START_REF] Zurita | First record and description of an exceptional unborn specimen of Cingulata Glyptodontidae: Glyptodon Owen (Xenarthra)[END_REF] but also in nine-banded armadillo fetuses (Le Verger et al., unpublished data). Outside cingulates, it would be also interesting to couple this kind of analysis with a study of gene expression for highly correlated regions in model organisms (e.g., for the zygomatic arch [START_REF] Percival | Developmental constraint through negative pleiotropy in the zygomatic arch[END_REF], or to examine the implication of developmental constraints on allometric patterns. A good way to complement our approach would also be to investigate muscular anatomy through dissections at different ontogenetic stages within species, as many detected covariations were found in regions of muscle insertion (e.g., the nuchal crest, mastoid process, and descending process of zygomatic arch).

In conclusion, morphological covariations represent an insufficiently known and yet pervasive aspect of morphological variation. A better knowledge of this complex phenomenon is an important step for the improvement of morphological phylogenetic characters, which remain essential for the incorporation of fossils in phylogenies. The present work has allowed a deep exploration of covariation patterns in the skull of cingulates, but it was by no mean exhaustive, which again highlights the immense field of study that the analysis of morphological variation (and covariation) represents (Hallgrimsson & Hall, 2005). Our study corresponds to a preliminary and exploratory step and argues for more in-depth analysis, including new coding strategies of covarying traits, which represents a promising new path for morphological phylogenetics. Pending further studies of this kind in cingulates, it is currently hard to state what the impact of our results could be on morphological matrices and on the reconstruction of cingulate relationships based on morphological data. Our analysis of the internal cranial anatomy has shown several resemblances between chlamyphorines and glyptodonts, as well as between the latter and the extinct pampatheres and the extinct genus Proeutatus. These findings are in partial agreement with molecular analyses and with previous morphological accounts [START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF][START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF][START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF][START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF] and might help to reach a more consensual vision of the phylogenetic relationships within the Cingulata in the future. In addition, our results

have shown the existence of pervasive patterns of cranial integration in the group, especially allometry. This pervasiveness of allometry may imply that if morphological evidence may exist to group small-sized chlamyphorines together with giant-sized glyptodonts [START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF][START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF], then it might also be largely hidden by allometric patterns. Although allometric and other covariation patterns are difficult to compare with characters already defined in morphological matrices, alternative coding strategies must be used to evaluate their impact on such phylogenetic hypotheses in the future. [START_REF] Superina | Family Chlamyphoridae (Chlamyphorid armadillos)[END_REF]. This account might however be slightly inaccurate as recent analyses of mitochondrial genomes suggested that several species can potentially be lumped together while others should be split [START_REF] Gibb | Shotgun mitogenomics provides a reference phylogenetic framework and timescale for living xenarthrans[END_REF]. In Dasypus novemcinctus, there was even a high level of congruence between new morphological and molecular data to propose that this species should be viewed as a species complex requiring further investigation [START_REF] Huchon | Armadillos exhibit less genetic polymorphism in North America than in South America: nuclear and mitochondrial data confirm a founder effect in Dasypus novemcinctus (Xenarthra)[END_REF][START_REF] Gibb | Shotgun mitogenomics provides a reference phylogenetic framework and timescale for living xenarthrans[END_REF][START_REF] Billet | The hidden anatomy of paranasal sinuses reveals biogeographically distinct morphotypes in the nine-banded armadillo (Dasypus novemcinctus)[END_REF][START_REF] Hautier | Beyond the carapace: skull shape variation and morphological systematics of long-nosed armadillos (genus Dasypus)[END_REF][START_REF] Feijó | Taxonomic revision of the long-nosed armadillos, Genus Dasypus Linnaeus, 1758 (Mammalia, Cingulata)[END_REF][START_REF] Feijó | Phylogeny and molecular species delimitation of long-nosed armadillos (Dasypus: Cingulata) supports morphology-based taxonomy[END_REF][START_REF] Arteaga | Conservation Genetics, Demographic History, and Climatic Distribution of the Nine-Banded Armadillo (Dasypus novemcinctus): An Analysis of Its Mitochondrial Lineages[END_REF]. In summary,

Supporting Information 1: Cabassous & Zaedyus

these recent examples underline that the systematics of many extant species within Cingulata may require revision. The identification of a well-defined taxonomic context is very important for the purposes of our study exploring static and ontogenetic covariation patterns within three extant species of armadillos -Dasypus novemcinctus (southern morphotype), Zaedyus pichiy [START_REF] Desmarest | Tableau méthodique des mammifères[END_REF], and Cabassous unicinctus [START_REF] Linnaeus | Systema naturae per regna tria naturae, secundum classes, ordines, genera, species, cum characteribus, differentiis, synonymis, locis[END_REF]. As mentioned above, the variation and systematics within Dasypus novemcinctus was recently studied at the molecular and morphoanatomical level [START_REF] Huchon | Armadillos exhibit less genetic polymorphism in North America than in South America: nuclear and mitochondrial data confirm a founder effect in Dasypus novemcinctus (Xenarthra)[END_REF][START_REF] Gibb | Shotgun mitogenomics provides a reference phylogenetic framework and timescale for living xenarthrans[END_REF][START_REF] Billet | The hidden anatomy of paranasal sinuses reveals biogeographically distinct morphotypes in the nine-banded armadillo (Dasypus novemcinctus)[END_REF][START_REF] Hautier | Beyond the carapace: skull shape variation and morphological systematics of long-nosed armadillos (genus Dasypus)[END_REF][START_REF] Feijó | Taxonomic revision of the long-nosed armadillos, Genus Dasypus Linnaeus, 1758 (Mammalia, Cingulata)[END_REF][START_REF] Feijó | Phylogeny and molecular species delimitation of long-nosed armadillos (Dasypus: Cingulata) supports morphology-based taxonomy[END_REF][START_REF] Arteaga | Conservation Genetics, Demographic History, and Climatic Distribution of the Nine-Banded Armadillo (Dasypus novemcinctus): An Analysis of Its Mitochondrial Lineages[END_REF] and these results were considered for our specimen selection within this species complex (Chapters 2, 3 & 4).

However, the systematics of the two other selected species, Cabassous unicinctus and Zaedyus pichiy, remain unclear. For this reason, and because museal specimens in our sample might have been previously misidentified, we tried to explore in more details their specific identification based on different criterions. We determined the relative age of specimens using discrete observation of bone sutures and performed analyses on the cranial shape using landmarks to investigate how specimens were distributed in the morphospace for each species. Using existing diagnoses, the distribution of specimens in the morphospace, their ontogenetic stage, size differences and geographical origin (when available), we discuss below our final selection of specimens within these two species.

Taxonomic context and sampling in Cabassous and Zaedyus

2.1

The Cabassous Case Cabassous unicinctus and Cabassous tatouay differ morpho-anatomically by a strong variation in size (average of greatest cranial size: 81.85 mm in Cabassous unicinctus and 108.5 mm Cabassous tatouay (Hayssen, 2014a(Hayssen, , 2014b))) and a ratio of palate length to maxillary tooth row length longer in C. tatouay than in the other three species (Hayssen, 2014a). Cabassous chacoensis does not occur in the ranges of the other species and differs from them by a curvature of the tooth row and mandibular ramus on both dorsoventral and mediolateral axes [START_REF] Wetzel | Revision of the naked-tailed armadillos genus Cabassous McMurtrie[END_REF] with the first and last teeth compressed anteroposteriorly rather than transversely (Hayssen, 2014c).

Molecular studies suggest a clear genetic distinction between Cabassous tatouay, Cabassous chacoensis and a clade gathering Cabassous centralis and Cabassous unicinctus, but not between the latter two species [START_REF] Gibb | Shotgun mitogenomics provides a reference phylogenetic framework and timescale for living xenarthrans[END_REF]. Cabassous centralis and Cabassous unicinctus differ in their geographical distribution position on either side of the northern range of the Andes (Hayssen, 2014b) but not clearly in their morphology, except possibly for the external surface of their pinna (Hayssen et al., 2013) (Figure SI.1). Moreover, it should be noted that two subspecies are known for Cabassous unicinctus [START_REF] Wetzel | Order cingulata[END_REF]: one distributed in the north and west of the Amazon River (Cabassous unicinctus unicinctus [START_REF] Linnaeus | Systema naturae per regna tria naturae, secundum classes, ordines, genera, species, cum characteribus, differentiis, synonymis, locis[END_REF]) and one distributed in the south-eastern part of Brazil (Cabassous unicinctus squamicaudis [START_REF] Lund | Conspectum dasypodum. Det Kongelige Danske Videnskabernes[END_REF]).

Sampling and a priori hypothesis

During the PhD

2.2

The Zaedyus Case

State of art and Diagnosis

The monospecific genus Zaedyus, belongs to the Euphractinae composed of 4 species - Genetic distances between genera leave little doubt as to the distinction between these species although the analysis of [START_REF] Gibb | Shotgun mitogenomics provides a reference phylogenetic framework and timescale for living xenarthrans[END_REF] suggests that Chaetophractus is a paraphyletic genus. Euphractus sexcinctus is well differentiated from other euphractines both molecularly and morpho-anatomically [START_REF] Abba | Systematics of hairy armadillos and the taxonomic status of the Andean hairy armadillo (Chaetophractus nationi)[END_REF]. Chaetophractus villosus differs quite strongly in size from the two closest species: head-and-body length averages 330 mm in Chaetophractus villosus [START_REF] Carlini | Chaetophractus vellerosus (Cingulata: Dasypodidae)[END_REF]; 245.1 mm in Chaetophractus vellerosus [START_REF] Carlini | Chaetophractus vellerosus (Cingulata: Dasypodidae)[END_REF] [START_REF] Thomas | Size differences in the little "pichi" armadillos[END_REF], which also slightly differ in size [START_REF] Frechkop | Etude systematique et zoogéographique des Dasypodidés conserves a l'lnstitut[END_REF]Squarcia & Casanave 1999;[START_REF] Superina | Zaedyus pichiy (Cingulata: Dasypodidae)[END_REF].

However, some studies distinguish the geographical distribution of the two subspecies [START_REF] Wetzel | Order cingulata[END_REF][START_REF] Sidorkewicj | Morphological characterization and sex-related differences of the mandible of the armadillos Chaetophractus vellerosus and Zaedyus pichiy (Xenarthra, Dasypodidae), with consideration of dietary aspects[END_REF] but the recent diagnosis of the species [START_REF] Superina | Zaedyus pichiy (Cingulata: Dasypodidae)[END_REF] no longer makes this distinction.

Sampling and a priori hypothesis

During the PhD, digital data of 45 specimens identified as Zaedyus pichiy in 6 museum collections worldwide were acquired using X-ray micro-computed tomography (μCT) (Appendices of

Methods

For both datasets, the same analyses were performed along considerations on the ontogeny and the geographical distribution. For the analysis of the Zaedyus pichiy sample, the presence or absence of teeth on the premaxillary was also taken into account in the interpretation of the results in order to consider the observations of Superina & Abba (2014) (see above).

Determination of ontogenetic stage

Contrary to Dasypus novemcinctus, in tolypeutines and euphractines there is only one functional generation of teeth [START_REF] Ciancio | Evolutionary implications of dental eruption in Dasypus (Xenarthra)[END_REF]. Therefore, the three dental variables used to determine ontogenetic stages in Dasypus (Section 3.1) cannot be used in Zaedyus or Cabassous.

component analysis. These tests were performed with the adonis function in the R package vegan v. 2.5-6 [START_REF] Oksanen | Vegan: Community Ecology Package. R package version 2.5-4. R Foundation for Statistical Computing[END_REF].

Neighbour joining trees

Using the distance matrix from the principal component scores, we performed neighbor-joining tree estimations [START_REF] Saitou | The neighbor-joining method: a new method for reconstructing phylogenetic trees[END_REF] for the total variance, using the function nj in the R package ape v.5.3 [START_REF] Paradis | ape 5.0: an environment for modern phylogenetics and evolutionary analyses in R[END_REF]. This phenetic analysis considers the overall dissimilarities between all the specimens.

Results

Cabassous sample selection

Ontogenetic stages and skull length

A bivariate plot of ossification scores versus skull length clearly distinguishes a group of large specimens from the rest of the sample (Figure 6). This group of large specimen gathers 7 specimens whose distribution is in the Cabassous tatouay area and 2 of unknown origin. This supports the a priori hypothesis of the presence of Cabassous tatouay in the sampling (n=9 specimens). The ossification scores and the distinction between ontogenetic stages in this potential cluster of Cabassous tatouay do not seem to covary with skull length. Although sampling is low for this cluster (n = 9), this result indicates either that there is little variation in size between a juvenile and an adult in this species, or that our observations on ossification are not adapted to the determination of ontogenetic stages within this particular group. No clear geographic cluster can be seen for the rest of the Cabassous specimens in the sample. unicinctus along a latitudinal gradient, which could be reminiscent of previously proposed subspecies (see above). However, the presence of 2 specimens from the southern region gathered with northern specimens shows that there is no exact correspondence between traditional subspecies and these clusters.

Permutational ANOVA

The pairwise distinction of the three clusters observed on PC1-2 and of other presumed taxonomic entities were tested (Tables SI.2), with the exclusion of the very young specimen (see above).

Although, some groups are poorly sampled (e.g., Cabassous centralis area = 4), the tests are still presented as an indication. This analysis shows that all the pairwise tested groups have a statistically different shape from one another across the variance except for potential groups within the cluster B of PC1-2 (specimens of unknown origin in cluster B with Cabassous unicinctus specimens of cluster B and the latter with the group formed by the combination of specimens of unknown origin in cluster B with the specimens originating from the distributional area of Cabassous centralis) (Tables SI.2). We can therefore conclude that statistically the three clusters of PCA are well dissociated from one another but that within cluster B, it is not possible to ensure

Conclusion and Selection

Geographical distributions and our analyses of ontogeny, cranial size and shape variation clearly showed that 9 large size specimens in the sample should be referred to Cabassous tatouay. For this reason, these specimens will be excluded from the sample planned to represent a developmental series of Cabassous unicinctus. Remaining specimens of unknown origins (n=8) as well as specimens originating within the distributional area of Cabassous centralis are not morphologically divergent from most specimens originating within the distributional area of Cabassous unicinctus (especially the northern part; see below). This is congruent with molecular analyses finding that Cabassous unicinctus and Cabassous centralis are only weakly differentiated based on their mitogenomes [START_REF] Gibb | Shotgun mitogenomics provides a reference phylogenetic framework and timescale for living xenarthrans[END_REF], which is also true for their overall morphology [START_REF] Hayssen | Cabassous centralis (Cingulata: Dasypodidae)[END_REF]. Based on these results, specimens originating within the distributional area of Cabassous centralis will be included within our Cabassous unicinctus dataset. The case of cluster C remains problematic. It may represent a different entity within or out of Cabassous unicinctus. Interestingly, the geographical origins of specimens in cluster C are partly overlapping with that of subspecies Cabassous unicinctus squamicaudis but two other specimens originating within the distributional area of this subspecies group with cluster B instead (mainly composed of specimens originating within the distributional area of Cabassous unicinctus unicinctus).

Therefore, the situation seems to disagree partly with current subspecific recognition within

Cabassous unicinctus and larger-scale studies, including molecular data and more specimens from the southern region are needed to clarify this aspect. Because of this uncertainty, we decided to perform our studies on Cabassous unicinctus on two data sets: one dataset corresponding to cluster B (n = 21 specimens) and one dataset including cluster B and cluster C (n = 27).

Zaedyus sample selection

Ontogenetic stages determination

The bivariate plot of the ossification index and skull length in Zaedyus pichiy shows that largest specimens generally present high ossification scores (Figure SI.8). A very young specimen, suspected to be a neonate or a fetus specimen, is separated from other specimens by a large gap in the bivariate plot. As it is morphologically very divergent, it will not be added to the following analyses. For the 44 remaining specimens, the criteria of [START_REF] Hubbe | A case study of extant and extinct Xenarthra cranium covariance structure: implications and applications to paleontology[END_REF] Cluster B seems to gather more southern specimens, but precise information is lacking for many specimens, including one of unknown origin in Chile.

Permutational ANOVA

The permutational analysis was performed between the two main clusters found in the PC1-2 morphospace and between specimens with a tooth on the premaxillary or not. The inclusion and exclusion of the two suspected Chaetophractus vellerosus specimens were also tested. The analysis indicates a statistically supported distinction between the two clusters whether cluster B includes the two suspected Chaetophractus vellerosus specimens or not (see Table SI.3). The analysis found no supported distinction between groups based on the presence/absence of a tooth on the premaxillary when the suspected Chaetophractus vellerosus specimens were excluded (Table SI.3). These analyses confirm a possible distinction between the two clusters on PC1-2, but more importantly, they invalidate the presence/absence of premaxillary teeth as a criterion for group distinction in our sample.

Neighbour joining tree

The reconstructed neighbour joining (NJ) tree (Figure SI.10) confirms a dissimilarity between two clusters A and B on the total variance within the sample and also underlines the stronger dissimilarity of the two suspected Chaetophractus vellerosus specimens relative to the rest of the sample. The ontogenetic stages as well as the presence of teeth on the premaxillary do not reflect any particular cluster in the NJ tree.

Conclusion and Selection

All the tests and analyses show a distinction of two large clusters in the sampling and the probable presence of two specimens of Chaetophractus vellerosus (one of which originates outside the Zaedyus pichiy distributional area) that separate well from those two clusters. Based on these results, we will not include in our dataset these two latter specimens. All other specimens seem to separate in two distinct entities, which might be geographically distinct, but none of which shows specimens originating outside of the distributional area of Zaedyus pichiy. This could well suggest different subspecies, but this does not seem to be congruent with currently accepted subspecies for this species [START_REF] Wetzel | Order cingulata[END_REF]. Another possibility could correspond to the known sexual dimorphism in the species, but our dataset has too many missing data to test this hypothesis (see . Proeutatus is enforced as the sister group of glytptodonts in accordance with most phylogenetic analyses using morphology [START_REF] Engelmann | The evolution and ecology of armadillos, sloths and vermilinguas[END_REF][START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF][START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF][START_REF] Herrera | A new Eocene dasypodid with caniniforms (Mammalia, Xenarthra, Cingulata) from northwest Argentina[END_REF]. B. Topology of the baseline cladogram. C. Topology of the strict consensus from the same analysis without constraint. See Supporting information 2 for phylogenetic analysis. ossification score for each specimen (Table S7). The cranial length value (LTCmeasure taken between landmark #1 and #84) used for this analysis was taken from [START_REF] Hautier | Beyond the carapace: skull shape variation and morphological systematics of long-nosed armadillos (genus Dasypus)[END_REF]. All cranial length, dental eruption and cranial ossification indexes are presented in Table S5. The combination of these three variables enabled us to confirm the ontogenetic separation of specimens in five stages. It was not possible to determine the degree of ossification for four specimens out of 96 because of missing bones. In addition, eight armadillos could not be associated with a dental stage because of the absence of the P4. Twelve specimens could not be assigned to an ontogenetic stage. Specimens with missing teeth could not be allocated to a precise stage and could not be included in the ontogenetic analyses.

Results

POSTNATAL ONTOGENETIC STAGES IN NINE-BANDED ARMADILLOS

For each of the remaining 84 specimens, the ontogenetic division based on the dental stages is in agreement with the ossification score and the cranial length (Figure S14). Only one specimen was attributed to stage (1), which corresponds to stillborn individuals (according to a collection label). This specimen is not included in the following analyses as its shape is too extreme compared to the rest of the sample. 11 specimens correspond to stage (2), which we call juvenile stage hereafter. This juvenile stage is characterized by the presence of only deciduous teeth and represents the largest range of cranial length in our ontogenetic delineation (Figure S14). Stages ( 3) and (4), which comprise seven and nine specimens respectively, are close and partly overlap graphically; they were combined into a single sub-adult stage. The stage ( 5) is composed of 56 specimens and is here considered as the adult stage. It is noteworthy that cranial suture closure still occurs within this adult stage (see also Rager et al., 2013). Based on this combination of proxies, ossification does not appear as the best marker for the determination of ontogenetic stages. However, combining these three proxies makes enabled us to make rather robust hypotheses on the ontogenetic stage of a specimen.

Parietal (Figure S19.D1-D3)

The allometric variation at this level is essentially the same as for the ontogenetic level except for the tentorial process, which presents no distinct variation (#73). With the log centroid size of the bone, we observe the same variation but with higher intensities. For graphical display, we used the projected regression scores of the shape data to represent shape variation related to changes in log skull centroid size [START_REF] Adams | A field comes of age: geometric morphometrics in the 21st century[END_REF]. Shape changes were visualized as vectors from the minimal shape (green) to the maximal shape (red) of the shape regression scores corresponding to the projection of the data points in shape space on to an axis in the direction of the regression vector (see [START_REF] Drake | The pace of morphological change: historical transformation of skull shape in St Bernard dogs[END_REF]. Multivariate regression of skull shape on log skull centroid size at the ontogenetic level representing 8.80% of the total shape variation. For graphical display, we used the projected regression scores of the shape data to represent shape variation related to changes in log centroid size [START_REF] Adams | A field comes of age: geometric morphometrics in the 21st century[END_REF]. Shape changes were visualized as vectors from the minimal shape (green) to the maximal shape (red) of the shape regression scores corresponding to the projection of the data points in shape space on to an axis in the direction of the regression vector (see [START_REF] Drake | The pace of morphological change: historical transformation of skull shape in St Bernard dogs[END_REF]. Phylogenetic regression of skull shape on log skull centroid size of Dataset-Tmax, representing 13.62% of the total shape variation. complex;fr,frontal;ju,jugal;lac,lacrimal;mx,maxillary;na,nasal;pa,parietal;pal,palatine;pe,petrosal;pmx,premaxillary;so,supraoccipital;sq,squamosal. Figure S32. Shape representation of the allometric shape changes detected for a given cranial unit (OBU) in Dataset-Tmax, represented between its minimal (greensmaller centroid size) and maximal (redlarger centroid size) shape (see Figure 29). Results of the analysis performed at the evolutionary level, and with the log skull centroid size taken as the size variable (see text). Each OBU is defined in three subsections organized horizontally:

1, landmarks and wireframe on an OBU of Cabassous used as a reference; 2, landamrks with a wireframe representing the minimal OBU shape; 3, landmarks with a wireframe representing the maximal OBU shape. A1-A3, alisphenoid-orbitosphenoid-pterygoid-basisphenoid complex in dorsal view. B1-B3, basioccipital-exoccipital complex in dorsal view. C1-C3, frontal in lateral view. D1-D3, petrosal in ventral view. E1-E3, supraoccipital in occipital view. Landmark numbers and orientation arrows were added for more readability as well as the overall representation of the unpaired bone (basioccipital, supraoccipital).

Figure S33. (continued from Figure 38). Shape representation of the allometric shape changes detected for a given cranial unit (OBU) in Dataset-Tmax, represented between its minimal (greensmaller centroid size) and maximal (redlarger centroid size) shape (see Figure 29). Results of the analysis performed at the evolutionary level, and with the log skull centroid size taken as the size variable (see text). Each OBU is defined in three subsections organized horizontally: 1, landmarks and wireframe on an OBU of Cabassous used as a reference; 2, landmarks with a wireframe representing the minimal OBU shape; 3, landmarks with a wireframe representing the maximal OBU shape. A1-A3, alisphenoid-orbitosphenoid-pterygoid-basisphenoid complex in lateral view. B1-B3, basioccipital-exoccipital complex in occipital view. C1-C3, frontal in ventral view. D1-D3, petrosal in lateral view. E1-E3, supraoccipital in ventral view. Landmark numbers and orientation arrows were added for more readability as well as the overall representation of the unpaired bone (basioccipital, supraoccipital).

Table S9. Statistical results of the Procrustes ANOVA from the multivariate regressions for each ontogenetic stage for 3B approach using the log skull centroid size (see Table S6). Table S13. List of landmarks after reduction of landmark set with their definition. *, internal landmark; **, amended definition for interspecific datasets. The modifications were made because the last tooth in Dasypus was not always present and the minimum interorbital length was confused with postorbital constriction (see Table 3).

Number Table S22. List of specimens for intraspecific sample. Available on the HAL open archive portal.

Table S23 List of linear S-distance pairs selected according to our threshold criteria at the ontogenetic level in the 3 species (DZC). Each distance is indicated by the landmarks that define it. For a given Cabassous dataset, results are shaded when they are below the threshold level. The numbering of pairs follows the text. Available on the HAL open archive portal.

Table S24. List of linear S-distance pairs selected according to our threshold criteria at the static level in the 3 species (DZC). Each distance is indicated by the landmarks that define it. For a given Cabassous dataset, results are shaded when they are below the threshold level. The numbering of pairs follows the text. Available on the HAL open archive portal.

Table S25. List of linear S-distance pairs selected according to our threshold criteria at the ontogenetic level in the 2 species (ZC). Each distance is indicated by the landmarks that define it. For a given Cabassous dataset, results are shaded when they are below the threshold level. The numbering of pairs follows the text. Available on the HAL open archive portal.

Table S26. List of linear S-distance pairs selected according to our threshold criteria at the static level in the 2 species (ZC). Each distance is indicated by the landmarks that define it. For a given Cabassous dataset, results are shaded when they are below the threshold level. The numbering of pairs follows the text. Available on the HAL open archive portal.

Table S27. Summary statistics of the standard major axis regression (SMA) for all the pairs of correlated Sdistances obtained according to our threshold criteria at the ontogenetic level in each of the 3 species. Each distance is indicated by the landmarks that define it. Available on the HAL open archive portal.

Table S28. Summary statistics of the standard major axis regression (SMA) for all the pairs of correlated Sdistances obtained according to our threshold criteria at the static level in each of the 3 species. Each distance is indicated by the landmarks that define it. Available on the HAL open archive portal.

Table S29. Correspondence between the EDMA and Mclust dendograms for each module (in %). The evaluation limit is fixed at the level of 4 modules following the results of the statistical gap (Figure S41). study on allometry. The patterns obtained in the three species are then analyzed at the evolutionary level to identify whether these covariations were also present in the morphological evolution of the group. The supported evolutionary correlations concern in particular the anterior root of zygomatic arch, a region particularly rich in muscular insertions.

Mclust Compatibility

In a complementary way, we perform the very first exploration of cranial modularity in cingulates at the intraspecific level and of their diversity in cranial shape at the evolutionary level. They reveal a partitioning of the integration into three anteroposteriorly distributed modules on the skull and identified potential cranial regions for further research of covariation patterns. Finally, we discuss the implications of these studies regarding the already existing phylogenetic hypotheses and the cranial characters used in the matrices. Our results on cranial integration are compared with existing matrices and phylogenetic analyses in order to identify possible groups of traits that may covary and to discuss their potential impact on the phylogenetic reconstruction within the group. Although it hints at a necessary revision of some characters, the comparison of the detected covariation patterns with morphological matrices proves difficult. We argue that alternative coding strategies (such as the use of continuous characters) need to be further explored for a better evaluation of the covariation and allometry among scored characters and for an overall improvement of our character constructions. Our exploratory work emphasizes again the great complexity of morphological variation and the resulting challenge of scoring independent morphological characters for phylogenetic analysis.

Résumé Étendu:

La variation morphologique est un phénomène omniprésent, qui a longtemps inspiré les naturalistes et les a amenés à proposer des classifications d'organismes basées sur les similitudes et les différences observées. Cependant, plus on examine la variation morphologique, plus on découvre son extrême complexité. Au cours des dernières décennies, l'utilisation de la variation morphologique comme source de caractères pour les analyses phylogénétiques a été fortement remise en question malgré la primauté de ces données pour l'étude de taxons éteints inaccessibles aux analyses moléculaires. L'importance primordiale des données morphologiques pour la reconstitution des relations de parentés des formes éteintes est entravée par les évaluations critiques de leurs performances, en particulier pour les analyses au sein des mammifères placentaires. Cette observation est conforme au fait que de nombreuses études ont appelé à une amélioration de nos méthodes phylogénétiques utilisant la morphologie, en particulier pour une exploration plus large des modèles de variation morphologique et une meilleure identification de la covariation entre les traits.

Les cingulés sont un groupe de mammifères placentaires qui appartiennent au superordre Xenarthra avec les fourmiliers et les paresseux. Les cingulata comprennent les tatous actuels et des taxons éteints tels que les glyptodontes. Ce clade représente un cas d'étude idéal pour l'exploration de la variation morphologique dans un contexte phylogénétique. Leur modeste diversité actuelle permet une exploration détaillée de l'ensemble du groupe, tandis que leur diversité passée, montrant des formes crâniennes très inhabituelles chez les mammifères, offre un large éventail d'investigations. L'intérêt majeur de ce groupe pour le sujet traité dans le présent travail réside dans le manque de congruence entre les analyses phylogénétiques utilisant des données morphologiques ou moléculaires. Dans ce travail, nous mettons d'abord en évidence le manque de consensus entre ces hypothèses et signalons les lacunes existantes dans notre connaissance morphologique du groupe, plus particulièrement en ce qui concerne l'anatomie crânienne interne et les schémas d'intégration (= tendance des traits à covarier) sur le crâne. Nous montrons qu'une exploration de ces deux aspects sera utile pour compléter les matrices morphologiques mais aussi pour mieux comprendre les covariations existantes entre plusieurs structures et caractères anatomiques qui peuvent induire en erreur la phylogénie morphologique.

Notre travail commence par une étude approfondie de l'anatomie interne du crâne dans un échantillon varié de Cingulata, en supposant que ces structures mal connues puissent fournir de nouvelles informations phylogénétiques. La reconstruction virtuelle en 3D (par microtomographie aux rayons X) de certains canaux et cavités liés à la vascularisation crânienne, à l'innervation ou à l'insertion de dents nous a permis de comparer les emplacements, les trajectoires et la forme de ces structures et de discuter de leur intérêt potentiel pour la systématique des Cingulata. Nous avons provisoirement reconstitué des scénarios évolutifs pour huit caractères sélectionnés sur ces structures, qui présentaient souvent une plus grande ressemblance des glyptodontes avec les pampatheres, avec le genre Proeutatus et/ou avec les chlamyphorines. Ce dernier aspect était en partie conforme aux récentes hypothèses moléculaires, mais des recherches supplémentaires sont nécessaires sur ces ressemblances et sur les effets potentiels du développement et de l'allométrie sur les variations observées. Dans l'ensemble, ces comparaisons nous permettent de mettre en évidence de nouvelles variations anatomiques qui pourraient être d'un grand intérêt pour explorer davantage l'histoire évolutive des cingulés et les origines des glyptodontes sur une base morphologique.

I

  would also like to thank especially Christian de Muizon, Directeur de Recherche at the Centre de Recherche en Paléontologie -Paris, who allowed me, with Guillaume, to do this PhD by being my supervisor. Our interactions were rarer, but he was always there when I needed his help. I am very grateful to him. My thanks also go to Sophie Montuire, Directrice de Recherche at the Université de Bourgogne, and to Timothy Gaudin, Professor at the University of Tennessee, for agreeing to be the reviewers of my PhD. I would also like to thank Isabelle Rouget, Professor at the Centre de Recherche en Paléontologie -Paris, Allowen Evin, Chargée de Recherche at the Institut des Sciences de l'Evolution Montpellier, and Robert J. Asher, Doctor at the University of Cambridge, for having accepted the invitation to be part of my PhD jury. To have them all on my jury is a great honor. Within the Centre de Recherche en Paléontologie -Paris and more broadly the Muséum national d'Histoire naturelle in Paris and at the Institut des Sciences de l'Evolution Montpellier, I interacted with many colleagues who allowed me to produce good work. Their help was indispensable, and I would like to thank them all. Thank you to Sylvie Crasquin for welcoming me into the paleontology laboratory in unit 7207. Thanks also to Didier Merle, Michel Laurin and Sylvain Charbonnier for always validating my administrative requests. Thank you to Angelina Bastos and Suzy Colas for helping me with all the administrative procedures, particularly for funding and travels. You have always welcomed me and helped me with patience and kindness. Thank you very much. Thanks to Christine Argot, Géraldine Véron and Guillaume Billet for giving me access to the study material. Thanks also to Claire Sagne, Sandra Daillie, Damien Olivier, Maxime Perretta and Vincent Pernègre, who work in the palaeontology collections of the Museum National d'Histoire Naturelle, for their help and friendship. Thanks to Julien Barbier for our discussions and for allowing me to share my research with the broader public. Thanks to Jérémie Kazan for our many discussions and for the superb reconstitution of the skull of Glyptodon. Thanks to Marta Bellato and Patricia Wils for scanning the Glyptodon from the Muséum national d'Histoire naturelle in Paris, and to Nathalie Poulet and Florent

  you to Lionel Hautier and Frédéric Delsuc, from the Institut des Sciences de l'Evolution Montpellier, for allowing me to use their dataset on several extant armadillos for my PhD. Many thanks to Laureano Gonzalez Ruiz, from the Universidad Nacional de la Patagonia, for allowing me to use his magnificent dataset composed mainly of fossil armadillos. I would also like to thank Adrienne Stroup and Ken Angielczyk of the Field Museum of Natural History in Chicago and Zhe Xi Luo of the University of Chicago for allowing me to work on a pampathere. Thanks to Eli Amson, from the Museum für Naturkunde in Berlin, for scanning several specimens of Zaedyus and Cabassous and sending them to me for study. Thanks to Pepijn Kamminga, Rob Langelaan and Arjen Speksnijder, from the Naturalis Center Biodiversity in Leiden, for sending me one of the rare juvenile specimens of Cabassous unicinctus present in European collections. Thanks to Roberto Portela Miguez, from the Natural History Museum in London, for allowing me to scan several specimens of extant armadillos. Thanks to Eleanor Hoeger, Neil Duncan, and especially Marisa Surovy of the American Museum of Natural History, for allowing me to scan several specimens of Zaedyus and Cabassous. Thank you also for arranging the shipment of the specimens. Thanks also to Alice Cibois and Manuel Ruedi, from the Museum d'Histoire Naturelle de Genève, for allowing me to scan several of their extant armadillo specimens. Many thanks to Daniel Brinkman of the Yale Peabody Museum in New Haven for allowing me to visit their collection. Thanks also for his kindness and exemplary hospitality. Finally, thanks to Soledad De Esteban-Trivigno of the Institut Català de Paleontologia M. Crusafont and Chris Klingenberg of the University of Manchester for allowing me to follow a course on integration and modularity in Sabadell which was very useful during this PhD. I would also like to thank Doctoral School 227 of the Muséum national d'Histoire naturelle and the Société des amis du Muséum for funding a large portion of my data acquisitions.

  Figure 1. Mosaic of extant cingulate species with details of their taxonomic affiliation based on recent molecular analyses[START_REF] Delsuc | The phylogenetic affinities of the extinct glyptodonts[END_REF][START_REF] Gibb | Shotgun mitogenomics provides a reference phylogenetic framework and timescale for living xenarthrans[END_REF][START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF]. The family Dasypodidae contains 7 extant species all attributed to the clade Dasypodinae (in blue). The family Chlamyphoridae contains 14 extant species distributed within three clades: Euphractinae (in red); Chlamyphorinae (in purple) and Tolypeutinae (in yellow). The colors chosen follow Mitchell et al. (2016), as for the rest of the manuscript. Specimens marked with an asterisk (*) correspond to species whose status is currently under discussion (see Chapter 3 & Supporting Information 1). The photographs are from the International Union for Conversation of Nature (= IUCN) website except for C. nationi from Mount Salvation Salton Sea (© Carol Milligan) and D. kappleri from Aya-Cuero et al. (2019).

Figure 2 .

 2 Figure 2. 3D model plate illustrating the skulls of extinct specimens of different families of living and extinct Cingulata. A) Peltephilus pumilus Ameghino, 1887 (Miocene, Santacrucian SALMApeltephilid). B) Stegotherium tauberi Ameghino, 1887 (Santacruciandasypodine). C) Vassallia maxima Castellanos, 1946 (Miocene/Pliocene, Montehermosan SALMApampathere). D) Glyptodon sp. Owen, 1839 (Pleistocene, Lujanian SALMAglyptodont). Scale = 2 cm.

Figure 7 .

 7 Figure 7. Transparent 3D model of a skull of Glyptodon sp. (MNHN.PAM.760) in lateral view with poorly studied internal structures of interest poorly studied in glyptodonts and other cingulates highlighted. The elements studied in this work correspond to the dental alveolar cavities (in grey) and some of the main vascular or nervous canals internal to the skull (in red). Scale = 1 cm. See Chapter 2.

Figure 9 .

 9 Figure 9. Illustration of the selected internal canals on the transparent cranium of Euphractus sexcinctus AMNH 133304 in right lateral (A) and ventral (B) views. Scale = 1 cm.

Figure 10 .

 10 Figure 10. Diversity of the dental alveolar cavities in our cingulate sample in lateral (red square), ventral (yellow square) and anterior (green square) view. Skulls are reconstructed with transparency to leave the cavities apparent. Colors of species names refer to their attribution at the subfamilial level according to molecular analyses (lower right panel); extinct species not allocated to one of these clades are shown in black. † represents an extinct taxon. Scale = 1 cm.

Figure 11 .

 11 Figure 11. Ontogenetic variation of internal canals selected in this study viewed on transparent skulls in each developmental series (Dasypus, Zaedyus and Cabassous). Note that early postnatal stages for Cabassous are not documented in our sample. See Chapter 3 for the determination of stages. Phylogenetic relationships are indicated with colors following Figure S4. The color of canals follows that of Figure 9. Abbreviations: pbplc, posterior branch of the palatine canal. Scale = 1 cm.

Figure 12 .

 12 Figure 12. Distribution of the ratio of greatest dental row height (GDRH) to greatest skull height (GSH) with respect to cranial size (= log(geometric mean); see Material & Methods). For each of the three developmental series, A, symbolizes the adult specimen. Skulls of specimens marked with an asterisk are illustrated in the graph. Scale = 1 cm.

Character 1 (

 1 discrete -unordered): Position of the most dorsal point of the dorsal convexity of the tooth row. State (0): Toothrow not dorsally convex. State (1): Anterior to middle of the tooth row. State (2): At the middle of the tooth row. State (3): Posterior to middle of the tooth row. Character 2 (discrete -unordered): Curvature of anterior teeth in anterior view.

Figure 13 .

 13 Figure 13. Interspecific variation of the canal for the frontal diploic vein in our sample, all illustrated in dorsal view. Red arrows mark the main external opening of the canal. Blue arrows mark the main internal path of the canal on the cranial midline. Colors of species names follow Figure 10. Scale = 1 mm.

Character 3 (

 3 discrete -unordered): Opening of the nasolacrimal canal in nasal cavity. State (0): Halfway up in the nasal cavity. State (1): Ventral in the nasal cavity, close to the palate.

Figure 14 .

 14 Figure 14. Interspecific variation in our sample of the reconstructed nasolacrimal (= red), sphenopalatine (= yellow) and palatine (= orange) canals shown in lateral view. Skulls are reconstructed with transparency. Colors of species names follow Figure 10. Abbreviations: cfpb, caudal foramen for palatine canal branch; pbplc, posterior branch of palatine canal. Scale = 1 cm.

Figure 15 .

 15 Figure 15. Interspecific variation in our sample of the reconstructed nasolacrimal (= red), sphenopalatine (= yellow) and palatine (= orange) canals shown in ventral view. Skulls are reconstructed with transparency. Colors of species names follow Figure 10. Abbreviations: cfpb, caudal foramen for palatine canal branch; pbplc, posterior branch of palatine canal. Scale = 1 cm.

Character 4

 4 (discrete -unordered): Sphenopalatine and palatine canal connection. State (0): No contact. State (1): Partial contact, with palatine canal running ventrally along the sphenopalatine canal and producing posterior branches. State (2): Complete fusion.

Figure 16 .

 16 Figure 16. Interspecific variation of the transverse canal in ventral view in our sample. Red arrows mark the main external opening of the canal. Blue arrows mark the branch crossing the midline. Green arrows mark the main posterior branch which connects to the inferior petrosal sinus (see text). Colors of species names follow Figure 10. Scale = 1 mm.

Character 5 (

 5 discrete -unordered): Orientation of the branch starting from the transverse canal foramen. State (0): Posteromedial. State (1): Medial or anteromedial. State (2): No canal.

Figure 17 .

 17 Figure 17. Interspecific variation in our sample of the orbitotemporal (= red), posttemporal (= pink) and capsuloparietal emissary vein (= blue) canals shown in lateral view. Caudal part of the skull is transparent. Parts of the canals showing transparency symbolize a groove instead of a fully enclosed canal. Colors of species names follow Figure 10. Scale = 1 cm.

Figure 18 .

 18 Figure 18. Interspecific variation in our sample of the orbitotemporal (= red), posttemporal (= pink) and capsuloparietal emissary vein (= blue) canals shown in ventral view. Transparent parts of the canals indicate a groove instead of a fully enclosed canal. Colors of species names follow Figure 10. Scale = 1 mm.

Figure 19 .

 19 Figure 19. Distribution of the internal vault inclination (IVI) with respect to cranial size (= log(geometric mean)) in our sample. For the three developmental series, A symbolizes the adult specimen. Specimens marked with an asterisk are illustrated by cranial reconstructions in sagittal view in the graph. Scale = 1 cm.

Figure 20 .

 20 Figure 20. Reconstructed evolutionary scenarios for the endocranial characters 1 -4 plotted on the reference cladogram with ancestral state estimation for internal nodes (see Material & Methods, Supporting information 2 and Figure S4). Each character is illustrated, and the relationship between color and coding is indicated within the figure itself. † represents extinct genera. Scale = 1 cm.

  d'Histoire naturelle (MNHN, collections Zoologie et Anatomie comparée, Mammifères et Oiseaux) in Paris (France), the Natural History Museum (BMNH) in London (UK), the Museum of Natural Science of the Louisiana State University (LSU) in Baton Rouge (USA), the American Museum of Natural History (AMNH) in New York (USA), the National Museum of Natural History (NMNH) in Washington (USA) and the Muséum d'Histoire Naturelle in Geneva (MHNG, Switzerland) (see Table

Figure 22 .

 22 Figure 22. Landmarks digitized on the skull of Dasypus novemcinctus (MNHN.CG.2006-565). Lateral (A), ventral (B), and dorsal (C) views. The skull in dorsal view is shown with bone transparency (25%). Scale-bar = 1 cm. List of landmarks can be found in Table3 and Table 4.

  Most ventral point of the postglenoid process 59-60 Most posterodorsal point of the postglenoid foramen 61-62 Most posterodorsal point of the zygomatic ridge of the squamosal 63-64 Most dorsal point of the external acoustic meatus on squamosal (in lateral view) 65-66 Most posterior point of the small alisphenoid process delimitating the carotid notch laterally 67-68 Most anteroventral point of the transverse canal foramen 69-70 Most anteroventral point of the foramen ovale 71-72 Most posterior point of the alisphenoid/squamosal suture in front of pyriform fenestra 74-75 Most anterodorsal point of the optic foramen 76-77 Ventral tip of entoglenoid process 78 Intersection between frontal/parietal suture and the midline 79 Intersection between parietal/supraoccipital suture and the midline 80-81 Triple contact point between the frontal/squamosal/parietal 82-83 Triple contact point between the parietal/squamosal/supraoccipital 84 Most distal point of the supraoccipital on the midline (occipital face) 85-86 Most posterior point of the nuchal process of the supraoccipital 87-88 Most anterodorsal point of the sulcus for the occipital artery 89-90 Most lateral point of basioccipital/basisphenoid suture 91-92 Intersection between the anteromedial edge of occipital condyle and foramen magnum 93-94 Triple contact point between the supraoccipital/exoccipital/petrosal* 95-96 Most posterolateral point of the jugular foramen 97-98 Most posterolateral point of the hypoglossal foramen 99-100 Most anterolateral point of the occipital condyle (in ventral view) 101 Most anteroventral point of the foramen magnum 102 Most posterodorsal point of the foramen magnum 103-104 Most medial point of promontorium of petrosal in ventral view 105-106 Most anteroventral point of mastoid process (= paroccipital process of petrosal) 107-108 Most ventral point of external aperture of cochlear canaliculus 109-110 Most anterior point of the fenestra vestibuli 111-112 Most anteroventral point of the external apertur of cochlear fossula Table 4. Definition of internal landmarks. * Landmark removed in 3B analyses. ** Projected landmark. Number Definition 73 Anteroventral tip of the tentorial process on the midline 113 Dorsal intersection of annular ridge and midline 114* Dorsal intersection between cribriform plate and median septum posterior to the latter 115-116 Maximum curvature point of the lateral occipital ridge in caudal cerebral fossa 117-118 Most dorsal point of the petrosal on the level of the crista tentoria transversally 119-120 Most anteromedial point of the foramen acusticum superius 121-122 Most anteromedial point of the foramen acusticum inferius 123-124 Most anterior point of epitympanic wing of petrosal 125-126 Maximum curvature point in the ventromedial area of the fossa subarcuata 127-128 Most dorsal point of the internal posterior aperture of the optic canal 129-130 Most ventromedial point on the annular ridge lateral to posterior median septum 131** Dorsal projection of the most posterior point of the frontal sinuses in the midline 3.1.2.3 Determination of ontogenetic stages The determination of the developmental stage of each specimen was based on dental eruption, cranial ossification, and cranial length. Except for size, these variables were each composed of various discrete observations scored numerically. The scored observations were then averaged to be compiled in a dental eruption index and a cranial ossification index. The observations on dental eruption were made on CT-images and on 3D reconstructions of the skulls and corresponded to the number of teeth present, as well as their class and generation. Based on our observations of the upper dentition, we defined five dental stages. Concerning the ossification, only bones whose suture closure vary along our ontogenetic series were scored. The cranial length value (LTCmeasure taken between landmarks #1 and #84) used for this analysis was directly sourced from the work of Hautier et al.

  anteriorly and the other posteriorly) and has different magnitudes of variation depending on the landmarks considered. Most of the landmarks of the anterior tip of the snout (#1; #[3][4][START_REF]25} Om<-diag(0,p) Om[row(Om)>col(Om)]<-omega; Om<-t(Om) Om[row(Om)[END_REF][6][7][8][9][10][START_REF]col="blue",lty=3) abline[END_REF][12][13][14][15][16][17][18][19][20] and the ones delineating the posterior end of the premolar row (#29-30), show an anterior displacement relative to other landmarks during growth. On the other hand, most landmarks of the snout posterior to the premaxillary and nasal display a posterior directed elongation relative to the other landmarks. In addition to this elongation, the posterior end of the snout (i.e., delimited anteriorly by the most anterior point of the zygomatic arches) narrows in larger specimens, especially at the level of the infra-orbital and maxillary foramina. The zygomatic arches extend more ventrally and the temporal fenestra widen considerably as the size increases, as expressed by the vectors associated to landmarks #22-23 and #51-52, and by the increase of the postorbital constriction (#41-42). In the posterior half of the skull, most of landmark displacements are directed towards the center of the braincase. During ontogeny, the proportions of the neurocranium decreases relative to the rest of the skull due to allometric growth. More local allometric changes are also highlighted: the landmark located at the posterior edge of the frontal sinuses (#131) is

(

  slightly increasing width) are less strong than in the ontogenetic allometry analyses. The reduction in the relative proportions of the braincase is more pronounced for landmarks located on the cranial roof (frontal and parietal midline landmarks (#113; #114; #131)) and the zygomatic-pterygoid region. The anterior border of the orbit widens as the post-orbital constriction becomes stronger with size. Strikingly, the landmark located on the maxillary-palatine suture (#21) strongly moves forward in comparison to other surrounding landmarks as size increases, much more than in the ontogenetic analysis. A very strong anterior (#19-21; #45-46) and weak posterior (#32) relative

Figure 27 .

 27 Figure 27. Allometry and growth pattern per cranial unit (OBU) and per postnatal ontogenetic stage. A) Bar graph showing the allometric proportions of shape variation per OBU and ontogenetic stage (see text). Bars with transparency indicate a statistically unsupported allometry for a given OBU and stage (at p-value > 0.05) (see Table6). B) Boxplot showing the variation of size for each OBU relative to its mean per stage (green, juvenile; yellow, subadult; red, adult), and for the whole sample (in black), as measured by the following ratio for every specimen: log OBU centroid size / mean log OBU centroid size at a given stage. Abbreviations of OBUs: as-os-pt-bs, alisphenoidorbitosphenoid-pterygoid-basisphenoid complex;bo-eo, basioccipital-exoccipital complex; fr, frontal; ju, jugal; lac, lacrimal; mx, maxillary; na, nasal; pa, parietal; pal, palatine; pe, petrosal; pmx, premaxillary; so, supraoccipital; sq, squamosal.

Cabassous

  and Zaedyus only have one dental generation (the possession of two dental generations seems to be restricted toDasypus -Ciancio et al., 2012), dental eruption could not be used to determine ontogenetic stage. For these taxa, we used the degree of ossification of the basicranium following the criteria of[START_REF] Hubbe | A case study of extant and extinct Xenarthra cranium covariance structure: implications and applications to paleontology[END_REF], who consider as adults only those armadillo specimens in which both the supraoccipital-exoccipital, basioccipital-basisphenoid and basioccipital-exoccipital contacts are completely closed (bones fused). Following these criteria, 123 we considered as strictly adult the specimens having these three contacts completely fused in Cabassous and Zaedyus. Conversely, a specimen with completely unfused supraoccipitalexoccipital contact was considered juvenile and specimens with intermediate degrees of ossification for these three sutures were attributed to the subadult stage. In summary, sampling for the ontogenetic level contains three ontogenetic stages (Zaedyus pichiy = 43; CabassousNS = 27; CabassousS = 21) whereas the static level corresponds to a subset of this sample consisting only of adult specimens (Zaedyus pichiy = 23; CabassousNS = 16; CabassousS = 14). A complete account of the observations for these criteria and attributions to ontogenetic stages for each

Figure 30 .

 30 Figure 30. Ontogenetic allometry on the entire skull (ES) of CabassousNS. Ontogenetic stages are represented with different colors (juvenile = green; subadult = yellow; adult = red; see text for more detail).For graphical display, we used the projected regression scores of the shape data to represent shape variation related to changes in log skull centroid size[START_REF] Adams | A field comes of age: geometric morphometrics in the 21st century[END_REF]. Shape changes were visualized as vectors from the minimal shape (green) to the maximal shape (red) of the shape regression scores corresponding to the projection of the data points in shape space on to an axis in the direction of the regression vector (see[START_REF] Drake | The pace of morphological change: historical transformation of skull shape in St Bernard dogs[END_REF]. Multivariate regression of skull shape on log skull centroid size at the ontogenetic level represented 6.60% of the total shape variation.

  , S28 & S29), both at the ontogenetic and static levels, the entire OBU is particularly impacted by allometric variation except for the sphenorbital fissure (#46). As size increases, the anterolateral edge of the alisphenoid in contact with the frontal and squamosal (#42) takes a much more anteromedial position. The internal and external opening of the optic canal (#65; #112) extend concurrently in an anterolateral direction, but to a greater extent for the external opening (at the ontogenetic level), thereby increasing the length of the canal. The ventral edge of the foramen ovale (#60) is located relatively more posterolateral in larger specimens, whereas the most posterior point of the alisphenoid/squamosal suture in front of pyriform fenestra (#62) is situated further posteromedially. Finally, the most ventromedial point on the annular ridge lateral to the posterior median septum (#114) moves slightly more posteromedially as size increases, which reduces the relative thickness of the annular ridge.

  allometric variations are accompanied by a slightly more pronounced and more posteriorly situated postorbital constriction (#40) in larger specimens, and a narrowing of the frontal shown by the greater proximity of the contact between the frontal and the parietal (#66) with the landmarks defining the triple frontal -parietal -squamosal contact (#69) and the triple frontal -squamosalalisphenoid contact (#42).

  the premaxillarymaxillary suture on the palate (#7) is located relatively more anteromedial in larger specimens, although this variation is weak. The dorsal part in contact with the frontal and lacrimal (#34) is situated more posteroventral, whereas its posteroventral part close to the posterior edge of the dental row (#19; #29) is located slightly further dorsally as size increases. The combination of these two allometric variations suggest a slight reduction in the posterior height of the bone in larger specimens. In addition, the most anterior point of the alveolar margin of the dental row (#27) is located a little more posterior in larger specimens. The position of the landmarks in contact with the zygomatic arch (#21; #48) and the contact with the nasal and frontal (#32) hardly vary with size at all. The same allometric variations are detected at the static level (Figure36) except for a much less anterior position of the midline contact with the palatine (#17) 143 in larger specimens. An allometric variation for this OBU is not significantly supported for the Cabassous datasets (Tables

CabassousNS.

  When size increases, the allometric variations are very different from that found for Zaedyus pichiy. The landmarks on the anterior part of the nasal assume a more posterior position (#1; #10) in larger specimens. The contact of the nasal with the premaxillary and maxillary (#4) takes a much more anterior position as size increases which indicates that a smaller portion of the nasal is in contact with the premaxillary in larger specimens, in contrast to the pattern found in Zaedyus. Finally, the frontal process of the nasal (#32) extends slightly more posterolaterally in larger specimens, as in Zaedyus, whereas the position of the landmark marking the nasal contact with the frontal at the midline level (#2) hardly varies.PalatineAt the ontogenetic level (Figure38), the palatine in Zaedyus pichiy is relatively more elongated anteroposteriorly (#17; #30) and narrower mediolaterally (#21; #44; #17; #30) as size increases. This elongation is coupled with a reduction in the width of the bone from the juvenile to the adult stage. This is particularly marked at the intersection between maxillary/palatine suture and the lateral edge of palate (#21) and caudal palatine foramen (#44). Allometric variation for this OBU is not significantly supported for the Cabassous datasets and for Zaedyus pichiy at the static level, but the p-values are close to the significance threshold (Tables 7, 8 & S20).

Figure 36 .

 36 Figure36. Vector representation of the allometric shape changes detected for a given cranial unit (OBU) in Zaedyus, represented between its minimal (greensmaller centroid size) and maximal (redlarger centroid size) shape (see Figure29). Results of the analysis performed at the static level, and with the log skull centroid size taken as the size variable (see text). For each OBU, the changes are shown in three subsections organized horizontally: 1, vectors from minimal to maximal shape with minimal OBU shape; 2, same as 1) with maximal OBU shape; 3, minimal OBU shape in transparency with vectors. A) basioccipital-exoccipital complex; A1-A2, dorsal view; A3, ventral view. B) frontal; B1-B2, lateral view; B3, ventral view. C) lacrimal; C1-C2, lateral view; C3, medial view. D) maxillary; D1-D2, lateral view; D3, medial view. Landmark numbers and orientation arrows were added for more readability as well as the overall representation of the unpaired bone (basioccipital). Abbreviations: A, anterior; D, dorsal; L, lateral; V, ventral.

  Zaedyus pichiy, the allometric variations of the petrosal are approximately the same between the static and ontogenetic levels(Figures 37 & 38). When size increases, the mastoid process (#90) lengthens ventrally, the depression marking the fossa subarcuata (#110) is shallower, the most dorsal point of the petrosal, located at the transverse level of the crista tentoria transversally (#102), assumes a more anteroventral position, whereas the most ventral point of external aperture of the cochlear canaliculus (#92) is positioned further dorsal. In contrast, the most anteroventral point of the external aperture of the cochlear fossula (#96) shows almost no variation.The most medial point of promontorium of the petrosal in ventral view (#88) extends farther anteriorly, and the most anterior point of epitympanic wing of the petrosal (#108) takes a relatively more dorsal position in larger specimens. In addition, the most anteromedial point of the foramen acusticum superius (#104) and the most anteromedial point of the foramen acusticum inferius (#106) are very slightly closer to one another in larger specimens.

Figure 37 .

 37 Figure 37. (continued from Figure36). Vector representation of the allometric shape changes detected for a given cranial unit (OBU) in Zaedyus, represented between its minimal (greensmaller centroid size) and maximal (redlarger centroid size) shape (see Figure29). Results of the analysis performed at the static level, and with the log skull centroid size taken as the size variable (see text). For each OBU, the changes are shown in three subsections organized horizontally: 1, vectors from minimal to maximal shape with minimal OBU shape; 2, same as 1) with maximal OBU shape; 3, minimal OBU shape in transparency with vectors. E) nasal; E1-E2, dorsal view; E3, ventral view. F) petrosal; F1-F2, medial view; F3, lateral view. G) premaxillary; G1-G2, ventral view; G3, medial view. H) squamosal; H1-H2, lateral view; H3, ventral view. Landmark numbers and orientation arrows were added for more readability. Abbreviations: A, anterior; L, lateral; V, ventral.

(# 4

 4 ) in larger specimens. As size increases, the anterior edge of the premaxillary on the midline (#8) also occupies a more ventral position, the most anterior point of the premaxillary anterior process (#12) extends farther anteroventrally and the most anterior part of the suture between the nasal and premaxillary (#10) is situated further anterior. The most posterior point of the premaxillarymaxillary suture on the palate (#7) assumes a more medial position showing a relative reduction in the posterior width of the premaxillary in larger specimens. Finally, the posterior point of the incisive foramen in ventral view (#16) exhibits a more posterolateral position, whereas the most anterior point of the incisive foramen in strict ventral view (#14) hardly varies.

  see above). The most posterodorsal point of the zygomatic ridge of the squamosal (#56) takes a slightly more posteroventromedial position as size increases, whereas the most dorsal point of the external acoustic meatus on squamosal (#58) is situated more dorsolaterally. In addition, the triple contact point between the parietalsquamosalsupraoccipital (#71) is located further anteroventral whereas the contact with the alisphenoid and frontal (#42) and the contact with the parietal and frontal (#69) assume a more medial position, reflecting the ontogenetic reduction in size of the neurocranium. In ventral view, the most posterior point of the alisphenoid/squamosal suture in front of pyriform fenestra (#62) is also relatively more medial in larger specimens.

For the

  Cabassous datasets (Figures34 & S28), the ontogenetic allometric variations are slightly less marked than for Zaedyus pichiy. The main differences with the latter concern the relatively more posteromedial position of the ventral contact between squamosal and jugal (#54), the more posteromedial position of the triple frontal-parietal-squamosal contact (#69) and a slightly more posterior position of the most posterior point on the alisphenoid/squamosal suture in front of the pyriform fenestra (#62) in larger specimens. There is also no ontogenetic increase in the distance separating landmarks on the zygomatic arch (#52, #54) from the landmarks on the lateral wall of the braincase (#42, #62, #69), in the anterior half of the bone, in contrast to the pattern in Zaedyus. Allometric variation for this OBU is not significantly supported for the Cabassous datasets at the static level, but the p-value is close to the significance threshold for the CabassousN dataset (Tables8 & S20). 3.2.3.2 Allometric variations in the interspecific datasets 3.2.3.2.1 Allometric variations on the entire skull (ES) at the evolutionary level

# 31 -

 31 34). The lateral parts of the orbit that connect with the anterior end of the zygomatic arches occupy a much more posterior position(#20-21; #37-38; #47-50) which constitutes a second indication of facial lengthening. This posterior displacement of the anterior zygomatic arches reduces the relative length of the zygoma. The postorbital constriction is also located in a much more posterior position in larger specimens, and also slightly narrower transversely (#39-40). The landmarks on the roof and lateral wall of the braincase almost all shift convergently towards the center of the braincase which indicates its relative reduction as size increases. The posterior part of the cranial vault (defined in this study as the part of the cranial roof protecting the brain) does not strictly follow this trend. The midline contact between the supraoccipital and the parietal (#67) assumes a more posteroventral position, as does the supraoccipital -parietal -squamosal triple contact (#70-71), indicating a decrease in depth of the posterior part of the vault in relation to the rest of the braincase as size increases.Contrary to the general trend of an allometric reduction in the size of the braincase, the processes of the nuchal crests (#73-74) extend further posteromedioventrally as size increases, and thus protrude further posteriorly. Finally, the most medial point of the promontorium of the petrosal (#87-88) is shifted more lateral in larger specimens contrasting with the general shrinking of the surrounding braincase elements. This variation indicates that the promontorium of the petrosal becomes more distant from the midline of basicranium in larger specimens. The distribution of specimens with respect to the regression line shows a clear distinction between the dasypodids located above the line and the chlamyphorids located below the regression line (Figure39).

#

  17; #18-19; #26-29; #31-32). The relative lengthening of the snout is also evidenced by the strong posterior extension of the midline apex of the postpalatal notch and of the maxillary foramen (#22-23; #30), although the position of the infraorbital foramen hardly varies (#24-25). The anterior edge of the orbit and zygomatic arch also exhibits a much more posterior position in larger specimens, in addition to being slightly more laterally situated(#20-21; #35-38; #47-50). The postorbital constriction (#39-40) is shifted in the same direction as most of the other points in the orbitotemporal region, narrowing by converging towards the center of the braincase, which shows a relative reduction in its proportions. The cranial vault is much lower in larger species with a more posteroventral position of the intersections between the frontoparietal and the parietal/supraoccipital sutures and the midline (#66-67) in larger specimens. The two internal points defined by the dorsal intersection of annular ridge and midline (#97), and the dorsal intersection between the cribriform plate and the median septum posterior to the latter (#98) are strongly shifted posteroventrally, becoming located almost at the same level as the most posterodorsal point of the foramen magnum (#86). It thus indicates increase in depth of the large

Figure 39 .

 39 Figure 39. Evolutionary allometry on the entire skull (ES) of DatasetExt. Clades are represented with different colors.For graphical display, we used the projected regression scores of the shape data to represent shape variation related to changes in log centroid size[START_REF] Adams | A field comes of age: geometric morphometrics in the 21st century[END_REF]. Shape changes were visualized as vectors from the minimal shape (green) to the maximal shape (red) of the shape regression scores corresponding to the projection of the data points in shape space on to an axis in the direction of the regression vector (see[START_REF] Drake | The pace of morphological change: historical transformation of skull shape in St Bernard dogs[END_REF]. Phylogenetic regression of skull shape on log skull centroid size of DatasetExt, represented 20.66% of the total shape variation.

Figure 40 .

 40 Figure 40. Evolutionary allometry on the entire skull (ES) of Dataset-Lmax. Clades and fossils taxa are represented with different colors.For graphical display, we used the projected regression scores of the shape data to represent shape variation related to changes in log centroid size[START_REF] Adams | A field comes of age: geometric morphometrics in the 21st century[END_REF]. Shape changes were visualized as vectors from the minimal shape (green) to the maximal shape (red) of the shape regression scores corresponding to the projection of the data points in shape space on to an axis in the direction of the regression vector (see[START_REF] Drake | The pace of morphological change: historical transformation of skull shape in St Bernard dogs[END_REF]. Phylogenetic regression of skull shape on log skull centroid size of Dataset-Lmax, represented 16.81% of the total shape variation.

  compared to the maximal shapes per OBU(DatasetExt, Figure 42; Figures 43 & 44). This is discussed only in the OBUs whose allometric variation was statistically supported (pvalue < 0.05) in the phylogenetic regressions. Only landmarks on the left side of the skull are mentioned. The results and shape changes explained by size for the Dataset-Tmax are not described below (except when different from the Dataset-Lmax) but are illustrated in Figures S32 & S33. To clarify, the taxa representing the minimum size for all datasets are chlamyphorines. The maximum size is represented by Priodontes for DatasetExt and by Glyptodon for Dataset-Lmax and Dataset-Tmax.

Figure 41 .

 41 Figure 41. Bar graphs showing the allometric proportions (R²) of each cranial unit's (OBU) total shape variation under the 3B approach (see text) for both evolutionary datasets. Allometric proportions are shown with the log skull centroid size taken as size variable. White bars indicate a statistically unsupported (NS) allometry for a given OBU (at p-value > 0.05). Abbreviations of OBUs: as-os-pt-bs, alisphenoid-orbitosphenoid-pterygoid-basisphenoid complex; bo-eo,basioccipital-exoccipital complex; fr, frontal; ju, jugal; lac, lacrimal; mx, maxillary; na, nasal; pa, parietal; pal, palatine; pe, petrosal; pmx, premaxillary; so, supraoccipital; sq, squamosal.

  the Dataset-Lmax (Figures 43 & 44), as size increases, the most posterior point of the alisphenoid/squamosal suture in front of the pyriform fenestra (#62) and the most anteroventral point of the foramen ovale (#60) are shifted anteriorly, but also dorsally for the former and ventrally for the latter (Figures 43 & 44). Together with the variation of more anterior landmarks (#65, optic canal -Figures 43 & 44), this indicates an anteroposterior shortening of the ventral portion of the alisphenoid, which is accompanied by an increase in height of its posterolateral portion. The most anteroventral point of the sphenorbital fissure (#46) occupies a much more anteroventral position in larger specimens. The most dorsal point of the internal posterior aperture of the optic canal (#112) and the most ventromedial point on the annular ring lateral to posterior median septum (114) move away from each other, resulting in an anteroposterior elongation of the sphenoidal jugum (Wible & Spaulding, 2013). The triple contact point between squamosal -frontal -alisphenoid (#42) takes a slightly more posteromedial position as size increases. Finally, the most anterodorsal point of the optic foramen (#65) moves to a more posteroventrolateral position and a greater separation from the much posterodorsally shifted internal posterior aperture of the optic canal (#112). This indicates a relative lengthening and reorientation (more dorsoventral) of the optic canal in larger specimens. Overall, the combined variation of most landmarks shows a strong increase in height of the as-os-pt-bs OBU as size increases (#62; #112; #114 shift dorsally; #42; #46; #60 shift ventrally). The Dataset-Tmax shows the same allometric variations (Figures S32 & S33).

  ), as size increases, the intersection between the anteromedial edge of the occipital condyle and foramen magnum (#76) hardly varies in position while the most anteroventral point of the foramen magnum (#85) is shifted posteriorly. The combination of these two allometric variations suggests a relative reduction in the sagittal diameter of the foramen magnum as size increases. The most anterolateral point of the occipital condyle (#84) extends more anterolaterally, which indicates a relative broadening of the occipital condyle with increasing size. The most posterolateral point of the jugular foramen (#80) is slightly shifted anteromedially, whereas the most posterolateral point of the hypoglossal foramen (#82) is relatively more posterolateral in larger specimens. The combination of these two allometric variations suggests a relative widening of the portion of the exoccipital separating the two foramina. Finally, the triple contact point between the supraoccipital -exoccipital -petrosal (#78) has a slightly more anteromedial position as size increases. In the Dataset-Lmax (Figures 43 & 44), some differences are observed with the previous dataset. From the smallest to the largest specimen, the intersection between the anteromedial edge of occipital condyle and foramen magnum (#76) assumes a more posteromedial and ventral position, which indicates a slight narrowing of the width of the foramen magnum. The triple contact point between the supraoccipital -exoccipital -petrosal (#78) is more medioventral, which indicates a relative reduction in the height of the exoccipital. The most anterolateral point of the occipital condyle (#84), hardly varies being only slightly more anterolateral in larger specimens. The most posterolateral point of the jugular foramen (#80) takes a more anterolateral and dorsal position while the most posterolateral point of the hypoglossal foramen (#82) is shifted posteromedially. The Dataset-Tmax shows the same allometric variations (Figures S32 & S33) as the Dataset-Lmax.

  in larger specimens. The combination of these allometric variations suggests a strong relative narrowing of the posterior half of the frontal. As size increases, the intersection between the internasal suture and the frontal bone (#2) is located more anteriorly and the triple contact point between frontal -maxillary -nasal (#32) has a more anteromedial position. The triple contact point between lacrimal -maxillary -frontal (#34) is shifted only slightly medially. The intersection between the lacrimal -frontal suture and the anterior orbital edge (#36) is located more posterolateral. The combination of these allometric variations (#2; #32; #36) suggests a relative lengthening of the anterior half of the frontal. Finally, the most dorsomedial point of the postorbital constriction (#40) is more posterior and slightly more medial in larger specimens. The combination of this change with that of landmark #36 suggests a slightly deeper postorbital constriction in larger specimens. In the Dataset-Lmax (Figures 43 & 44), from the smallest to the largest specimen, most allometric variations are similar to those observed for the DatasetExt. The dorsal intersection of annular ridge and midline (#97) takes a more ventral position in larger specimens than in the DatasetExt. The Dataset-Tmax shows the same allometric variations (Figures S32 & S33) as the two other datasets.

  specimens. The most dorsal point of the petrosal on the transverse level of the crista tentoria (#102) is slightly shifted anterodorsally. The maximum point of curvature in the ventromedial area of the fossa subarcuata (#110) moves to a more anteromedial position, which creates a shallower fossa subarcuata. The most ventral point of the external aperture of the cochlear canaliculus (#92) is also located more anterior and dorsal in larger specimens. The position of the most anteroventral point of the external aperture of cochlear fossula (#96) converges towards the latter, taking a more anterior position. Therefore, this indicates that the external aperture of the cochlear fossula and the aperture of the cochlear canaliculus are relatively closer to one another in larger specimens. The most anteromedial point of the foramen acusticum superius (#104) and the most anteromedial point of the foramen acusticum inferius (#106) are shifted dorsomedially, which indicates a relative thickening of the pars cochlearis of the petrosal. The most medial point of the promontorium in ventral view (#88) occupying a much more posterodorsal position, while the most anterior point of the petrosal's epitympanic wing (#108) is only slightly shifted posteroventrally and laterally. The Dataset-Lmax (Figures 43 & 44) and the Dataset-Tmax show essentially the same allometric variations (Figure S32 & S33) as DatasetExt.SquamosalIn the DatasetExt (Figure42), from the smallest to the largest specimen, the triple contact point between the parietal -squamosal -supraoccipital (#71) takes a more ventral position, whereas the triple contact point between the frontal -squamosal -parietal (#69) is located relatively more posteriorly. The most posterodorsal point of the zygomatic ridge of the squamosal (#56) is shifted dorsally, and the most dorsal point of the external acoustic meatus (#58) is located more anteroventrally in larger specimens. The combination of these allometric variations makes the posterior root of the zygomatic arch much wider and higher in larger specimens. Allometric variation in the zygomatic process of the squamosal occurs primarily at the most dorsal point of the jugal -squamosal suture (#52), which extends much further anteriorly as size increases.Together with the variation of other landmarks, this indicates that the squamosal portion of the zygomatic arch is more elongated in larger specimens. Finally, the most posterior point of the alisphenoid -squamosal suture in front of the pyriform fenestra (#62) assumes a more anterior and medial position in larger specimens. The ventral view (Figure42) also clearly shows a greater distance separating landmarks on the zygomatic arch (#52, #54) from those on the sidewall of the braincase (#42, #62, #69), in the anterior half of the bone. This indicates that the zygomatic arch protrudes further laterally in larger specimens.

  of the lateral occipital ridge in the caudal cerebral fossa (#100) has a relatively more medioventral position in larger specimens. The triple contact point between the parietal -squamosalsupraoccipital (#71) is located relatively more ventrally, described above for the squamosal. The triple contact point between the supraoccipital -exoccipital -petrosal (#78) is positioned slightly more dorsomedial and the most posterodorsal point of the foramen magnum (#86) more posterodorsal in larger specimens. The combination of these two allometric variations indicates a reduction in the proportions of the ventral part of the supraoccipital as size increases.The) and the Dataset-Tmax show the same allometric variations (Figures S32 & S33) as the DatasetExt.

  More posterior position of the anterior edge of the orbit and zygomatic arches. ii) More lateral position of the promontorium of the petrosal indicating its greater separation from the midline of the basicranium.

2 .

 2 As in Section 3.2, we have produced two datasets for Cabassous. The first dataset is referred as CabassousN (nontogenetic = 21; nstatic = 14). The second dataset is referred as CabassousNS (nontogenetic = 27; nstatic = 16). Results for the larger dataset CabassousNS are presented in the main text of the present work while results for the dataset CabassousN are presented in the supplementary data for each analysis. In order to preserve a maximum number of landmarks for the investigation of the pairs of selected distances at the evolutionary level, we favored the Dataset-Lmax also used for the evolutionary allometry analysis (refer to Section 3.2). It allowed a compromise between keeping the maximum number of landmarks and including a large panel of extant taxa and fossils (at least one pampathere, and one Santacrucian and one Pleistocene glyptodont). 4.1.2.2. Geometric morphometrics Digital data were acquired using X-ray µCT facilities at the MRI-ISEM facility platform of the University of Montpellier (France), at the American Museum of Natural History (AMNH, NYC, US), at the AST-RX platform of the Muséum national d'Histoire naturelle (MNHN, Paris, France), and the CT-lab of the Museum für Naturkunde (Mfn, Berlin, Germany). Image stacks

Figure 45 .

 45 Figure 45. Selected pairs of correlated distances at the ontogenetic level common to the 3 species (= DZC) (see text). Pairs of distances are represented simultaneously on a transparent skull for each species in dorsal and lateral view. Each distance pair is numbered in relation to Table13and the colors distinguish the different pairs. Covarying distances ending with bars are isometric. Pairs in which one of the two distances has arrows pointing towards the landmarks are allometric, the distance with arrows being the one increasing the fastest (see Table14). Scale = 1 cm.

  to Dasypus Coordinated variation of the height of the anterior part of the braincase compared to the rest of the braincase -Allom. similar to Dasypus 9: non-significant Faster (or isometric) anteroposterior growth of the dorsal part of the braincase (vault) compared to more ventral parts of the middle and caudal cranial fossae. 63-97/100-114 (Pair 2) + 12* 2* (DZC onto.) --------------------------Isom. similar to Dasypus & Cabassous Reduction in relative length and more transverse orientation of the optic canal as it becomes more distant from the basicranium 65the distance between the anteroventral root of the zygomatic arch and the auditory region than of the distance between the orbital edge and the auditory region -to instrasp. Faster growth in width between the posterolateral edge of the palate and the ventral base of the zygomatic arch than between the central part of the palate and the anterodorsal edge of the zygomatic arch ---------------------------------------19-21/17-48 (Pair 10) + 4* Allom. similar to instrasp.

  the distance between the posterolateral edge of the palate and the maxillary foramen than of the more dorsal distance contained between the anterior edge of the orbit and the posteromedial edge shows a coordinated variation between the S-distance from the most ventral point of the tentorial process (#63) to landmark #97 and the S-distance between the maximum curvature point of the lateral occipital ridge in the caudal cerebral fossa (#100) and the most ventromedial point on the annular ridge lateral to the posterior median septum (#114). Scrutiny of the correlation between the corresponding R-distances suggests a faster anteroposterior growth of the dorsal part of the vault compared to that of the oblique ventral axis of the middle and caudal cranial fossae in Cabassous and Zaedyus, whereas Dasypus shows an isometrically coordinated variation(Wible & Spaulding, 2013; Figure 45; Table

Figure 46 .

 46 Figure 46. Selected pairs of correlated distances at the static level common to the 3 species (= DZC) (see text). Pairs of distances are represented simultaneously on a transparent skull for each species in dorsal and lateral view. Each distance pair is numbered in relation to Table13and the colors distinguish the different pairs. Covarying distances ending with bars are isometric. Pairs in which one of the two distances has arrows pointing towards the landmarks are allometric, the distance with arrows being the one increasing the fastest (see Table14). Scale = 1 cm.

Figure 47 .

 47 Figure 47. Selected pairs of correlated distances at the ontogenetic level common to the 2 species (= ZC) (see text). Pairs of distances are represented simultaneously on a transparent skull for each species in dorsal and lateral view. Each distance pair is numbered in relation to Table13and the colors distinguish the different pairs. Covarying distances ending with bars are isometric. Pairs in which one of the two distances has arrows pointing towards the landmarks are allometric, the distance with arrows being the one increasing the fastest (see Table14). Scale = 1 cm.

Figure 48 .

 48 Figure 48. Selected pairs of correlated distances at the static level common to the 2 species (= ZC) (see text). Pairs of distances are represented simultaneously on a transparent skull for each species in dorsal and lateral view. Each distance pair is numbered in relation to Table13and the colors distinguish the different pairs. Covarying distances ending with bars are isometric. Pairs in which one of the two distances has arrows pointing towards the landmarks are allometric, the distance with arrows being the one increasing the fastest (see Table14). Scale = 1 cm.

Figure 50 .

 50 Figure 50. Selected pairs of correlated distances n°5 at the evolutionary level (see text). Pairs of distances are represented simultaneously on a transparent skull for minimal and maximal S-distances (Figure 49). A, lateral view. B, ventral view. Each distance pair is numbered in relation to Table13. Covarying distances ending with bars are isometric. Pairs in which one of the two distances has arrows pointing towards the landmarks are allometric, the distance with arrows being the one increasing the fastest (see Table15). Scale = 1 cm.

Figure 51 .

 51 Figure 51. Selected pairs of correlated distances (n°10 and 12) at the evolutionary level (see text). Pairs of distances are represented simultaneously on a transparent skull for minimal and maximal S-distances (Figure 49). A & C, lateral view. B & D, ventral view. Each distance pair is numbered in relation to Table 13. Covarying distances ending with bars are isometric. Pairs in which one of the two distances has arrows pointing towards the landmarks are allometric, the distance with arrows being the one increasing the fastest (see Table15). Scale = 1 cm.

Figure 52 .

 52 Figure 52. 3D reconstruction of masticatory muscle and tendons of insertion of Dasypus using dice-CT (courtesy of L. Hautier). Skull and left mandible in left lateral view. Abbreviation: m., musculus. Scale = 1 cm.

Figure 53 .

 53 Figure53. Selection of the number of stable modules using the gap statistic for each species at the ontogenetic level (represented by a juvenile and an adult specimen in lateral view, with landmarks) and at the static level (represented by an adult only). The slope break showing the number of statistically stable modules (see text), is marked by a dotted grey line.

Figure 55 .

 55 Figure 55. Principal Component Analysis on the DatasetExt with a neighbor-joining tree estimation for the total variance. Morphological shape changes on each axis are represented from the minimal (green) to the maximal (red) value of each axis. Landmarks discussed in the text are numbered for enhanced readability.

  Figures S48 & S49). Dasypodines show strong dissimilarity with other taxa (Figure 56, Figures S48 & S49). Tolypeutines are split and represent the extant clade most resembling fossil taxa (Figure 56, Figures S48 & S49). Vassallia appears close to the glyptodonts (Figure 56, Figures S48 & S49). Finally, Peltephilus and Proeutatus are close to the group formed by the latter two (Figure 56, Figures S48).

Figure 56 .

 56 Figure 56. Principal Component Analysis on the Dataset-Lmax with a neighbor-joining tree estimation for the total variance. Morphological shape change on each axis are represented from the minimal (green) to the maximal (red) value of each axis. Landmarks discussed in the text are numbered for enhanced readability.

Figure 57 .

 57 Figure 57. Principal Component Analysis on the Dataset-M-face with a neighbor-joining tree estimation for the total variance. Morphological shape changes on each axis are represented from the minimal (green) to the maximal (red) value of each axis. Landmarks discussed in the text are numbered for more readability. A skull of Dasypus novemcinctus in ventral and lateral views is added to illustrate the module in each view. Scale = 1cm.

  ), the orbit-neurocranium module shows a very strong anterodorsal migration of the posterior edge of the dental row (#28-29), whereas the most posterior point of the palatine midline (#30) hardly varies in comparison. The most dorsal point of the infraorbital foramen (#24-25) takes a much more ventromedial relative position. The intersection between jugal -maxillary suture and ventral edge of zygomatic arch (#20-21) moves more posterodorsal but also more medial. The anterior orbital edge(#35-36; 47-50) is located much more posterior, and this is accompanied by a slightly more dorsal position for the intersection between the lacrimal -frontal suture and the anterior orbital edge (#35-36) and a slightly more ventral position for the triple contact point between maxillary -jugal -lacrimal (#47-48). In contrast to the orbital edge, the rest of the anterodorsal part of the module (i.e., most landmarks on the frontal bone) is shifted relatively anteriorly or anteroventrally(#33-34; #39-40; #97,98). In addition, the triple contact point between squamosal-frontal-alisphenoid extends further anterolaterally (#41-42). The most anteroventral point of the sphenorbital fissure (#45-46) and the most dorsal point of the internal posterior aperture of the optic canal (#111-112) occupy a more posterolateral position. This shape mostly corresponds to dasypodines which are included in the highest values of PC1 while glyptodonts and Vassallia possess the lowest values. The other taxa are found at more intermediate values. We can nevertheless note that Priodontes tends to more closely resemble the dasypodines on axis 1 than the other taxa.

Figure 59 .

 59 Figure 59. Principal Component Analysis on the Dataset-M-vault-basicranium with a neighbor-joining tree estimation for the total variance. Morphological shape changes on each axis are represented from the minimal (green) to the maximal (red) value of each axis. Landmarks discussed in the text are numbered for more readability. A skull of Dasypus novemcinctus in ventral and lateral views is added to illustrate the module in each view. Scale = 1cm.

Figure 60 .

 60 Figure 60. Plot of specimens in the analysis of static allometry on the entire skull (ES) of Zaedyus pichiy (Section 3.2). Specimens in blue correspond to gp1 (see Supporting Information 1) and specimens in red correspond to gp2 (see Supporting Information 1). Each group is represented by a skull in dorsal (top) and lateral (bottom) view. Sex is known for only three specimens and is reported on the figure. Scale = 1 cm.

Figure 62 .

 62 Figure 62. Summary and schematization of widespread allometric patterns in cingulates (found at the intraspecific and evolutionary levels; see Section 3.2), here represented on a Dasypus novemcinctus cranium (MNHN.CG.2006-565) shown (from top) in dorsal, lateral, ventral, lateral, and sagittal views.

Figure 63 .

 63 Figure 63. Summary and schematization of the selected pairs of correlated distances pairs found at the intraspecific and evolutionary levels in our samples in cingulates, represent here on a Dasypus novemcinctus cranium (MNHN.CG.2006-565) shown in ventral and lateral views.

Figure 65 .

 65 Figure65. Evolutionary scenario for some characters of[START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF] and[START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF] potentially impacted by our study with the definition and mapping of characters on the baseline cladogram of our study. The coding follows the revision of[START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF] when the character is revised, otherwise it follows[START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF]. Coding for Calyptophractus, "Metopotoxus", Eucinepeltus, "Cochlops" and Glyptodon are available in Section 2. Branches combining several states mark a polymorphism.

Figure 66 .

 66 Figure 66. Skull of Dasypus novemcinctus (MNHN.CG.2006-565) and anatomical relocation of the GW characters potentially related to the patterns of integration found in our study (see Table 16) in dorsal (top left), lateral (middle left), ventral (bottom left), face (top right) and occipital (bottom, right) view.

Figure 68 .

 68 Figure 68. Covariation between the selected S-distances 50-94 and 21-18 (pair n°5) with a comparison between intraspecific and evolutionary level. A, both levels for regressions have similar slopes which suggest a widespread covaration pattern in cingulates. B, potential coding strategies C1 (quantification of the orthogonal distance of taxa relative to the regression line) and C2 (taxa position along the regression line).

2. 1 . 1

 11 State of the Art and DiagnosisThe genus Cabassous[START_REF] Mcmurtrie | The animal kingdom arranged in conformity with its organization. By the Baron Cuvier, and translated from the French, with notes and additions[END_REF] belongs to the Tolypeutinae also composed of the genera Priodontes(Cuvier, 1825) and Tolypeutes[START_REF] Illiger | Prodromus Systematis Mammalium et Avium: Additis Terminis Zoographicis Utriusque Classis, Eorumque Versione Germanica[END_REF] with which the cranial diagnoses allow a clear differentiation. Cabassous is currently composed of four species, with two of them having partly overlapping geographical distributions (Figure SI.1) -Cabassous unicinctus and Cabassous tatouay(Hayssen, 2014a; Hayssen, 2014b).

Figure SI. 1 .

 1 Figure SI.1. Phylogenetic relationships within the Cabassous clade[START_REF] Gibb | Shotgun mitogenomics provides a reference phylogenetic framework and timescale for living xenarthrans[END_REF] and geographical distribution of each species. 1, geographical area of Cabassous unicinctus unicinctus, and 2, geographical area of Cabassous unicinctus squamicaudis[START_REF] Wetzel | Order cingulata[END_REF]. The photographs and maps are from the International Union for Conversation of Nature (= IUCN) website.

  Euphractus sexcinctus[START_REF] Linnaeus | Systema naturae per regna tria naturae, secundum classes, ordines, genera, species, cum characteribus, differentiis, synonymis, locis[END_REF]; Chaetophractus villosus[START_REF] Desmarest | Tableau méthodique des mammifères[END_REF];Chaetophractus vellerosus; and Zaedyus pichiy. Chaetophractus nationi is currently considered a synonym for Chaetophractus vellerosus(Abba et al., 2015) (Figure SI.3).

Figure SI. 3 .

 3 Figure SI.3. Phylogenetic relationships within the Euphractinae clade[START_REF] Gibb | Shotgun mitogenomics provides a reference phylogenetic framework and timescale for living xenarthrans[END_REF] and geographical distribution of each species. 1, potential geographical area of Zaedyus pichiy caurinus and, 2, potential geographical area of Zaedyus pichiy pichiy[START_REF] Wetzel | Order cingulata[END_REF]. The photographs and maps are from the International Union for Conversation of Nature (= IUCN) website.

Figure SI. 5 .

 5 Figure SI.5. Ontogenetic stages determined based on Hubbe et al. (2016), as compared to the ossification score and the total length of the skull. The ontogenetic stages correspond to juvenile (cercle); subadult (triangle); adult (square); specimen problematic (see text) (cross).

4. 1 . 2

 12 Principal components analysis On the first two axes of the analysis (= 41.17% of the variance), 3 clusters are visible in the morphospace and one specimen stands out independently of these three groups (Figure SI.6). PC1 is dominated by shape variations similar to craniofacial allometry (Chapter 3). The main shape variations on PC2 corresponds to shifts in the front of the tooth row; the position of the infraorbital foramen; the position of the posterolateral end of the nasal and that of the two posterior root of the zygomatic arches. The isolated individual corresponds to a very young specimen (lowest ossification scores -Figure SI.5) in comparison with the other specimens. Otherwise, ontogeny does not seem correlated with the distribution of groups in the morphospace defined by these two axes. Cluster A shows a clear separation between the 9 large-sized specimens (see above) and the rest of the dataset which supports their tentative attribution to Cabassous tatouay. The cluster B in the center of the morphospace consists of specimens originating within the northern part of the distributional area of Cabassous unicinctus (i.e., Cabassous unicinctus unicinctus in Figure SI.1), two specimens from the southern region (i.e., Cabassous unicinctus squamicaudis in Figure SI.1), all remaining specimens of unknown origins and specimens originating within the distributional area of Cabassous centralis. This cluster therefore shows no distinction between Cabassous centralis and Cabassous unicinctus unicinctus. and the cluster C corresponds to specimens originating within the distributional area of Cabassous unicinctus squamicaudis (Figure SI.1). This distribution in the morphospace suggests a clear distinction between two subsets in Cabassous

  For the symmetrical matrix, the lower triangle corresponds to the R 2 values and the upper triangle corresponds to the p-value. Each group is defined in Figure SI.6. 4.1.4 Neighbour joining The neighbour joining (NJ) analysis allows us to visualize more precisely the phenetic distances between specimens over the whole variance. The NJ tree obtained is congruent with the permutational test and the first two PCA axes (Figure SI.7). Beside the very young specimen, two groups are very distant from other specimens (cluster B): the cluster A (Cabassous tatouay) and the cluster C. Specimens originating from the distributional areas of Cabassous centralis are found nested within the cluster B together with many specimens originating within the northern part of the distributional area of Cabassous unicinctus, specimens of unknown origins and 2 specimens originating within the southern part of the distributional area of Cabassous unicinctus. In addition, the ontogenetic stages do not seem to have a major influence on phenetic distances as they are distributed all over the NJ tree.

Figure

  Figure SI.7. Unrooted neighbour-joining trees performed from PCA in Cabassous. Each category for species, geographical distribution and ontogenetic stages are represented in Figure SI.6.

  on ossification of the basicranium enables us to tentatively distinguish between the ontogenetic stages present in the sample. This criterion separates three distinct areas on the bivariate plot for juveniles, subadults and adults, except for two specimens which have low ossification scores while being large and identified as adults with Hubbe et al.'s criteria (Figure SI.8). The specimen designated as a potential C. vellerosus is recognized as a juvenile. Besides a rather good separation of ontogenetic stages, there are no obvious groupings related to geographical origin (compared to specimens of unknown origin) or to the presence/absence of teeth on the premaxillary.

Figure

  Figure SI.8. Ontogenetic stages determined based on[START_REF] Hubbe | A case study of extant and extinct Xenarthra cranium covariance structure: implications and applications to paleontology[END_REF], as compared to the ossification score and the total length of the skull with a focus without the youngest specimen with a plot of the presence/absence of premaxillary teeth[START_REF] Superina | Zaedyus pichiy (Cingulata: Dasypodidae)[END_REF]. The ontogenetic stages correspond to neonate (cross); juvenile (cercle); subadult (triangle); adult (square).

4. 2 . 2

 22 Principal components analysisOn the first two axes of the analysis (= 31.48% of the variance), 2 large clusters are formed in the morphospace and two specimens stand out of these groups (Figure SI.9) (see below). The position of the zygomatic arches, the nuchal crests, and the cranial roof all vary on this axis while PC2 is mainly dominated by the variation of the nasal bone. The Bolivian specimen (Chaetophractus vellerosus area) takes an off-centered position in relation to the rest of the sample and this is also the case of a specimen of unknown origin. The clear separation in the morphospace of the Bolivian specimen from most of the sample seems to support its referral to Chaetophractus vellerosus. The status of the other off-centered specimen, of unknown origin, remains unclear (Chaetophractus vellerosus?) and will be further addressed in the following analyses. The separation of two large clusters in the PC1-2 morphospace, both of which contain specimens originating from the Zaedyus pichiy distributional area and specimens with premaxillary teeth and of all ontogenetic stages, raises questions on the existence of two large distinct entities within the sample. Interestingly, the only 2 of the three individuals in cluster A (Figure SI.9) with precisely known geographical origins come from the northern part of the Zaedyus pichiy distributional area.

Figure

  Figure SI.9. Results of the PCA performed on morphometric data in Zaedyus with a focus on geographical distribution, ontogenetic stage, and presence/absence of premaxillary teeth, distribution in the morphospace. Shape changes were visualized as vectors from the minimal shape (green) to the maximal shape (red) of each PC axes.

Figure

  Figure SI.10. Unrooted neighbour-joining trees performed from PCA in Zaedyus. Each category for geographical distribution, ontogenetic stages and presence/absence of premaxillary teeth are represented in Figure SI.9.

Figure S1 .

 S1 Figure S1. Morphological phylogenetic analysis of Billet et al. (2011) only with extant specimens. Tree length = 346 (on 5 trees of maximum parsimony), CI = 0.743, RI = 0.637. The color follows the work of Mitchell et al. (2016). Each taxon is illustrated by a skull in lateral view. Scale = 1 cm.

Figure S2 .

 S2 Figure S2. Illustration of the internal and external openings of each selected canal on a specimen of Euphractus sexcinctus (AMNH 133304) in transparent and non-transparent views. A, B, F and H, lateral view; C, ventral view; D and E, oblique internal view; G, lateral view of the braincase inner part; I, occipital view. Colors of the canals follow Figure 9. Abbreviations: afdv, accessory frontal diploic vein internal opening; aospc, anterior opening of the sphenopalatine canal; aotc, anterior opening of the orbitotemporal canal, asmf, accessory suprameatal foramen; fdv, foramen for the frontal diploic vein; ifdv, internal foramen for the frontal diploic vein; iocev, internal opening of the capsuloparietal emissary vein canal; lacf, lacrimal foramen; nlc, nasolacrimal canal; oncpl, opening in nasopharyngeal canal of palatine canal; otg, orbitotemporal groove; pf, palatine foramina; poptc, posterior opening of the posttemporal canal; ptgf, postglenoid foramen; ramus temporalis canal; rtotc, rami temporales foramina from the orbitotemporal canal; rtptc, rami temporales foramina from the posttemporal canal; smf, suprameatal foramen; spf, sphenopalatine foramen; tc, tranverse canal; tcf, tranverse canal foramen. Scale = 1 cm.

Figure S3 .

 S3 Figure S3. Cranial measurements (TableS2) illustrated on a transparent cranium in lateral (top) and dorsal (bottom) view of Glyptodon sp. MNHN.F.PAM 760. Abbreviations: GDRH, greatest dental row height; GSH, greatest skull height; GSL, greatest skull length; GSW, greatest skull width; IVI, internal vault inclination (= angle between the anteroposterior axis of the cranium (defined by the line connecting the most anterior and posterior edges of the dental row) and the straight line connecting the most dorsal point of the annular ring and the most ventral point of the tentorial process). Scale = 1 cm.

Figure

  FigureS4. A, modified backbone constraint from[START_REF] Mitchell | Ancient DNA from the extinct South American giant glyptodont Doedicurus sp. (Xenarthra: Glyptodontidae) reveals that glyptodonts evolved from Eocene armadillos[END_REF] used for our phylogenetic analysis (see text). Proeutatus is enforced as the sister group of glytptodonts in accordance with most phylogenetic analyses using morphology[START_REF] Engelmann | The evolution and ecology of armadillos, sloths and vermilinguas[END_REF][START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF][START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF][START_REF] Herrera | A new Eocene dasypodid with caniniforms (Mammalia, Xenarthra, Cingulata) from northwest Argentina[END_REF]. B. Topology of the baseline cladogram. C. Topology of the strict consensus from the same analysis without constraint. See Supporting information 2 for phylogenetic analysis.

Figure S5 .

 S5 Figure S5. Reconstructed canals in Utaetus buccatus in right lateral (top) and ventral (bottom) views. The preserved parts of the cranium (caudal cranium) are shown with transparency. Abbreviations: cevc, capsuloparietal emissary vein canal; cevg, capsuloparietal emissary vein groove; fdvc, frontal diploic vein canal; nlc, nasolacrimal canal; otc, orbitotemporal canal; otg, orbitotemporal groove; rtc, rami temporales canals; rtcevc, rami temporales from capsuloparietal emissary vein canal; tc, tranverse canal. Scale = 1 cm.

Figure S6 .

 S6 Figure S6. Illustration of the foramen for the frontal diploic vein identified in the study by Gaudin & Lyon (2017) on Holmesina floridanus (UF 191448) (A) and the anterior opening of the orbitotemporal canal in Vassallia maxima (FMNH P14424) in a right lateral view with transparency (B) and a view focused on the orbitotemporal region (C). Abbreviations: aotc, anterior opening of the orbitotemporal canal; fdv, foramen for the frontal diploic vein. Scale = 1 cm.

Figure S7 .

 S7 Figure S7. Identification of the bones enclosing the nasolacrimal canal in Euphractus sexcinctus (AMNH 133304) illustrated by a skull in right lateral view (top). The slices analyzed are indicated on the skull by their number in the image stack and illustrated below. The nasolacrimal canal is reconstructed in red on each slice, on the left side of the image. Abbreviations: lac, lacrimal; mx, maxillary; nlc, nasolacrimal canal; pmx, premaxillary. Scale = 1 cm.

Figure S8 .

 S8 Figure S8. Comparative illustration of the trajectory of the palatine canal in glyptodonts and other cingulates (illustrated here by Euphractus sexcinctus (AMNH 133304)). A, lateral internal view on a skull sectioned on the midline. B, same view as A but with the palatine canal reconstructed. C, same view as A with skull transparency and with the sphenopalatine and palatine canals reconstructed. Abbreviations: aospc, anterior opening of the sphenopalatine canal; ioplc, internal opening of the palatine canal; npc, nasopharyngeal canal; plg, palatine grove; spc, sphenopalatine canal. Scale = 1cm.

Figure S9 .

 S9 Figure S9. Illustration of the position of the sphenopalatine and palatine canals in relation to the nasopharyngeal canal in Euphractus sexcinctus (AMNH 133304), Vassallia maxima (FMNH P14424) and Glyptodon sp. (MNHN.F.PAM 760). A. Selected slides (numbered according to their position in the image stack) indicated on the skull in lateral view. B. Slides in coronal view. C. Canals are indicated on skull in transparency in lateral view (same as A). The same colors were used for canals: orange, palatine canal; yellow, sphenopalatine canal. Abbreviations: npc, nasopharyngeal canal; plc, palatine canal; plg, palatine groove; spc, sphenopalatine canal. Scale = 1 cm.

Figure S10 .

 S10 Figure S10. Identification of the canal for the ramus superior of the stapedial artery in Tolypeutes matacus (FMNH 28345). External opening is illustrated on a skull in ventral view with a focus on the auditory region. Canal trajectory in relation to the other braincase canals is representing on a transparent skull in lateral view with a focus on the neurocranium. Several parts of the canal (external opening, contact with the orbitotemporal and posttemporal canal, etc.) are also illustrated by numbered slides (in relation to the total number of slides) and indicated on the skulls. Abbreviations: cevc, capsuloparietal emissary vein canal; crsu, canal for the ramus superior of the stapedial artery; otc, orbitotemporal canal; otg, orbitotemporal groove; ptc, posttemporal canal. Scale = 1 cm.

Figure S11. 3

 3 Figure S11. 3 Different cases of contact/non-contact between the three braincase canals analyzed in our study (including the region of confluence) in Tolypeutes matacus (FMNH 28345), Euphractus sexcinctus (AMNH 133304) and Glyptodon sp. (MNHN.F.PAM 760). Selected slides (numbered according to the total slide number) are indicated on skull in lateral view and canals are coloured on one side of each slide. Abbreviations: cevc, capsuloparietal emissary vein canal; cevg, capsuloparietal emissary vein groove; ptc, posttemporal canal; rc, region of confluence; rtc, ramus temporalis canal. Scale = 1 cm.

Figure

  Figure S12. CT-scan sections representing the five dental stages defined in relation to the eruption of deciduous (dPM) and permanent teeth (PM). The analyzed locus always corresponds to the 4 th premolar represented here by an arrow. Based on our observations of the upper dentition, we defined five dental stages: (1) dPMs starting to mineralize or erupting; (2) all dPMs well mineralized, possibly all erupted, no PM in the crypts (i.e., PM not mineralized); (3) all dPMs erupted, with part of the PMs mineralized but still in the crypts (not yet reaching the alveoli); (4) part of the dPMs about to be replaced by PMs (one or several PMs has/have erupted through the alveoli, but remain(s) almost unworn); (5) all PMs erupted and no remain of dPMs left (see Supporting Information 3).

Figure S13 .

 S13 Figure S13. Bivariate linear regressions among three dentary measurements and the LTC. A. With the height of the P4/dPM4. B. With the height of the alveoli of the PM4/dPM4. C. With the height of the growth front of the P4/dPM4. Each measurement is illustrated in the section to the right of each graph. For each simple regression, the slope equation and R² are specified. In each case, specimens, whose dental stage (2 or 5) is unknown, were determined a posteriori (see Supporting Information 3).

Figure S14 .

 S14 Figure S14. Ontogenetic stages determined based on dental eruption, as compared to the ossification score and the total length of the skull (LTC). The dental stages correspond here to: 1, stillborn (n = 1); 2, juvenile (n = 11); 3, subadult 1 (n = 7); 4, subadult 2 (n = 9); 5, adult (n = 56). The black dots refer to specimens (n = 12) whose dental stage could not be determined. See Supporting Information 3 for more detail.

Figure S15 .

 S15 Figure S15. Allometric trajectories among three nine-banded armadillo's morphotypes (Southern, Central and Northern) at ontogenetic (Aillustrated by juvenile and adult specimens in dorsal view) and static (Billustrated by adult specimens in dorsal view) levels. The y-axis values are the principal component 1 of the predicted values of a multivariate regression of shape on size; the x-axis values are the log-transformed skull centroid sizes for each specimen. For each level, the HOS test, Procrustes ANOVA and Pairwise comparisons of the allometric trajectory angles results are shown (in bold, the R² and p-value for the first two analyses and the angles between the slope and its intercept with a significant p-value). Scale bar: 1 cm. (see Material and Methods).

Figure S16 .

 S16 Figure S16. Vector representation in southern morphotype of the allometric shape changes detected for the entire skull and a given cranial unit (OBU), represented between its minimal (greensmaller centroid size) and maximal (redlarger centroid size) shape (see Figure 23) with the associated R² and p-value. Results of the analyses performed at the ontogenetic level, and with the log skull centroid size taken as the size variable (see text). For each OBU, the changes are shown in one view with vectors from minimal to maximal shape with the minimal OBU shape shown in transparency. A) Entire skull in dorsal view. B) Entire skull in lateral view. C) Alisphenoidorbitosphenoid-pterygoid-basisphenoid complex in dorsal view. D) Basioccipital-exoccipital complex in ventral view. E) Frontal in ventral view. F) Jugal in medial view. G) Maxillary in medial view. H) Nasal in ventral view. I) Palatine in dorsal view. J) Parietal in dorsal view. K) Petrosal in lateral view. L) Premaxillary in medial view. M) Squamosal in ventral view. N) Supraoccipital in occipital view. Landmark numbers and orientation arrows were added for more readability as well as the overall representation of the unpaired bones (basioccipital and supraoccipital). Abbreviations: A, anterior; D, dorsal; L, lateral; V, ventral.

Figure S17 .

 S17 Figure S17. Multivariate regression for each OBU at the ontogenetic level using log skull centroid size.

Figure S18 .

 S18 Figure S18. Multivariate regression for each OBU at the static level with log skull centroid size.

Figure S19 .

 S19 Figure S19. Vector representation of the allometric shape changes detected for a given cranial unit (OBU), represented between its minimal (greensmaller centroid size) and maximal (redlarger centroid size) shape (see Figure23). Results of the analysis performed at the static level, and with the log skull centroid size as the size variable (see text). For each OBU, the changes are shown in three subsections organized horizontally: 1, vectors from minimal to maximal shape with minimal OBU shape; 2, same as 1) with maximal OBU shape; 3, minimal OBU shape in transparency with vectors. A) Alisphenoid-orbitosphenoid-pterygoid-basisphenoid complex; A1-A2, lateral view; A3, dorsal view. B) Frontal; B1-B2, lateral view; B3, dorsal view. C) Palatine; C1-C2, ventral view; C3, dorsal view. D) Parietal; D1-D2, ventral view; D3, dorsal view. Landmark numbers and orientation arrows were added for more readability. Abbreviations: A, anterior; L, lateral; V, ventral.

Figure S20 .

 S20 Figure S20. Common allometric analyses. Trajectories are derived from homogeneity of slope test, plotting log transformed geometric means in the x-axis (i.e., log skull centroid size) and the PC1 of the predicted values of multivariate regression of shape ratios on size in the y-axis (Shape (Predicted)) (see Material and Methods).

Figure S21 .

 S21 Figure S21. Retrodeformation applied on the skull of "Metopotoxus" anceps (YPM-PU 15612) with an illustration of the original specimen and a comparison between the two meshs. A, dorsal view; B, ventral view; C, lateral view; D, face view; E, occipital view. Abbreviations: A, anterior; L, lateral; V, ventral. Scale-bars = 1 cm.

Figure S22 .

 S22 Figure S22. Retrodeformation applied on the skull of Proeutatus lagena (YPM-PU 15613) with an illustration of the original specimen and a comparison between the two meshs. A, dorsal view; B, ventral view; C, lateral view; D, face view; E, occipital view. Abbreviations: A, anterior; L, lateral; V, ventral. Scale-bars = 1 cm.

Figure S23 .

 S23 Figure S23. Retrodeformation applied on the skull of Stegotherium tauberi (YPM-PU 15565) with an illustration of the original specimen and a comparison between the two meshs. A, dorsal view; B, ventral view; C, lateral view; D, face view; E, occipital view. Abbreviations: A, anterior; L, lateral; V, ventral. Scale-bars = 1 cm.

Figure S24 .

 S24 Figure S24. Landmarks digitized on the skull of Dasypus novemcinctus (lateral view), Zaedyus pichiy (ventral view) and Cabassous unicinctus (ventral view with bone transparency (25%)) with details on the deleted landmarks for Dataset-Lmax and Dataset-Tmax. Scale-bar = 1 cm. List of landmarks can be found in Table13.

Figure S25 .

 S25 Figure S25. Topology of trees used for phylogenetic regression for each evolutionary dataset (A, B and C) (for more detail see Material & Methods -Chapter 2 & Section 3.2). CM, Central Morphotype; GM, Guianan Morphotype; NM, Northern Morphotype; SM, Southern Morphotype. †, extinct species.

Figure S26 .

 S26 Figure S26. Ontogenetic allometry on the entire skull (ES) of CabassousN. Ontogenetic stages are represented with different colors (juvenile = green; subadult = yellow; adult = red; see text for more detail).For graphical display, we used the projected regression scores of the shape data to represent shape variation related to changes in log skull centroid size[START_REF] Adams | A field comes of age: geometric morphometrics in the 21st century[END_REF]. Shape changes were visualized as vectors from the minimal shape (green) to the maximal shape (red) of the shape regression scores corresponding to the projection of the data points in shape space on to an axis in the direction of the regression vector (see[START_REF] Drake | The pace of morphological change: historical transformation of skull shape in St Bernard dogs[END_REF]. Multivariate regression of skull shape on log skull centroid size at the ontogenetic level representing 8.80% of the total shape variation.

Figure S27 .

 S27 Figure S27. Bar graphs showing the allometric proportions (R²) of each cranial unit's (OBU) total shape variation under the 3B approach (see text), at the ontogenetic (A) and static (B) levels in CabassousN. Allometric proportions are shown with the log skull centroid size taken as size variable. On the virtually dislocated skull (in right lateral view), the allometric proportions are reported in corresponding colors. White bars indicate a statistically unsupported (NS) allometry for a given OBU (at p-value > 0.05). Abbreviations of OBUs: as-os-pt-bs, alisphenoid-orbitosphenoid-pterygoid-basisphenoid complex; bo-eo, basioccipital-exoccipital complex; fr, frontal; ju, jugal; lac, lacrimal; mx, maxillary; na, nasal; pa, parietal; pal, palatine; pe, petrosal; pmx, premaxillary; so, supraoccipital; sq, squamosal.

Figure S28 .

 S28 Figure S28. Vector representation of the allometric shape changes detected for a given cranial unit (OBU) in CabassousN, represented between its minimal (greensmaller centroid size) and maximal (redlarger centroid size) shape (see Figure29). Results of the analysis performed at the ontogenetic level, and with the log skull centroid size taken as the size variable (see text). For each OBU, the changes are shown in three subsections organized horizontally: 1, vectors from minimal to maximal shape with minimal OBU shape; 2, same as 1) with maximal OBU shape; 3, minimal OBU shape in transparency with vectors. A) alisphenoid-orbitosphenoidpterygoid-basisphenoid complex; A1-A2, lateral view; A3, dorsal view. B) frontal; B1-B2, lateral view; B3, ventral view. C) jugal; C1-C2, lateral view; C3, medial view. D) petrosal; D1-D2, medial view; D3, lateral view. E) squamosal; E1-E2, lateral view; E3, ventral view. F) parietal; F1-F2, ventral view; F3, dorsal view. Landmark numbers and orientation arrows were added for more readability. Abbreviations: A, anterior; L, lateral; V, ventral.

Figure S29 .

 S29 Figure S29. Vector representation of the allometric shape changes detected for a given cranial unit (OBU) in CabassousNS, represented between its minimal (greensmaller centroid size) and maximal (redlarger centroid size) shape (see Figure29). Results of the analysis performed at the static level, and with the log skull centroid size taken as the size variable (see text). For each OBU, the changes are shown in three subsections organized horizontally: 1, vectors from minimal to maximal shape with minimal OBU shape; 2, same as 1) with maximal OBU shape; 3, minimal OBU shape in transparency with vectors. A) alisphenoid-orbitosphenoid-pterygoidbasisphenoid complex; A1-A2, lateral view; A3, dorsal view. B) jugal; B1-B2, lateral view; B3, medial view. C) petrosal; C1-C2, medial view; C3, lateral view. D) nasal; D1-D2, dorsal view; D3, ventral view. Landmark numbers and orientation arrows were added for more readability. Abbreviations: A, anterior; D, dorsal; L, lateral; V, ventral.

Figure S30 .

 S30 Figure S30. Evolutionary allometry on the entire skull (ES) of Dataset-Tmax. Clades and fossils taxa are represented with different colors.For graphical display, we used the projected regression scores of the shape data to represent shape variation related to changes in log centroid size[START_REF] Adams | A field comes of age: geometric morphometrics in the 21st century[END_REF]. Shape changes were visualized as vectors from the minimal shape (green) to the maximal shape (red) of the shape regression scores corresponding to the projection of the data points in shape space on to an axis in the direction of the regression vector (see[START_REF] Drake | The pace of morphological change: historical transformation of skull shape in St Bernard dogs[END_REF]. Phylogenetic regression of skull shape on log skull centroid size of Dataset-Tmax, representing 13.62% of the total shape variation.

Figure S31 .

 S31 Figure S31. Bar graphs showing the allometric proportions (R²) of each cranial unit's (OBU) total shape variation under the 3B approach (see text) for both evolutionary datasets. Allometric proportions are shown with the log skull centroid size taken as size variable. White bars indicate a statistically unsupported (NS) allometry for a given OBU (at p-value > 0.05). Abbreviations of OBUs: as-os-pt-bs, alisphenoid-orbitosphenoid-pterygoid-basisphenoid complex; bo-eo, basioccipital-exoccipital complex; fr, frontal; ju, jugal; lac, lacrimal; mx, maxillary; na, nasal; pa, parietal; pal, palatine; pe, petrosal; pmx, premaxillary; so, supraoccipital; sq, squamosal.

  of incisive foramen in strict ventral view 17 Intersection between palatine/maxillary suture and the palate midline 18-19 Intersection between maxillary/palatine suture and lateral edge of palate 20-21 Intersection between jugal/maxillary suture and ventral edge of zygomatic arch 22-23 Most dorsal point of the maxillary foramen 24-25 Most dorsal point of the infraorbital foramen 26-27 Most anterior point of the alveolar margin of the dental row 28-29 Most posterior point of the alveolus margin of the dental row *between maxillary/jugal/lacrimal 49-50 Intersection between anterior orbital edge and jugal/lacrimal suture 51-52 Most dorsal point of the jugal/squamosal suture 53-54 Most ventral point of the jugal/squamosal suture 55-56 Most posterodorsal point of the zygomatic ridge of the squamosal 57-58 Most dorsal point of the external acoustic meatus on squamosal (in lateral view) of the supraoccipital on the midline (occipital face) 73-74 Most posterior point of the nuchal process of the supraoccipital 75-76 Intersection between the anteromedial edge of occipital condyle and foramen magnum 77-78 Triple contact point between the supraoccipital/exoccipital/petrosal 79-80 Most posterolateral point of the jugular foramen 81-82 Most posterolateral point of the hypoglossal foramen Table cribriform plate and median septum posterior to the latter 99-100* Maximum curvature point of the lateral occipital ridge in caudal cerebral fossa 101-102* Most dorsal point of the petrosal on the level of the crista tentoria transversally 103-104* Most anteromedial point of the foramen acusticum superius 105-106* Most anteromedial point of the foramen acusticum inferius 107-108* Most anterior point of epitympanic wing of petrosal 109-110* Maximum curvature point in the ventromedial area of the fossa subarcuata 111-112* Most dorsal point of the internal posterior aperture of the optic canal 113-114* Most ventromedial point on the annular ridge lateral to posterior median septum

Figure S34 .

 S34 Figure S34. Examples of non-selected pairs of correlated distances illustrated on a skull of Dasypus novemcinctus SM.In red, a pair of covarying distances related to a lengthening of the skull (i.e., long, and parallel distances covering the skull anteroposteriorly). Other pairs of this nature (long, parallel and overlapping) in different directions (e.g., skull height) did not appear among the pairs above the threshold criteria. In blue, a pair of covarying distances that signaled an increase in the length of the snout relative to a decrease in the proportions of the neurocranium (= craniofacial allometrynegative correlation) already well-known in nine-banded armadillos (Chapter 3). Scale = 1 cm.

Figure S35 .

 S35 Figure S35. Frequencies of the pairs of correlated distances according to the values of R² (i.e., the square of correlation coefficient r) for each species at the ontogenetic level (represented by a juvenile and an adult specimen in lateral view) and at the static level (represented by an adult specimen in lateral view). The color gradient from purple to red represents the detected R² values from 0.5 to 1.

Figure S36 .

 S36 Figure S36. Covariation in the selected pair n°3 (65 -92 / 106 -112) illustrated by the SMA plot (see Material & Methods) for each species (green = juvenile; yellow = subadult; red = adult). Extreme specimens are identified by a circle on the plots and presented in ventral view for each species with the distances illustrated.

Figure S37 .

 S37 Figure S37. Covariation in the selected pair n°4 (38 -80 / 50 -92) illustrated by the SMA plot (see Material & Methods) for each species. Extreme specimens are identified by a circle on the plots and presented in lateral view for each species with the distances illustrated.

Figure S38 .

 S38 Figure S38. Covariation in the selected pair n°5 (50 -94 / 21 -108) illustrated by the SMA plot (see Material & Methods) for each species. Extreme specimens are identified by a circle on the plots and presented in lateral view for each species with the distances illustrated.

Figure S40 .

 S40 Figure S40. Landmarks digitized on the skull of Dasypus novemcinctus (lateral view), Zaedyus pichiy (ventral view) and Cabassous unicinctus (dorsal view, with transparency). The red dotted circle marks the area corresponding to the tympanic bulla that was virtually cleared in Zaedyus pichiy. The red landmark numbers correspond to the landmarks not selected for EDMA (see text). Scale-bar = 1 cm.

Figure S41 .

 S41 Figure S41. Selection of the number of stable modules using the gap statistic for CabassousN at the ontogenetic level (represented by a juvenile and an adult specimen in lateral view, with landmarks) and at the static level (represented by an adult only). The slope break showing the number of statistically stable modules (see text) is marked by a dotted grey line.

Figure S42 .

 S42 Figure S42. Dendogram obtained following the hierarchical clustering applied to the EDMA results for each species at the ontogenetic level, with bootstrap values. In red, anterior-face or face module; in purple, mid-face module; in green, orbit-neurocranium module; in blue, vault-basicranium module.

Figure S43 .

 S43 Figure S43. Dendogram obtained following the hierarchical clustering applied to the EDMA results for each species at the static level, with bootstrap values. In red, anterior-face or face module; in purple, mid-face module; in green, orbit-neurocranium module; in blue, vault-basicranium module.

Figure S44 .

 S44 Figure S44. Dendogram obtained following the hierarchical clustering applied to the EDMA results for each species at the ontogenetic level, with a mapping on skull. In red, anterior-face or face module; in purple, mid-face module; in green, orbit-neurocranium module; in blue, vault-basicranium module.

Figure S45 .

 S45 Figure S45. Dendogram obtained following the hierarchical clustering applied to the EDMA results for each species at the static level, with a mapping on skull. In red, anterior-face or face module; in purple, mid-face module; in green, orbit-neurocranium module; in blue, vault-basicranium module.

Figure S46 .

 S46 Figure S46. Mapping of the modules obtained for CabassousN at the ontogenetic, and static levels. In red, anteriorface or face module; in purple, mid-face module; in green, orbit-neurocranium module; in blue, vault-basicranium module.

Figure S47 .

 S47 Figure S47. Retrodeformation applied on the skull of "Metopotoxus" anceps (YPM-PU 15612) with an illustration of the original specimen and a comparison between the two meshs. A, dorsal view; B, ventral view; C, lateral view; D, face view; E, occipital view. Abbreviations: A, anterior; L, lateral; V, ventral. Scale-bars = 1 cm.

Figure S48 .

 S48 Figure S48. Principal Component Analysis on the Dataset-Tmax with a neighbor-joining tree estimation for the total variance. Morphological shape change on each axis are represented from the minimal (green) to the maximal (red) value of each axis.

Figure S49 .

 S49 Figure S49. Principal Component Analysis on the Dataset-G with a neighbor-joining tree estimation for the total variance. Morphological shape change on each axis are represented from the minimal (green) to the maximal (red) value of each axis.

Figure S50 .

 S50 Figure S50. Plate of cingulate craniums in dorsal view. Abbreviations: cr, cranial roof; nc, nuchal crest; o, orbit; pc, postorbital constriction; s, snout; tf, temporal fossa; za, zygomatic arch. Scale = 1cm.

Table 1 .

 1 List of specimens.

	Family/Clade	Species	Institutional number	Locality	Period	Age range	Reference
	Bradypodidae	Bradypus tridactylus	MNHN ZM-MO-1999-1065	French Guiana; Petit saut rive droite	Extant	0	Linnaeus, 1758
	Myrmecophagidae	Tamandua tetradactyla	NHM 3-7-7-135	Brazil; Mato Grosso; Chapada	Extant	0	Linnaeus, 1758
	Peltephilidae	Peltephilus pumilus †	YPM-PU 15391	Argentina; Santa Cruz formation; Coy inlet	Santacrucian	17.5-16.3	Ameghino,
	Dasypodidae	Utaetus buccatus †	AMNH 28668	Argentina; Gran Barranca	Barrancan	41.6-39.0	Ameghino,
	Dasypodinae	Dasypus novemcinctus *	AMNH 33150	Colombia; Quindui; Salento	Extant	0	Linnaeus, 1758
	Dasypodinae	Dasypus novemcinctus **	AMNH 133261	Brazil; Goias; Anapolis	Extant	0	Linnaeus, 1758
	Dasypodinae	Dasypus novemcinctus ***	AMNH 133328	Brazil; Mato Grosso do Sul; Maracaju	Extant	0	Linnaeus, 1758
	Dasypodinae	Dasypus novemcinctus ****	AMNH 255866	Bolivia; Beni; Cercado	Extant	0	Linnaeus, 1758
	Dasypodidae	Stegotherium tauberi †	YPM-PU 15565	Argentina; Santa Cruz formation	Santacrucian	17.5-16.3	Ameghino,
	Euphractinae	Prozaedyus exilis †	YPM-PU 15579	Argentina; Santa Cruz formation; Kilik Aike	Santacrucian	17.5-16.3	Ameghino,
	Euphractinae	Prozaedyus proximus †	YPM-PU 15567	Argentina; Santa Cruz formation; Coy inlet	Santacrucian	17.5-16.3	Ameghino,
	Euphractinae	Euphractus sexcinctus	AMNH 133304	Brazil; Goias; Anapolis	Extant	0	Linnaeus, 1758
	Euphractinae	Chaetophractus villosus	AMNH 173546	South America -No more precision	Extant	0	Desmarest,
	Euphractinae	Zaedyus pichiy *	ZMB 49039	Argentina; Oso Marino	Extant	0	Desmarest,
	Euphractinae	Zaedyus pichiy **	MHNG 1627.053	Argentina; Chubut; Punta Ninfas	Extant	0	Desmarest,
	Euphractinae	Zaedyus pichiy ***	MHNG 1276.076	Argentina; Chubut; Fofo Cahuel	Extant	0	Desmarest,
	Euphractinae	Zaedyus pichiy ****	FMNH 23810	Argentina; Chubut	Extant	0	Desmarest,
	Euphractinae	Doellotatus sp. †	UF 260533	Argentina; Santa Cruz formation; Quebrada Honda	Santacrucian	17.5-16.3	Bordas, 1932
	Tolypeutinae	Cabassous unicinctus **	NBC 26326.B	Suriname	Extant	0	Linnaeus, 1758
	Tolypeutinae	Cabassous unicinctus ***	AMNH 133386	Brazil; Mato Grosso do Sul; Maracaju	Extant	0	Linnaeus, 1758
	Tolypeutinae	Cabassous unicinctus ****	MNHN 1999-1044	French Guiana	Extant	0	Linnaeus, 1758
	Tolypeutinae	Tolypeutes matacus	FMNH 28345	Brazil; Mato Grosso; Descalvado	Extant	0	Desmarest,
	Tolypeutinae	Priodontes maximus	AMNH 208104	Zoo -No more precision	Extant	0	Kerr, 1792
	Chlamyphorinae	Chlamyphorus truncatus	AMNH 5487	Argentina; Mendoza	Extant	0	Harlan, 1825
	Chlamyphorinae	Calyptophractus retusus	NMNH 283134	Bolivia; Santa Cruz	Extant	0	Burmeister, 1863
	Chlamyphoridae	Proeutatus lagena †	YPM-PU 15613	Argentina; Santa Cruz formation	Santacrucian	17.5-16.3	Ameghino,
	Pampatheriinae	Vassallia maxima †	FMNH P14424	Argentina; Catamarca; Corral Quemado	Montehermosan	6.8-4.0	Castellanos, 1946
	Glyptodontinae	"Metopotoxus" anceps †	YPM-PU 15612	Argentina; Santa Cruz formation; Lago Pueyrredón	Santacrucian	17.5-16.3	Scott, 1903
	Glyptodontinae	Propalaehoplophorus minus †	AMNH 9197	Argentina; Santa Cruz formation; Corriguen Kaik	Santacrucian	17.5-16.3	Ameghino,
	Glyptodontinae	"Cochlops" debilis †	YPM-PU 15592	Argentina; Santa Cruz formation; Guer Aike	Santacrucian	17.5-16.3	Ameghino,
	Glyptodontinae	Eucinepeltus complicatus †	AMNH 9248	Argentina; Santa Cruz formation; Kilik Aike Norte	Santacrucian	17.5-16.3	Ameghino,
	Glyptodontinae	Glyptodon sp. †	MNHN PAM-759	Argentina; Buenos Aires	Pleistocene	3.0-0.011	Owen, 1839
	Glyptodontinae	Glyptodon sp. †	MNHN PAM-760	Argentina; Buenos Aires	Pleistocene	3.0-0.011	Owen, 1839

Table 2 .

 2 Data matrix with character scores for each genus. Character 1 and 7 are discrete and character 8 is continuous (see text). Symbols: -, not applicable; ?, missing data.

	Taxa	Character 1	Character 2	Character 3	Character 4	Character 5	Character 6	Character 7	Character 8
	Bradypus	1	1	0	0	2	0		3.66
	Tamandua	-	-	0	0	0	0		11.06
	Peltephilus †	1	0	0	1	2	1		-4.85
	Dasypus	0	2	1	1	0	1		17.73
	Stegotherium †	0	1	1	1	2	1		20.83
	Prozaedyus †	3	1	?	?	0	1		?
	Doellotatus †	2	0	?	?	?	1		8.08
	Euphractus	2	1	1	1	0	1		6.58
	Chaetophractus	2	1	1	1	0	1		3.96
	Zaedyus	3	1	1	1	0	1		1.67
	Chlamyphorus	3	0	1	2	2	1		18.29
	Calyptophractus	3	0	1	2	2	2		11.68
	Cabassous	0	1	1	1	0	1		8.57
	Tolypeutes	2	0	1	1	2	1		-1.04
	Priodontes	0	1	1	1	0	0		-2.11
	Proeutatus †	1	1	0	?	1	2		17.92
	Vassallia †	3	0	0	?	1	1		0.08
	Propalaehoplophorus †	3	0	0	?	1	2		18.56
	"Metopotoxus" †	3	0	0	?	1	2		19.45
	"Cochlops" †	3	0	0	2	1	2		21.2
	Eucinepeltus †	3	0	0	?	1	2		?
	Glyptodon †	3	0	0	2	2	2		35.84
	† extinct species.

3.1 Ontogenetic and static allometry in the skull and cranial units of nine- banded armadillos (Cingulata: Dasypodidae: Dasypus novemcinctus)

	ABSTRACT
	A large part of extant and past mammalian morphological diversity is related to variation
	in size through allometric effects. Previous studies suggested that craniofacial allometry is the
	dominant pattern underlying mammalian skull shape variation, but cranial allometries were rarely
	characterized within cranial units such as individual bones. Here, we used 3D geometric
	morphometric methods to study allometric patterns of the whole skull (global) and of cranial units
	(local) in a postnatal developmental series of nine-banded armadillos (Dasypus novemcinctus ssp.).
	« […] les patrons allométriques de la variation sont si répandus dans la nature qu'ils expliquent souvent
	des variations d'une ampleur surprenante, tant au sein des populations qu'entre les espèces. ».
	Hallgrímsson et al., 2019, Translated.
	"[…] allometric patterns of variation are so pervasive in nature, often accounting for surprising
	magnitudes of variation both within populations and among species.".
	Hallgrímsson et al., 2019.

Table 3 .

 3 Definition of external landmarks. * Suture exoccipital/supraoccipital marks by a bulge in adult.

	Number

Table 5 .

 5 Results of the multivariate regression for ES and 3B with log skull centroid size at the ontogenetic and static levels. Index: a, slope coefficient; Intercept; R², allometric proportion of shape variation; p-value, significance following the permutation test. The shaded lines correspond to the tests with a non-significant p-value (> 0.05).

					Log Skull Centroid Size
			Ontogenetic Level			Static Level
		a	intercept	R²	p-value	a	intercept	R²	p-value
	Entire Skull	0.2273	-2.8776	0.27618 0.0001	0.2307	-2.9312	0.06311 0.0001
	Premaxillary	2.6620	-6.7570	0.04242 0.0054	2.3270	-5.9140	0.00558 0.9774
	Maxillary	2.5780	-6.5430	0.10665 0.0001	3.2890	-8.3600	0.03148 0.1040
	Nasal	1.6900	-4.2890	0.08368 0.0004	1.4820	-3.7670	0.01127 0.6700
	Frontal	5.2690	-13.376	0.29873 0.0001	5.1750	-13.155	0.05965 0.0200
	Lacrimal	1.8680	-4.7420	0.01568 0.2802	2.4230	-6.1600	0.00429 0.9425
	Jugal	3.2730	-8.3090	0.06006 0.0015	3.7490	-9.5290	0.01476 0.5640
	Palatine	4.0190	-10.202	0.09004 0.0006	9.7290	-24.730	0.08829 0.0053
	Parietal	2.2530	-5.7180	0.06661 0.0005	5.1620	-13.121	0.06036 0.0120
	Squamosal	3.7480	-9.5130	0.11490 0.0001	4.6370	-11.787	0.03084 0.0875
	As-Os-Pt-Bs	3.8850	-9.8610	0.07351 0.0001	7.4030	-18.819	0.04347 0.0178
	Supraoccipital	3.5370	-8.9790	0.10031 0.0001	4.0930	-10.405	0.02223 0.3164
	Bo-Eo	4.7010	-11.933	0.19612 0.0001	4.0220	-10.223	0.02801 0.1756
	Petrosal	2.6430	-6.7100	0.06281 0.0001	5.5540	-14.119	0.04270 0.0242

Table 6 .

 6 Results of the multivariate regression for ES and 3B with log skull centroid size for each ontogenetic stage. Index: a, slope coefficient; Intercept; α*, angle of the slope with the horizontal axis in the common allometry analyses; R², allometric proportion of the shape variation; p-value, significance following the permutation test. The shaded lines correspond to the tests with a non-significant p-value (> 0.05).

	Log Skull Centroid Size

108

3.1.3.5 Size variation per OBU and allometry

Table 7 .

 7 Results of the multivariate regression for ES and 3B with log skull centroid size at the ontogenetic and static levels in Zaedyus pichiy. Index: a, slope coefficient; b, intercept; Df, degrees of freedom; F, Fisher-test; MS, mean square; N, sample size; P, p-value, significance following the permutation test; R², allometric proportion of shape variation; SS, sum of squares; Z, Z-test. The shaded lines correspond to the tests with a non-significant p-value (> 0.05).

	Zaedyus pichiy
	Ontogenetic level

162 Nasal 23 22 0.019532 0.0195324 0.2102 5.5891 2.1173 0.0129 0.722 -8.893 Frontal 23 22 0.022633 0.022633 0.20588 5.4445 3.0799 0.0006 0.7772 -9.5733 Lacrimal 23 22 0.021984 0.0219842 0.11079 2.6165 1.7958 0.0227 0.766 -9.435

	Jugal	23 22 0.008264 0.0082635 0.06704 1.5091 0.94584 0.1763 0.4696 -5.7847
	Palatine	23 22 0.01663	0.0166303 0.11519 2.734	1.4436 0.0768 0.6662 -8.2063
	Parietal	23 22 0.011271 0.0112708 0.1035 2.4245 1.4867 0.0651 0.5484 -6.7557
	Squamosal	23 22 0.019251 0.0192512 0.09987 2.3299 2.0271 0.0204 0.7168 -8.8292
	As-Os-Pt-BS	23 22 0.014352 0.0143518 0.08039 1.8357 1.4037 0.0677 0.6189 -7.6234
	Supraoccipital 23 22 0.016417	0.016417	0.0668 1.5032 0.90453 0.1862 0.6619 -8.1534
	Bo-Eo	23 22 0.016452 0.0164522 0.14644 3.6028 2.3628 0.0028 0.6626 -8.1622
	Petrosal	23 22 0.029284 0.0292841 0.13351 3.2356 2.7029 0.0034 0.884	-10.89

In the two Cabassous datasets

(Figures 34, 35

Table 8 .

 8 Results of the multivariate regression for ES and 3B with log skull centroid size at the ontogenetic and static levels in CabassousNS. Index: a, slope coefficient; b, intercept; Df, degrees of freedom; F, Fisher-test; MS, mean square; N, sample size; P, p-value, significance following the permutation test; R², allometric proportion of shape variation; SS, sum of squares; Z, Z-test. The shaded lines correspond to the tests with a non-significant p-value (> 0.05).

	CabassousNS
	Ontogenetic level

Table 9 .

 9 Results of the phylogenetic regression for ES and 3B with log skull centroid size at the evolutionary level in DatasetExt. Index: a, slope coefficient; b, intercept; Df, degrees of freedom; F, Fisher-test; MS, mean square; N, sample size; P, p-value, significance following the permutation test; R², allometric proportion of shape variation; SS, sum of squares; Z, Z-test. The shaded lines correspond to the tests with a non-significant p-value (> 0.05).

Table 10 .

 10 Results of the phylogenetic regression for ES and 3B with log skull centroid size at the evolutionary level in Dataset-Lmax.

										DatasetExt
					With phylogenetic correction							Without phylogenetic correction
		N Df	SS	MS	R2	F	Z	P	a	b	N Df	SS	MS	R2	F	Z	P	a	b
	Entire Skull	21 20 0.012966 0.0129665 0.20666 4.9493 3.4998 0.0008 0.0125	-0.1565	21 20 0.06719 0.067193 0.18719 4.3758 2.3742 0.0103 0.178 -2.23
	Premaxillary	21 20 0.013417 0.013417 0.05754 1.1601 0.52361 0.3174 0.004975 -0.062309	21 20 0.03762 0.037618 0.03958 0.7831 -0.061462 0.534 0.1332 -1.6684
	Maxillary	21 20 0.013333 0.013333 0.09742 2.0508 1.6793 0.0473 0.01592 -0.19942	21 20 0.11655 0.116552 0.11817 2.5462 1.5222 0.0799 0.2345 -2.9367
	Nasal	21 20 0.001726 0.0017261 0.02733 0.5339 -0.52278 0.7121 0.001522 -0.019059	21 20 0.03568 0.03568 0.09503 1.9952 1.1491 0.1286 0.1297 -1.6248
	Frontal	21 20 0.020507 0.0205066 0.19747 4.6751 3.0704 0.0015 0.01118 -0.14002	21 20 0.03434 0.034344 0.06611 1.345 0.74271 0.2274 0.1273 -1.5941
	Lacrimal	21 20 0.0134	0.013399 0.02891 0.5657 -0.38893 0.6506 0.01035 -0.12958	21 20 0.09487 0.094868 0.08821 1.8381 1.2101	0.099 0.2116 -2.6494
	Jugal	21 20 0.012809 0.012809 0.04824 0.963 0.26292 0.4016 -0.004458 0.055831	21 20 0.04307 0.04307 0.05601 1.1273 0.47204 0.3314 0.1425 -1.7852
	Palatine	21 20 0.039987 0.039987 0.15348 3.4449 1.684 0.0336 0.07202 -0.90192	21 20 0.41403 0.41403 0.18033 4.1801 1.7066 0.0346 0.442 -5.535
	Parietal	21 20 0.009333 0.0093328 0.08075 1.6691 1.0305 0.143 0.008161 -0.10221	21 20 0.04211 0.042113 0.08227 1.7032 1.0291 0.1552 0.141 -1.765
	Squamosal	21 20 0.019611 0.0196112 0.0967 2.0341 1.7482 0.0343 0.01313 -0.16444	21 20 0.07234 0.072343 0.077 1.585	1.0241 0.1572 0.1847 -2.3136
	As-Os-Pt-BS	21 20 0.03549 0.03549 0.09459 1.985 1.3125 0.097 0.04096 -0.51294	21 20 0.21793 0.217931 0.20222 4.8162 2.7289 0.0003 0.3206 -4.0156
	Supraoccipital	21 20 0.028419 0.0284194 0.16076 3.6395 2.6716 0.0005 0.0143	-0.1791	21 20 0.05192 0.05192 0.07333 1.5035 0.92309 0.1785 0.1565 -1.96
	Bo-Eo	21 20 0.011857 0.011857 0.13824 3.0479 2.2474 0.004 0.01094 -0.13696	21 20 0.035615 0.035615 0.17068 3.9104 2.7612 0.0003 0.1296 -1.6234
	Petrosal	21 20 0.021752 0.0217523 0.11375 2.4387 2.1206 0.0127 0.02388 -0.29912	21 20 0.13427 0.13427 0.14995 3.3518 2.1794 0.0119 0.2517 -3.152
		N Df	SS	MS	R2	F	Z	P	a	b	N Df	SS	MS	R2	F	Z	P	a	b
	Entire Skull	26 25 0

Index: a, slope coefficient; b, intercept; Df, degrees of freedom; F, Fisher-test; MS, mean square; N, sample size; P, p-value, significance following the permutation test; R², allometric proportion of shape variation; SS, sum of squares; Z, Z-test. The shaded lines correspond to the tests with a non-significant p-value (> 0.05).

.013565 0.0135651 0.16081 4.599 3.5601 0.0007 0.003741 -0.046893 26 25 0.12504 0.125037 0.16775 4.8375 2.7696 0.0029 0.1485 -1.8619

	Premaxillary	--	-	-	-	-	-	-	-	-	--	-	-	-	-	-	-	-	-
	Maxillary	26 25 0.01133 0.01133 0.06318 1.61186 1.1995 0.1159 0.02032 -0.25475	26 25 0.23169 0.231691 0.10632 2.8553 1.7249 0.0496 0.2022 -2.5345
	Nasal	--	-	-	-	-	-	-	-	-	--	-	-	-	-	-	-	-	-
	Frontal	26 25 0.013605 0.0136046 0.13871 3.8652 2.9501 0.0008 0.006618 -0.082961	26 25 0.15953 0.159526 0.17195 4.9839 2.6064 0.0044 0.1678 -2.1031
	Lacrimal	26 25 0.00985 0.0098514 0.0199 0.4872 -0.61769 0.7359 0.01483 -0.18589	26 25 0.15317 0.153172 0.08529 2.2379 1.4821 0.0558 0.1644 -2.0608
	Jugal

Table 11 .

 11 Summary of common allometric variations at different levels and in different datasets at the ES and 3B level as size increases (versus Log Skull Centroid Sizesee text).

Table 13 .

 13 Summary statistics of the standard major axis regression (SMA) for the pairs of correlated S-distances selected for description at the ontogenetic (*) and static level (**), common to the 3 species (= DZC) or between only Zaedyus and Cabassous (= ZC). Each distance is indicated by the landmarks (L) that define it. Results are shaded when they are below the threshold levels. The numbering of pairs follows the text and Figures45-48. *, ontogenetic level; **, static level.

	S-Distances

Table 14 .

 14 Summary statistics of the standard major axis regression (SMA) for the pairs of correlated log(R-distances) selected for description at the ontogenetic (*) and static level (**) for each species (and both Cabassous datasets). Each distance is indicated by the landmarks (L) that define it. The lower and upper limit of the slope are estimated with the construction of a confidence interval of 95%. The R 2 and the P-value are indicated but not discussed. The numbering of pairs follows the text and Figures45-48.

	R-Distances

  The numbering of pairs follows the text and Figures[45][46][47][48] inferior; L, landmark; Sup., superior.

								Evolutionary level -Dataset-Lmax
	Pair	Distance 1 (x)	Distance 2 (y)	S-Distances			R-Distances
	n°	L1	L2	L3	L4	R²	P-value	R²	P-value	Slope	Slope Inf. Slope Sup.
	1	42	66	69	97	0.4394 2.24E-04	0.9181 1.52E-14 0.8453	0.7496	0.9534
	2	63	97	100	114	0.8682 4.70E-12	0.9708 2.22E-16 1.0076	0.9377	1.0828
	3	65	92	106	112	0.8612 8.79E-12	0.9598 2.22E-16 0.9655	0.8874	1.0504
	4	38	80	50	92	0.8271 1.26E-10	0.9842 2.22E-16 1.0346	0.9813	1.0907
	5	50	94	21	108	0.8402 4.84E-11	0.9894 2.22E-16 1.0909	1.0447	1.1391
	6	19	78	29	90	0.9093 5.19E-14	0.9546 2.22E-16 1.0902	0.9967	1.1924
	7	21	97	48	98	0.7009 9.70E-08	0.9805 2.22E-16 1.0407	0.9814	1.1037
	8	60	66	97	112	0.4203 3.41E-04	0.8584 1.12E-11 0.7023	0.5998	0.8224
	9	94	97	66	114	0.0783	0.16601	0.7329 2.45E-08 1.0009	0.8064	1.2423
	10	19	21	17	48	0.7953 9.67E-10	0.9347 9.89E-16 0.8876	0.7972	0.9883
	11	19	60	29	92	0.8254 1.41E-10	0.9490 2.22E-16 0.7932	0.7213	0.8723
	12	19	23	30	38	0.3123 3.00E-04	0.6894 1.54E-07 0.7054	0.5590	0.8902

Table 16 .

 16 Summary of the potential relationships between the analyzed morphological characters (GW) and the patterns of integration found in cingulates. Characters concerning only the mandible are not added in this table (= 24/163 GW). * common to intraspecific and evolutionary levels; ** only found at the intraspecific or evolutionary level.

	Potential link with widespread patterns of integration*	Potential link with variably supported patterns of integration**	No link found	Not applicable with our landmark dataset

  Among the 36 specimens, 27 have a known geographical origin (see Appendices of Chapter 3 for the table and Figure SI.2). None are present in the geographical range of Cabassous chacoensis and none present its distinctive dental characters (see above). Four specimens originate from the area of Cabassous centralis. One specimen was collected in Colombia without more precision, which could correspond to the geographical areas of Cabassous centralis and Cabassous unicinctus. Most of the remaining 22 specimens are present in areas where Cabassous unicinctus occurs (Appendices of Chapter 3 for the table and Figure SI.2). 15 are distributed in the area containing only Cabassous unicinctus and seven are distributed in the overlapping geographic region between Cabassous unicinctus and Cabassous tatouay (Appendices of Chapter 3 for the table and Figure SI.2). Among them, seven specimens are large (i.e. > 100 mm), which is also the case for two specimens of unknown geographical origin. On this basis, we could hypothesize that the initial sampling includes nine Cabassous tatouay, four Cabassous centralis, and 15 Cabassous unicinctus. For the eight additional specimens, seven have unknown origins and one corresponds to the specimen collected in Colombia. There is some doubt about their taxonomic attribution between Cabassous centralis and Cabassous unicinctus.

	Figure SI.2. Summary map showing
	the geographical distribution of
	Cabassous specimens investigated in
	this study. In red, Cabassous tatouay;
	in orange, Cabassous centralis; in
	light green, Cabassous unicinctus
	from Cluster B (see below); in dark
	green, Cabassous unicinctus from
	Cluster C (see below). 1, northern
	Amazon corresponding to the
	geographical area of Cabassous
	unicinctus unicinctus. 2, southern
	Amazon corresponding to the
	geographical area of Cabassous
	unicinctus squamicaudis. Specimens
	reported with a white star denote the
	absence of geographical information
	besides the country of origin.

3

, digital data of 36 specimens identified as Cabassous unicinctus in 7 museum collections worldwide were acquired using X-ray micro-computed tomography (μCT) (see Appendices of Chapter 3 for the table), all of which were labelled as Cabassous unicinctus

  ; 273 mm in Zaedyus pichiy (see details[START_REF] Superina | Zaedyus pichiy (Cingulata: Dasypodidae)[END_REF]. The major difficulty therefore lies in differentiating between the two smaller species Chaetophractus vellerosus and Zaedyus pichiy. On the skull,[START_REF] Superina | Zaedyus pichiy (Cingulata: Dasypodidae)[END_REF], mentioned that these two species essentially differ by the presence (Chaetophractus vellerosus) or absence (Zaedyus pichiy) of a tooth on the premaxillary and a slight frontal depression present in Zaedyus pichiy. However, the presence of teeth on the premaxillary of Zaedyus pichiy has already been mentioned (e.g.,[START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF].[START_REF] Abba | Systematics of hairy armadillos and the taxonomic status of the Andean hairy armadillo (Chaetophractus nationi)[END_REF] added that the snout of Zaedyus pichiy is thinner and more elongated than that of Chaetophractus vellerosus. The geographical distribution also differs between the two species with a distribution in northern Argentina and Bolivia for Chaetophractus vellerosus and a more

southern Argentinean distribution for Zaedyus pichiy but with a small area of overlap in central Argentina

(Figure SI.3)

. In addition, Zaedyus pichiy includes two known subspecies, Zaedyus pichiy pichiy Desmarest, 1804 and Zaedyus pichiy caurinus

  Chapter 3 for the table). As size is not clearly diagnostic between Chaetophractus vellerosus and Zaedyus pichiy (see above), most of the a priori attributions are based on the geographical origin of the specimens. Unfortunately, only a reduced proportion of the sample has a known geographical origin (17/45). Among these, sixteen originate from the distributional area of Zaedyus pichiy, and one specimen from Bolivia, within the area of distribution of Chaetophractus

	Figure SI.4. Summary map showing the
	geographical distribution of potential
	Zaedyus specimens investigated in this
	study. In red, suspected Chaetophractus
	vellerosus; in light blue, Zaedyus from
	Cluster B (see below); in dark blue,
	Zaedyus from Cluster A (see below). 1,
	Mendoza province corresponding to the
	geographical area of Zaedyus pichiy
	caurinus. 2, southern part of Argentina
	corresponding to the geographical area
	of Zaedyus pichiy pichiy. Specimens
	reported with a star denote the absence
	of geographical information besides the
	country of origin.

vellerosus

(Figure SI.4)

. The analyses of skull shape were performed mainly to ensure that the specimens of unknown origin are Zaedyus pichiy and not Chaetophractus vellerosus (see below).

  Their ontogenetic stages are better discriminated, and the largest specimens have relatively high ossification scores(Figure SI.6). One specimen remains problematic because it is partially deteriorated at the basicranium level which leads to a decrease in the ossification index (see Appendices of Chapter 3 for the table). However, the detectable sutures and its size tend to consider this specimen as adult (Appendices of Chapter 3 for the table). Based on these observations, the sampling may consist 2 juveniles, 2 subadults and 5

adults of C. tatouay and of 3 juveniles, 8 subadults and 16 adults for the remaining Cabassous specimens. It is summarized in Table SI.1.

Table SI .

 SI

1. Summary of ontogenetic stage composition by groups (see text).

Table SI .

 SI 2. Statistical results of each permutational multivariate analysis of variance in Cabassous.

Table SI .

 SI 3. Statistical results of each permutational multivariate analysis of variance in Zaedyus. Each group is defined in Figure SI.9.

Table S1 .

 S1 List of adult specimens used for assessing the intraspecific variation in Dasypus, Zaedyus and Cabassous.

	Family/Clade	Species	Institutional number	Locality
	Dasypodinae	Dasypus novemcinctus	AMNH 255866	Bolivia, Beni, Cercado
	Dasypodinae	Dasypus novemcinctus	AMNH 211668	Bolivia, Beni, Cercado, ca. 23 kilometers west of San Javier
	Dasypodinae	Dasypus novemcinctus	AMNH 262658	Bolivia, Pando, Nicolas Suarez, 5 kilometers upstream from Cachuela
	Dasypodinae	Dasypus novemcinctus	AMNH 263287	Bolivia, Santa Cruz, Andres Ibanez, Ayacucho
	Dasypodinae	Dasypus novemcinctus	AMNH 205727	Uruguay, Lavalleja, Zapican, 12 kilometers west southwest of Zapican
	Euphractinae	Zaedyus pichiy	FMNH 23810	Argentina, Chubut
	Euphractinae	Zaedyus pichiy	AMNH 94327	Argentina, Chubut, Sarmiento, Colhue Huapi Lake
	Euphractinae	Zaedyus pichiy	MNHN 1883-158	Argentina, Santa Cruz
	Euphractinae	Zaedyus pichiy	ZMB 46103	South America, Argentina, Puero Jenkins, -47,75779, -65,90836
	Euphractinae	Zaedyus pichiy	ZMB 46104	South America, Argentina, Oso Marino, -47,9237, -65,83145
	Tolypeutinae	Cabassous unicinctus	MNHN 1999-1044	French Guiana
	Tolypeutinae	Cabassous unicinctus	MNHN 1998-2255	French Guiana, Petit-Saut
	Tolypeutinae	Cabassous unicinctus	AMNH 137196	South America, Brazil, Para, Tapajos River, Igarape Brabo
	Tolypeutinae	Cabassous unicinctus	AMNH 74113	South America, Peru, Loreto, Maynas
	Tolypeutinae	Cabassous unicinctus	MVZ 155192	Peru, Rio Cenepa

Table S2 .

 S2 Cranial measurements in mm for GSL, GSW, GSH, GDRH and Geometric mean, and in degree for IVI (see FigureS3). Symbol: ?, missing data.

	Species	GSL	GSW	GSH	GDRH	IVI	Geometric mean
	Bradypus tridactylus	75.67	49.15	42.92	13.79	3.66	54.25
	Tamandua tetradactyla	124.82	41.56	50.71	0	11.06	64.07
	Peltephilus pumilus †	93.9	49.04	42.17	22.76	-4.85	57.91
	Utaetus buccatus †	?	?	?	?	?	?
	Dasypus novemcinctus *	38.69	19.28	17.77	0.8	0.8	23.67
	Dasypus novemcinctus **	54.14	24.89	20.04	3.02	10.26	30.00
	Dasypus novemcinctus ***	79.36	33.52	26.28	4.61	10.18	41.19
	Dasypus novemcinctus ****	89.04	39.07	37.65	5.78	17.73	50.78
	Stegotherium tauberi †	138.9	49.29	46.11	3.05	20.83	68.09
	Prozaedyus †	66.71	30.45	29.34	7.16	?	39.06
	Euphractus sexcinctus	105.97	66.55	47.09	15.17	6.58	69.25
	Chaetophractus villosus	89.39	58.46	37.48	14.07	3.96	58.07
	Zaedyus pichiy *	29.31	18.31	13.86	0.55	?	19.52
	Zaedyus pichiy **	56.43	33.47	24.76	6.39	3.04	36.03
	Zaedyus pichiy ***	63.56	39.03	27.18	7.2	2.4	40.70
	Zaedyus pichiy ****	71.65	42.59	29.18	8.52	1.67	44.65
	Doellotatus sp. †	?	?	37.35	15.36	8.08	?
	Cabassous unicinctus **	69.94	40.62	35.69	8.24	16.79	46.63
	Cabassous unicinctus ***	77.96	38.79	34.72	6.19	12.85	47.17
	Cabassous unicinctus ****	87.41	47.09	37.78	9.53	8.57	53.77
	Tolypeutes matacus	69.16	31.89	28.95	8.46	-1.04	39.96
	Priodontes maximus	189.35	80.34	53.58	7.12	-2.11	93.41
	Chlamyphorus truncatus	36.56	24.3	20.41	6.35	18.29	26.27
	Calyptophractus retusus	42.86	27.38	23.41	8.22	11.68	30.17
	Proeutatus lagena †	110.98	61.64	50.89	17.86	17.92	70.35
	Vassallia maxima †	243.85	138.42	105.18	63.82	0.08	152.55
	"Metopotoxus" anceps †	138.22	98.17	76.17	38.95	19.45	101.11
	Propalaehoplophorus minus †	141.27	117.01	80.33	44.41	18.56	109.91
	"Cochlops" debilis †	145.82	102.54	89.25	45.64	21.2	110.10
	Eucinepeltus complicatus †	180.25	139.63	93.44	54.93	?	132.98
	Glyptodon sp. †	331.59	336.88	209.27	124.07	35.84	285.93

Table S10 .

 S10 Statistical results of the homogeneity of slope test between ontogenetic stages using the log skull centroid size (see FigureS20). A significant p-value (< 0.05unshaded line) implies that at least one of the groups has a different allometric trajectory from the others.HOS test between ontogenetic stages using Log Skull Centroid Size

														Log Skull Centroid Size
			Df		Juvenile (N = 10) RSS		SS		R²				F	Subadult (N = 15) Z	p-value					Adult (N = 51)
	Df Entire skull	SS	MS	R² 0.11318	F 0.0081105 Z	p-value	Df 0.046327	SS	MS 2.5081	R² 5.6213	F	Z 0.0001	p-value	Df	SS	MS	R²	F	Z	p-value
	Entire Skull Premaxillary 9	0.012341	0.0123409 0.88453 0.45026	6.5522 0.0377180 3.4243	0.0005	14 0.037934 0.011540 1.4925 0.0115404	0.34846 1.3684	6.9526 0.0849 4.2238	0.0002	50	0.005156	0.0051561	0.06311	3.3010	3.8848	0.0002
	Maxillary				0.29504	0.0197750		0.053459		2.3459	3.3933		0.0001
	Premaxillary	9	0.012367	0.0123670	0.07737	0.6709	-0.6599	0.7393	14	0.053930	0.0539300	0.25597	4.4723	2.6821	0.0016	50	0.003260	0.0032557	0.00558	0.2749	-2.0260	0.9774
	Nasal				0.16745	0.0043138		0.021381		0.9017	0.3639		0.3743
	Maxillary Frontal	9	0.014352	0.0143516 0.35370 0.29837	3.4020 0.0213300 2.6405	0.0053	14 0.038601 0.019914 2.1106 0.0199143	0.24496 2.8602	4.2175 0.0022 3.0692	0.0008	50	0.006498	0.0064982	0.03148	1.5928	1.2830	0.1040
	Nasal Lacrimal	9	0.007942	0.0079419 1.16630 0.21065	2.1350 0.1044800 1.1938	0.1068	14 0.078316 0.001262 3.1354 0.0012626	0.05470 2.2786	0.7523 0.0111 -0.1102	0.5587	50	0.001321	0.0013211	0.01127	0.5586	-0.3919	0.6700
	Frontal Jugal	9	0.038097	0.0380970 0.92418 0.50433	8.1396 0.0466330 2.9802	0.0005	14 0.043969 0.036748 1.7661 0.0367480	0.36966 1.5098	7.6237 0.0618 3.2273	0.0004	50	0.016091	0.0160908	0.05965	3.1082	2.1868	0.0200
	Palatine				0.83270	0.1219600		0.113540		5.1262	3.0572		0.0001
	Lacrimal	9	0.006499	0.0064990	0.04779	0.4015	-0.9360	0.8327	14	0.131630	0.1316320	0.37951	7.9511	0.0023	0.0023	50	0.003540	0.0035418	0.00429	0.2112	-1.5767	0.9425
	Parietal				0.36319	0.0356900		0.078882		3.4393	3.0782		0.0001
	Jugal Squamosal	9	0.022055	0.0220550 0.60170 0.14280	1.3327 0.0242220 0.6379	0.2647	14 0.033267 0.050156 1.4090 0.0501560	0.18160 1.8926	2.8846 0.0271 1.6142	0.0394	50	0.008480	0.0084764	0.01476	0.7341	-0.1278	0.5640
	Palatine As-Os-Pt-Bs 9	0.000801	0.0008009 1.05100 0.00776	0.0626 0.0396680 -2.5716	0.9931	14 0.032396 0.084873 1.3210 0.0848730	0.37248 1.4538	7.7166 0.0722 2.3607	0.0031	50	0.056860	0.0568620	0.08829	4.7450	2.1024	0.0053
	Parietal Supraoccipital 9	0.010730	0.0107300 0.63526 0.17248	1.6674 0.0214840 0.9414	0.1762	14 0.028882 0.025883 1.1837 0.0258828	0.29289 0.9168	5.3847 0.1822 2.6930	0.0014	50	0.016008	0.0160080	0.06036	3.1475	1.9868	0.0120
	Bo-Ex				0.48188	0.0119230		0.017738		0.8660	0.6395		0.2658
	Squamosal Petrosal	9	0.014418	0.0144170 0.58855 0.13981	1.3003 0.0202500 0.7748	0.2253	14 0.030539 0.033621 1.2042 0.0336210	0.23893 1.0264	4.0813 0.1520 3.2314	0.0006	50	0.012920	0.0129168	0.03084	1.5593	1.3391	0.0875
	As-Os-Pt-Bs	9	0.016600	0.016600	0.11073	0.9961	0.1391	0.4488	14	0.011670	0.0116700	0.05703	0.7862	-0.3946	0.6605	50	0.032930	0.0329280	0.04347	2.2269	2.0606	0.0178
	Supraoccipital	9	0.007747	0.0077470	0.08856	0.7774	-0.1792	0.5530	14	0.021395	0.0213948	0.15893	2.4564	1.7216	0.0421	50	0.010060	0.0100551	0.02223	1.1140	0.4710	0.3164
	Bo-Eo	9	0.019054	0.0190545	0.26473	2.8804	2.1222	0.0124	14	0.009230	0.0092305	0.09176	1.3133	0.7344	0.2475	50	0.009730	0.0097300	0.02801	1.4119	0.9354	0.1756
	Petrosal	9	0.019448	0.0194481	0.24980	2.6638	2.2019	0.0071	14	0.009377	0.0093770	0.07592	1.0680	0.3282	0.3881	50	0.018560	0.0185574	0.0427	2.1858	1.9228	0.0242

Table S11 .

 S11 List of Zaedyus and Cabassous specimens. The material studied is stored in the collections of the Muséum national d'Histoire naturelle (MNHN, collections Zoologie et Anatomie comparée, Mammifères et Oiseaux) in Paris (France), the Natural History Museum (NHM) in London (UK), the American Museum of Natural History (AMNH) in New York (USA), the Muséum d'Histoire Naturelle in Geneva (MHNG, Switzerland), Naturalis Biodiversity Center (NBC) in Leiden (Netherlands), the Field Museum of Natural History (FMNH) in Chicago (USA), the Museum für Naturkunde (MfN -ZMB) in Berlin (Germany), the Museum of Vertebrate Zoology (MVZ) in Berkeley (USA), and the Institut des Sciences de l'évolution (ISEM) in Montpellier.

	Institution	Museum-N°	Genus	species	Distribution
	AMNH	25668	Zaedyus	pichiy	Argentina, Santa Cruz, Corpen Aike, Chico River
	AMNH	17448	Zaedyus	pichiy	Argentina, Santa cruz, Corpen Aike, Chico River, 100 miles from coast
	AMNH	94327	Zaedyus	pichiy	Argentina, Chubut, Sarmiento, Colhue Huapi Lake
	AMNH	25667	Zaedyus	pichiy	Argentina, Santa Cruz, Corpen Aike, Chico River
	NHM	27-6-4-56	Zaedyus	pichiy	?
	NHM	90-2-20-7	Zaedyus	pichiy	?
	NHM	46-5-13-17	Zaedyus	pichiy	?
	NHM	99-8-5-10	Zaedyus	pichiy	?
	NHM	76-9-26-14	Zaedyus	pichiy	?
	NHM	22-11-23-1	Zaedyus	pichiy	?
	FMNH	23810	Zaedyus	pichiy	Argentina, Chubut
	FMNH	28506	Zaedyus	pichiy	Argentina, Santa Cruz, Paso Ibanez
	MHNG	1276.076	Zaedyus	pichiy	Argentina, Chubut, Fofo Cahuel
	MHNG	1627.053	Zaedyus	pichiy	Argentina, Chubut, Punta Ninfas
	MNHN	1917-135	Zaedyus	pichiy	?
	MNHN	2007-382	Zaedyus	pichiy	?
	MNHN	1897-446	Zaedyus	pichiy	?
	MNHN	1897-440	Zaedyus	pichiy	?
	MNHN	1883-158	Zaedyus	pichiy	Argentina, Santa Cruz
	MNHN	1897-445	Zaedyus	pichiy	?
	MNHN	1897-472	Zaedyus	pichiy	?
	MNHN	1897-456	Zaedyus	pichiy	?
	MNHN	1897-450	Zaedyus	pichiy	?
	MNHN	1897-468	Zaedyus	pichiy	?
	MNHN	1897-470	Zaedyus	pichiy	?
	MNHN	1897-447	Zaedyus	pichiy	?
	MNHN	1897-442	Zaedyus	pichiy	?
	MNHN	1897-449	Zaedyus	pichiy	?
	MNHN	1897-457	Zaedyus	pichiy	?
	MNHN	1897-454	Zaedyus	pichiy	?
	MNHN	1897-1268	Zaedyus	pichiy	Argentina, Barraca Blanca
	MNHN	1897-461	Zaedyus	pichiy	?
	MNHN	1897-452	Zaedyus	pichiy	?
	MNHN	1897-473	Zaedyus	pichiy	?
	MNHN	1971-1045	Zaedyus	pichiy	Chili, L.E. Peña
	MNHN	2007-369	Zaedyus	pichiy	?
	MNHN	2007-375	Zaedyus	pichiy	Argentina, Patagonia
	ZMB	49038	Zaedyus	pichiy	South America, Argentina, Oso Marino, -47,9237, -65,83145
	ZMB	46104	Zaedyus	pichiy	South America, Argentina, Oso Marino, -47,9237, -65,83145
	ZMB	85890	Zaedyus	pichiy	?
	ZMB	48627	Zaedyus	pichiy	South America, Argentina, Puero Jenkins, -47,75779, -65,90836
	ZMB	48626	Zaedyus	pichiy	?
	ZMB	46103	Zaedyus	pichiy	South America, Argentina, Puero Jenkins, -47,75779, -65,90836
	AMNH	133386	Cabassous	unicinctus (N)	South America, Brazil, Mato Grosso do Sul, Maracaju
	AMNH	133335	Cabassous	unicinctus (S)	Brazil, Mato Grosso do Sul, Maracaju
	AMNH	133336	Cabassous	unicinctus (S)	Brazil, Mato Grosso do Sul, Maracaju
	AMNH	37546	Cabassous	unicinctus (S)	South America, Brazil, Mato Grosso, Diamantino
	AMNH	14862	Cabassous	centralis	South America, Colombia, Magdalena, Santa Marta
	AMNH	137196	Cabassous	unicinctus (N)	South America, Brazil, Para, Tapajos River, Igarape Brabo
	AMNH	14863	Cabassous	centralis	South America, Colombia, Antioquia, Valparaiso
	AMNH	23441	Cabassous	centralis	South America, Colombia, Magdalena, Santa Marta
	AMNH	60636	Cabassous	centralis	South America, Venezuela, Zulia, Maracaibo
	AMNH	74113	Cabassous	unicinctus (N)	South America, Peru, Loreto, Maynas

Table S11 .

 S11 Continued.

	Institution	Museum-N°	Genus	species	Distribution
	AMNH	98459	Cabassous	unicinctus (N)	South America, Peru, Loreto, Maynas
	AMNH	133318	Cabassous	unicinctus (S)	South America, Brazil, Goias, Anapolis
	AMNH	133334	Cabassous	unicinctus (S)	South America, Brazil, Mato Grosso do Sul, Maracaju
	AMNH	136256	Cabassous	centralis or unicinctus (N)	Colombia
	NHM	3-7-12-2	Cabassous	centralis or unicinctus (N)	?
	NHM	7-6-15-9	Cabassous	centralis or unicinctus (N)	?
	NHM	16-6-5-36	Cabassous	centralis or unicinctus (N)	?
	NHM	71-2503	Cabassous	unicinctus (S)	264 km N of Xavantina, Mato Grosso, Brazil
	NHM	78-12-13-1	Cabassous	unicinctus (N)	Demerara, Guyana
	ISEM	V3455	Cabassous	centralis or unicinctus (N)	?
	MNHN	2007-374	Cabassous	centralis or unicinctus (N)	?
	MNHN	1953-457	Cabassous	centralis or unicinctus (N)	?
	MNHN	1998-2255	Cabassous	unicinctus (N)	Petit-Saut, Guyana
	MNHN	1917-159	Cabassous	centralis or unicinctus (N)	?
	MNHN	1999-1044	Cabassous	unicinctus (N)	French Guyane
	MVZ	155192	Cabassous	unicinctus (N)	Peru, Rio Cenepa
	NCB	26326B	Cabassous	unicinctus (N)	Suriname

Table S14 .

 S14 Landmark coordinates without treatment for new intra-and interspecific sample. CM, Central Morphotype; GM, Guianan Morphotype; NM, Northern Morphotype; SM, Southern Morphotype. †, extinct species. Available on the HAL open archive portal.

Table S15 .

 S15 Comparison of the number of landmarks between each dataset for the entire skull and each cranial unit (see also Table3). In red, too low landmark number or not well distributed over the cranial unit -no analysis on the OBU (see Materiel & Methods -Section 3.2).

			Landmark Number
	ES/OBU	Section 3.1	Zaedyus/Cabassous/DatasetExt	Dataset-Lmax	Dataset-Tmax
	Entire Skull	131	114	100	90
	Premaxillary	9	8	4
	Maxillary	13	13	12	10
	Nasal	5	5	4
	Frontal	10	9	9
	Lacrimal	5	5	5
	Jugal	5	5	3
	Palatine	4	4	3
	Parietal	5	5	5
	Squamosal	12	8	6
	As-Os-Pt-BS	10	7	7
	Supraoccipital	7	7	7
	Bo-Eo	7	6	5
	Petrosal	10	10	10

Table S16 .

 S16 Landmark composition of each OBU for interspecific datasets. Green, present; Red, absent. *, internal landmark; **, amended definition for interspecific datasets. The modifications were made because the last tooth in Dasypus was not always present and the minimum interorbital length was confused with postorbital constriction (see Table3). Available on the HAL open archive portal.

Table S17 .

 S17 List of landmarks placed on each Zaedyus and Cabassous specimens, with a precision on the estimated landmarks (in red by TPS; in orange by symmetrization) (see Material & Methods -Section 3.2). Available on the HAL open archive portal.

Table S18 .

 S18 List of landmarks placed on specimens for evolutionary analyses, with a precision on the estimated landmarks (in red not estimated because the specimens are too distant morphologically; in orange by symmetrization) (see Material & Methods -Section 3.2). CM, Central Morphotype; GM, Guianan Morphotype; NM, Northern Morphotype; SM, Southern Morphotype. †, extinct species. Available on the HAL open archive portal.

Table S19 .

 S19 Ontogenetic table with the ossification score, the dental score and LTC for Zaedyus and Cabassous specimens. Available on the HAL open archive portal.

Table S20 .

 S20 Results of the multivariate regression for ES and 3B with log skull centroid size at the ontogenetic and static levels in CabassousN. Index: a, slope coefficient; Intercept; R², allometric proportion of shape variation; p-value, significance following the permutation test. The shaded lines correspond to the tests with a non-significant pvalue (> 0.05).

Table S21 .

 S21 Results of the multivariate regression for ES and 3B with log skull centroid size at the evolutionary level in Dataset-Tmax. Index: a, slope coefficient; Intercept; R², allometric proportion of shape variation; p-value, significance following the permutation test. The shaded lines correspond to the tests with a non-significant p-value (> 0.05).

		N Df	SS	MS	R2	F	Z	P	a	b	N Df	SS	MS	R2	F	Z	P	a	b
	Entire Skull	21 20 0.004021 0.0040208 0.08798 1.833 2.3369 0.0131 0.251 -3.128	14 13 0.0030862 0.0030862 0.10763 1.4473 1.4068 0.0859 0.2501 -3.1207
	Premaxillary 21 20 0.02856 0.02856 0.08014 1.6553 1.0793 0.1438 0.6689 -8.3377	14 13 0.029611 0.029611 0.12225 1.6713 1.0101 0.1665 0.7746 -9.6663
	Maxillary	21 20 0.008393 0.0083927 0.07057 1.4425 1.0897 0.1371 0.3626 -4.5198	14 13 0.005318 0.0053176 0.07025 0.9067 -0.030925 0.5236 0.3282 -4.0963
	Nasal	21 20 0.008648 0.0086475 0.10084 2.1307 1.3423 0.0967 0.3681 -4.5879	14 13 0.013845 0.0138445 0.26438 4.3128 2.1081 0.0211 0.5296 -6.6096
	Frontal	21 20 0.012914 0.0129135 0.11924 2.5723 2.1635 0.0103 0.4498 -5.6065	14 13 0.007022 0.0070217 0.11652 1.5827 1.1544 0.1225 0.3772 -4.7071
	Lacrimal	21 20 0.02541 0.025406 0.05663 1.1405 0.47507 0.3319 0.6309 -7.8638	14 13 0.019096 0.019096 0.07463 0.9678 0.25322 0.4177 0.622 -7.763
	Jugal	21 20 0.027921 0.0279207 0.16691 3.8066 2.3979 0.0027 0.6614 -8.2438	14 13 0.020704 0.0207045 0.18429 2.7111 1.8066 0.0224 0.6477 -8.0829
	Palatine	21 20 0.026266 0.026266 0.11466 2.4606 1.3753 0.0699 0.6415 -7.9958	14 13 0.025141 0.025141 0.15672 2.2302 1.2338 0.1031 0.7137 -8.9069
	Parietal	21 20 0.015113 0.0151128 0.11705 2.5188 1.6261 0.04 0.4866 -6.0651	14 13 0.011179 0.0111786 0.13004 1.7937 1.0874 0.1368 0.4759 -5.9392
	Squamosal	21 20 0.031691 0.031691 0.13255 2.9032 2.2681 0.0129 0.7046 -8.7828	14 13 0.020563 0.020563 0.13552 1.8812	1.359	0.0852 0.6455 -8.0552
	As-Os-Pt-BS

21 20 0.07721 0.077212 0.22588 5.5439 3.1506 0.0001 0.4383 -13.71 14 13 0.061909 0.061909 0.28863 4.8689 2.7324 0.0016 1.12 -13.98

  Supraoccipital 21 20 0.021318 0.021318 0.09282 1.9441 1.3838 0.078 0.5779 -7.2035 14 13 0.017234 0.017234 0.10819 1.4557 0.85002 0.21 0.5909 -7.3744 Bo-Eo 21 20 0.005677 0.0056768 0.05865 1.1838 0.54565 0.3058 0.2982 -3.7172 14 13 0.007925 0.0079248 0.11736 1.5955 1.1186 0.1247 0.4007 -5.0007 Petrosal 21

20 0.025862 0.0258623 0.15028 3.3603 2.9825 0.0004 0.6365 -7.9341 14 13 0.026571 0.0265709 0.22036 3.3917 3.0227 0.0002 0.7337 -9.1567

										Cabassous N
					Ontogenetic level								Static level
		N Df	SS	MS	R2	F	Z	P	a	b	N Df	SS	MS	R2	F	Z	P	a	b
	Entire Skull	27 26 0

.014259 0.0142593 0.13619 3.9414 3.5213 0.0001 0.002118 -0.026173 27 26 0.15314 0.153141 0.1721 5.197 3.2209 0.0003 0.1626 -2.0093

	Premaxillary	--	-	-	-	-	-	-	-	-	--	-	-	-	-	-	-	-	-
	Maxillary	27 26 0.015518 0.0155176 0.06229 1.6608 1.1795 0.1227 0.0142	-0.1755	27 26 0.23186 0.231861 0.09483 2.6192 1.6938 0.05217 0.2001 -2.4724
	Nasal	--	-	-	-	-	-	-	-	-	--	-	-	-	-	-	-	-	-
	Frontal	27 26 0.015061 0.0150609 0.11761 3.3323 2.6231 0.0063 0.02483	-0.30682	27 26 0.31208 0.312077 0.24034 7.9095 3.3207 0.0002 0.2321 -2.8683
	Lacrimal	27 26 0.00882 0.0088156 0.01769 0.4502 -0.72294 0.7698 0.01545	-0.19095	27 26 0.17115 0.171152 0.09355 2.5801 1.6994 0.0314 0.1719 -2.1242
	Jugal	--	-	-	-	-	-	-	-	-	--	-	-	-	-	-	-	-	-
	Palatine	--	-	-	-	-	-	-	-	-	--	-	-	-	-	-	-	-	-
	Parietal	27 26 0.007496 0.0074962 0.05912 1.5708 0.94073 0.1717 0.003698 -0.04569	27 26 0.15401 0.154014 0.19621 6.1026 2.8276 0.0005 0.1631 -2.015
	Squamosal	27 26 0.015233 0.0152327 0.06286 1.6769 1.0003 0.1639 0.01403	-0.17332	27 26 0.13928 0.139276 0.10497 2.932 1.7968 0.0251 0.1551 -1.9162
	As-Os-Pt-BS	27 26 0.0442 0.044205 0.10411 2.9052 1.9533 0.0289 -0.00425	0.05251	27 26 0.4001 0.4001 0.20198 6.3275 3.3434 0.0002 0.2629 -0.32478
	Supraoccipital	27 26 0.022044 0.022044 0.1138 3.2102 2.4608 0.0025 -0.00446	0.05511	27 26 0.12583 0.125828 0.11033 3,1002 2.1818 0.0104 0.1474 -1.8213
	Bo-Eo	27 26 0

.018599 0.018599 0.19149 5.9213 3.0963 0.0001 0.004096 -0.050605 27 26 0.15271 0.152708 0.32225 11,887 3.7057 0.0001 0.1624 -2.0065 Petrosal 27 26 0.031344 0.0313443 0.13179 3.795 3.0261 0.0002 0.0007881 -0.0097381 27 26 0.4008 0.4008 0.21758 6,9519 3.1092 0.0002 0.2631 -3.2506

	Dataset-Tmax
	With phylogenetic correction	Without phylogenetic correction

Table S30 .

 S30 Assignment of each landmark to each module for each species at each level (i.e., ontogenetic and static) and calculation of the percentage assignment of a landmark to a module for each level (i.e., ontogenetic and static) as a result of concatenation between each species. In red, anterior-face or face module; in purple, mid-face module; in green, orbit-neurocranium module; in blue, vault-basicranium module. Available on the HAL open archive portal.

Table S31 .

 S31 Taxonomic composition of each dataset. CM, Central Morphotype; GM, Guianan Morphotype; NM, Northern Morphotype; SM, Southern Morphotype. † extinct species. Available on the HAL open archive portal.

Table S32 .

 S32 Landmark composition of each dataset. CM, Central Morphotype; GM, Guianan Morphotype; NM, Northern Morphotype; SM, Southern Morphotype. † extinct species. Available on the HAL open archive portal.

Table S33 .

 S33 Landmark coordinates of Propalaehoplophorus minus, "Cochlops" debilis and Eucinepeltus complicatus. † extinct species. Available on the HAL open archive portal. Table S34. List of landmarks placed of Propalaehoplophorus minus, "Cochlops" debilis and Eucinepeltus complicatus, with a precision on the estimated landmarks (in orange by symmetrization; red, deleted landmarks). Available on the HAL open archive portal.

† extinct species; * perinatal stage; ** juvenile; *** subadult; **** adult.

25 0.13618 0.13618 0.17817 5.2032 2.5905 0.0014 0.155 -1.943 Squamosal

If growing at the same pace, smaller distances will be found to increase faster than larger distances when standardized using the skull size.

Figure 49. SMA plot of S-distances pairs selected (see Material & Methods) for the evolutionary level.

[START_REF] Gaudin | The phylogeny of living and extinct armadillos (Mammalia, Xenarthra, Cingulata): a craniodental analysis[END_REF] but also Fariña & Vizcaíno, 2001). In particular, strong morphological changes are observed in these regions in fossil forms such as glyptodonts[START_REF] Scott | Mammalia of the Santa Cruz beds. I. Edentata[END_REF] Figures 50 & 51), some of which may related to the selected pairs (see below).

Many of the specimens were sent as scans or they were sent by mail for me to scan them. As a result, we were not able to do any verification before scanning them. This constraint also concerns the sampling of Zaedyus pichiy.

Figure S39. SMA plot of log(R-distances) pairs selected (see Material & Methods) for the evolutionary level.

La variation morphologique est un phénomène complexe dont l'utilisation dans les analyses phylogénétiques est souvent critiquée. De nombreuses études ont appelé à une exploration plus large des modèles de variation morphologique et à une meilleure identification de la covariation entre les traits pour améliorer les phylogénies morphologiques. Les cingulés représentent un cas d'étude idéale pour cet objectif car ils illustrent un cas typique de conflit entre les reconstructions phylogénétiques morphologiques et moléculaires, en particulier pour l'origine des glyptodontes (éteints). Dans ce travail, nous mettons d'abord en évidence cette incongruence et soulignons les lacunes existantes concernant notre connaissance de l'anatomie crânienne interne et des patrons d'intégration sur le crâne des cingulés. L'exploration de ces deux aspects est pertinente pour l'enrichissement des matrices morphologiques et pour une meilleure compréhension des covariations existantes entre les caractères, qui peuvent induire en erreur les phylogénies morphologiques. Notre travail commence par une étude approfondie de l'anatomie interne du crâne (axée sur certains canaux et cavités liés à la vascularisation et l'innervation crânienne, ou à l'insertion de dents) dans un échantillon diversifié de Cingulata. Nous reconstruisons provisoirement les scénarios évolutifs de huit traits sélectionnés sur ces structures. Ceux-ci suggèrent une plus grande ressemblance des glyptodontes avec les pampatheres, le genre Proeutatus et/ou avec les chlamyphorines, ce qui est en partie congruent avec les phylogénies moléculaires. Ensuite, nous explorons les patrons d'intégrations crâniens au sein de plusieurs espèces de tatous actuels et nous testons si les modèles trouvés au niveau intraspécifique sont également soutenus au niveau évolutif, c'est-à-dire entre les espèces, en utilisant un riche échantillon de cingulés actuels et éteints. Nous nous concentrons d'abord sur l'un des facteurs d'intégration les plus puissants connus chez les mammifères -l'allométrie -afin de cibler les patrons de covariations crâniens liés à la variation de taille. Notre analyse de l'allométrie crânienne nous a permis de mettre en évidence plusieurs patrons allométriques crâniens très répandus chez les cingulés. Les patrons allométriques détectés les plus forts correspondent à l'allométrie crânio-faciale (une face relativement longue pour les crânes de grandes tailles), mais des patrons allométriques forts et étendus ont également été détectés pour la constriction postorbitale, l'arc zygomatique, les crêtes nucales, le processus mastoïdien du pétreux, le toit crânien et le foramen magnum. Ensuite, nous effectuons une exploration sélective de paires de distances fortement covariantes dans les mêmes échantillons, ce qui nous permet de mettre en évidence d'autres fortes corrélations crâniennes. Les corrélations supportées tant au niveau intraspécifique qu'au niveau évolutif concernent notamment la racine antérieure de l'arc zygomatique, une région particulièrement riche en insertions musculaires. Puis, nous présentons la toute première exploration de la modularité crânienne des cingulés au niveau intraspécifique qui révèle une partition de l'intégration en trois modules répartis antéro-postérieurement sur le crâne. Nos résultats sont enfin comparés aux matrices morphologiques existantes et aux hypothèses phylogénétiques. Bien qu'elle laisse entrevoir une révision nécessaire de plusieurs caractères, la comparaison des patrons d'intégrations détectés avec les matrices morphologiques s'avère difficile. Cela souligne la nécessité d'explorer davantage des stratégies de codage alternatives pour une meilleure évaluation de la covariation et de l'allométrie parmi les caractères notés et pour une amélioration globale de nos constructions de caractères.

Acknowledgements

3D Cranial Shape Variation in Cingulata

ABSTRACT

Morphological variation impacts the shape in different coordinated manners. 3D geometric morphometrics (GMM) is a widely used method that allows quantification of shape differences between objects using landmark coordinates. A few studies have quantified variations in skull shape in cingulates, but never on the whole diversity within the clade using 3D coordinates. This kind of study is desirable to document variations in cranial shape at the evolutionary level in the group, and to uncover a wider range of potential covariations. We investigate the cranial shape diversity of cingulate species with 3D GMM using Principal Component Analysis. We explore seven evolutionary datasets incorporating a large diversity of extant and fossil cingulates. These seven datasets correspond to analyses on the entire skull and on the modules defined in the preceding section. The detected variations in shape are reminiscent of several allometric variations detected in previous sections of this thesis, but also demonstrate additional shape changes that occurred in the group.

APPENDICES

Only the skull length and ossification index will be used for these genera. [START_REF] Hubbe | A case study of extant and extinct Xenarthra cranium covariance structure: implications and applications to paleontology[END_REF] propose to consider as adult specimens only those xenarthran specimens (including almost all cingulate genera) in which both the supraoccipital-exoccipital and basioccipital-exoccipital contact are completely closed. They add that the basioccipital-basisphenoid suture is fused in their sample. Accordingly, we consider as strictly adult, specimens having these three bony contacts completely fused if these are consistent with the length of their skull. Their criteria work relatively well with our ossification index. (see results). Conversely, a specimen with completely unfused supraoccipital-exoccipital contact will be considered juvenile (for other more precision on timing of cranial suture closure refer to Rager et al., 2013). Consequently, the degrees of intermediate ossification correspond to subadult stages. The skull length (see Section 3.1) and ossification index for each specimen in Cabassous and Zaedyus datasets are available in Appendices of Chapter 3 for the table.

3.2

Quantification and processing

Refer to Section 3.2.

Principal Component Analysis (PCA)

Once the data was processed, we performed a principal component analysis of shape variation to determine how our specimens are distributed in the morphospace of each dataset (Dryden & Mardia, 1998). Our aim is to quickly identify if there are one or more shape clusters on PC1 and PC2 in our sample and then perform more specific analyses. This analysis was performed using the plotTangentspace function in the geomorph R package.

Permutational Multivariate Analysis of Variance

After the principal component analysis, we extracted the matrix scores of the principal components in order to analyze the variance of the selected groups. With Euclidean distances, the permutational multivariate analysis of variance enables the partition of sums of squares using dissimilarities (e.g., [START_REF] Plateau | Birds have peramorphic skulls, too: anatomical network analyses reveal oppositional heterochronies in avian skull evolution[END_REF]. Using a random permutation (= 10 000), the analysis allows to define if the shape variation of two groups is significantly different (p-value < 0.05) or not. This test is similar to a MANOVA and allows us to test the pairwise distinction of groups within the same principal a statistical difference between specimens of known or unknown origin and between specimens originating from the distributional areas of Cabassous centralis or Cabassous unicinctus.

Supporting Information 2: Matrix and Analytical Parameters

For de description of each characters and the previous coded taxa see [START_REF] Billet | Oldest cingulate skulls provide congruence between morphological and molecular scenarios of armadillo evolution[END_REF].

Parameters:

Supporting Information 3: Determination of Ontogenetic Stages.

To perform analyses at the ontogenetic level and then at a static level, it is necessary to determine as precisely as possible the relative ontogenetic stage of each specimen.

Material and methods

PROTOCOL

The determination of the developmental stage of each specimen is based on dental eruption, cranial ossification, and cranial length. Except for size, these variables are each composed of various discrete observations scored numerically (see below). The scored observations are then averaged and compiled in a dental eruption index or a cranial ossification index. The observations on dental eruption were made on CT-images and on 3D reconstructions of the skulls and correspond to the number, the class, and the generation of the teeth (deciduous premolar, dPM; permanent premolar, PM; molar, M). The genus Dasypus is the only known xenarthran taxon that retains two functional generations of teeth [START_REF] Ciancio | Evolutionary implications of dental eruption in Dasypus (Xenarthra)[END_REF]. The adult upper toothrow of D. novemcinctus is composed of seven premolars and one molar. The use of CT-images was critical as it permitted to detect the presence of forming tooth buds in crypts. Based on our observations of the upper dentition, we defined five dental stages: (1) dPMs starting to mineralize or erupting;

(2) all dPMs well mineralized, possibly all erupted, no PM in the crypts (i.e., PM not mineralized); (3) all dPMs erupted, with part of the PMs mineralized but still in the crypts (not yet reaching the alveoli); (4) part of the dPMs about to be replaced by PMs (one or several PMs has/have erupted through the alveoli, but remain(s) almost unworn); [START_REF]25} Om<-diag(0,p) Om[row(Om)>col(Om)]<-omega; Om<-t(Om) Om[row(Om)[END_REF] all PMs erupted and no remain of dPMs left (Figure S12). As only one premolar generation was present in stages ( 2) and ( 5), we considered three measurements on the fourth premolar locus (the most represented tooth in our sampling) to discriminate between these stages: total height of the tooth, height of the alveoli, and height of the growth front (Figure S13; Table S6). We then plotted each of these variables relative to the length of the skull (LTC; see below) to delineate graphically the stages ( 2) and ( 5) (Figure S13). Cranial ossification was characterized based on suture closures (0: not in contact, 1: unfused, 2: partly fused, 3: fused). Only bones whose suture closure varies along our ontogenetic series were scored. Seven sutures were then scored, and the mean of these scores was computed to give the

Supporting Information 4: allometric variation at the static level

The variations described correspond to cases where the allometric variation is different from the variation described in the main text (ontogenetic level).

Alisphenoid-Orbitosphenoid-Pterygoid-Basisphenoid complex (Figure S19.A1-A3)

Most of the allometric static variation is concentrated on the lateral edge of the bone complex. As the size increases, the entoglenoid process is more massive (#77). The most posteroventral point of the suture between the alisphenoid and squamosal is relatively more ventral (#72). The pterygoid wing is longer and oriented more laterally (#66). Otherwise, we found the same variation than at the ontogenetic level for the sphenorbital fissure (#48); the dorsal transverse ridge delimiting the ethmoidal fossa anteriorly (#130) and the contact between frontal, squamosal and alisphenoid (#44). There is no major difference when using the log centroid size of the OBU.

Frontal (Figure S19.B1-B3)

Two trends can be noted. The first corresponds to a homogeneous anterior extension of the frontal (landmarks #2; #34). The second corresponds to a relative reduction in the proportions of the rest of the structure when the size increases (= frontal parts posterior to the postorbital constriction) (#36, #38, #42; #44, #78, #81, #113, #131). This is a trend already obtained at the ontogenetic level, except that at the static level the intensity of the shape variation is practically the same for all the landmarks. There is no difference using the log centroid size of the bone at this level.

Palatine (Figure S19.C1-C3)

The allometric variation at this level is similar to the one obtained for the ontogenetic level, except for the two lateral landmarks (#21; #46) which only mark a reduction lateromedial of the bone width when size increase. As difference with the ontogenetic level, the same differences observed between the analyses with different centroid sizes are observed except that the intensity of the variations is much lower. With the log centroid size of the bone, we observe the same variation but with higher intensities.

ABSTRACT Extended Abstract:

Morphological variation is a pervasive phenomenon, which has long inspired naturalists and led them to propose classifications of organisms based on observed similarities and differences. However, the more we examine morphological variation, the more we discover its extreme complexity. In recent decades, the use of morphological variation as a source of characters for phylogenetic analyses has been strongly questioned despite the primacy of these data for the study of extinct taxa inaccessible to molecular analyses. The prime importance of morphological data for reconstructing relationships of extinct forms is hampered by critical assessments of its performance, particularly for analyses within placental mammals. This observation is in line with the fact that many studies have called for an improvement of our phylogenetic methods using morphology, especially for broader exploration of patterns of morphological variation and a better identification of the covariation among traits.

Cingulates are a group of placental mammals that belong to the superorder Xenarthra together with anteaters and sloths. The Cingulata includes the extant armadillos and extinct taxa such as glyptodonts. This clade represents an ideal case study for the exploration of morphological variation in a phylogenetic context. Their modest extant diversity permits a detailed exploration of the entire group, while their past diversity, showing cranial shapes very unusual in mammals, offers a wide range of investigations. The major interest of this group for the subject treated in the present work lies in the lack of congruence between phylogenetic analyses using morphological or molecular data. In this work, we first highlight the lack of consensus between these hypotheses and point out the existing gaps in our morphological knowledge of the group, more specifically concerning the internal cranial anatomy and the integration patterns (= tendency of traits to covary) on the skull. We show that an exploration of these two aspects will be useful to complete morphological matrices but also to better understand the existing covariations among several anatomical structures and characters that can mislead morphological phylogenetics.

Our work starts with an in-depth study of the internal anatomy of the skull in a diverse sample of Cingulata, assuming that these poorly known structures can deliver new phylogenetic information. The virtual 3D reconstruction (using X-ray microtomography) of selected canals and cavities related to cranial vascularization, innervation or tooth insertion allowed us to compare the locations, trajectories and shape of these structures and to discuss their potential interest for cingulate systematics. We tentatively reconstructed evolutionary scenarios for eight selected traits on these structures, which often showed a greater resemblance of glyptodonts with pampatheres, with the genus Proeutatus and/or with chlamyphorines. This latter aspect was partly congruent with recent molecular hypotheses, but more research is needed on these resemblances and on the potential effects of development and allometry on the observed variations. Overall, these comparisons enable us to highlight new anatomical variation that may be of great interest to further explore the evolutionary history of cingulates and the origins of glyptodonts on a morphological basis.

Then, our work explores patterns of morphological integration on the skull of cingulates in two steps. We first focus on one of the most powerful integration factors known in mammals -allometry -in order to target cranial covariation patterns related to size variation. Our work on this aspect starts with an exploratory approach on one of the best sampled cingulate species, the nine-banded armadillo. It enables us to identify allometric patterns in this species at two scales -the entire skull and cranial units -and at two levels of integration -the static and ontogenetic levels. Based on this exploratory study, we test with the same approach the existence of similar allometric patterns in two other extant and distantly related species of cingulates (in the genera Cabassous and Zaedyus). All these patterns are then compared to an evolutionary analysis of allometry gathering most extant cingulate species and most of the emblematic fossil groups (with a focus on glyptodonts). This comparison makes it possible to determine if certain allometric patterns detected at the species level were at play during the evolution of cingulates. It highlights several covariations between the size and shape of the skull that seem to be present across the whole group.One of the strongest allometric patterns detected corresponds to the craniofacial allometry, i.e., a more elongated face in larger crania, which is already well known in mammals. In addition, strong and widespread allometric changes were also detected for the postorbital constriction, the zygomatic arch, the nuchal crests, the mastoid process of the petrosal, the cranial roof or the foramen magnum.

The second step on morphological integration corresponds to an in-depth study of the strongest covariations within cranial linear distances in the three species of armadillos initially sampled for allometry. Our selective exploration of pairs of covarying distances highlight additional strong cranial correlations not detected in our previous

Abstract:

Morphological variation is a complex phenomenon whose use in phylogenetic analyses is often criticized. Many studies have called for a broader exploration of patterns of morphological variation and a better identification of the covariation among traits to improve morphological phylogenetics. Cingulates represent an ideal case study for this objective since they illustrate a typical case of conflict between morphological and molecular phylogenetic reconstructions, especially for the origins of the extinct glyptodonts. In this work, we first highlight this incongruence and point out the existing gaps concerning our knowledge of the internal cranial anatomy and the patterns of integration on the skull of cingulates. An exploration of these two aspects is relevant to the enrichment of morphological matrices and to a better understanding of the existing covariations among characters, which can mislead morphological phylogenetics. Our work starts with an in-depth study of the internal anatomy of the skull (focused on selected canals and cavities related to cranial vascularization, innervation or tooth insertion) in a diverse sample of Cingulata. We tentatively reconstruct the evolutionary scenarios of eight selected traits on these structures. These suggest a greater resemblance of glyptodonts with pampatheres, with the genus Proeutatus and/or with chlamyphorines, which is partly congruent with molecular phylogenies. Then, we explore patterns of cranial integration within several species of extant armadillos and test if the patterns found at the instrapecific level are also supported at the evolutionary level, i.e., among species, using a rich sample of extant and extinct cingulates. We first focus on one of the most powerful integration factors known in mammals -allometry -in order to target cranial covariation patterns related to size variation. Our analysis of cranial allometry enabled us to highlight several cranial allometric patterns that are widespread in cingulates. One of the strongest allometric patterns detected corresponds to the craniofacial allometry (relatively long face in large crania), but strong and widespread allometric changes were also detected for the postorbital constriction, the zygomatic arch, the nuchal crests, the mastoid process of the petrosal, the cranial roof and the foramen magnum. Second, we perform a selective exploration of pairs of strongly covarying distances in the same samples which enable us to highlight additional strong cranial correlations. The correlations supported at both the intraspecific and evolutionary levels concern in particular the anterior root of zygomatic arch, a region particularly rich in muscular insertions. Third, we present the very first exploration of cranial modularity in cingulates at the intraspecific level that reveals a partitioning of the integration into three anteroposteriorly distributed modules on the skull. Our results are finally compared with existing morphological matrices and phylogenetic hypotheses. Although it hints at a necessary revision of several characters, the comparison of the detected patterns of integration with morphological matrices proves difficult. This highlights the necessity to further explore alternative coding strategies for a better evaluation of the covariation and allometry among scored characters and for an overall improvement of our character constructions.

Résumé :