Sélim Natahi
email: selim.natahi@gmail.com

Michael Coquerelle

Véronique Darras

Brigitte Faugère

Fisher T Christopher

Grégory Pereira

Priscilla Bayle

Christopher T Fisher

El_Openo_Sep5_Ind18 El

Opeño Jacona-Zamora Valley

Evaluating the efficiency of isolated calvaria bones shape changes in the identification and differentiation of artificial cranial modification techniques among pre-Hispanic west Mesoamerican populations

Keywords: Artificial cranial modification, isolated calvaria bones, 3D geometric morphometrics, Mesoamerican Archaeology Id Site Region Age ACM type Period JR24_sep1 JR24 Acámbaro Valley Adult Tabular Oblique Late Formative

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

• In Mesoamerican archaeology, identifying and characterizing artificial cranial modifications is of great value as they can provide valuable information about the social and/or cultural identity of an individual.

• The state of preservation of the bone occasionally limits the possibility of diagnosing and differentiating artificial cranial modifications.

• To test whether artificial cranial modifications could be identified and characterized when a cranium is partially preserved, we used 3D geometric morphometrics to quantify the shape differences of isolated calvaria bones among four groups of individuals with distinct forms of artificial cranial modifications and a control group of unmodified skulls.

• The shape of isolated calvaria bones can be informative for the identification and the characterization of artificial cranial modification in western and central Mesoamerica.

INTRODUCTION

Artificial Cranial Modification (ACM) is a pervasive cultural phenomenon, practiced in all continents (except Antarctica; [START_REF] Dingwall | Artificial cranial deformation. A contribution to the study of ethnic mutilations[END_REF] with the earliest reported evidence of expression dating back to Late Pleistocene in Australia [START_REF] Brothwell | Possible evidence of a cultural practice affecting head growth in some late Pleistocene East Asian and Australasian populations[END_REF][START_REF] Brown | Artificial cranial deformation: a component in the variation in Pleistocene Australian Aboriginal crania[END_REF][START_REF] Antón | Artificial cranial deformation and fossil Australians revisited[END_REF][START_REF] Durband | Artificial cranial deformation in Kow Swamp 1 and 5: A response to Curnoe (2007)[END_REF][START_REF] Brown | Nacurrie 1: mark of ancient Java, or a caring mother's hands, in terminal Pleistocene Australia?[END_REF][START_REF] Durband | Brief communication: Artificial cranial modification in Kow Swamp and Cohuna[END_REF] and North-East China [START_REF] Wu | Study on the Upper Cave man of Choukoutien[END_REF][START_REF] Brothwell | Possible evidence of a cultural practice affecting head growth in some late Pleistocene East Asian and Australasian populations[END_REF][START_REF] Ni | Earliestknown intentionally deformed human cranial fossil from Asia and the initiation of hereditary hierarchy in the early Holocene[END_REF][START_REF] Zhang | Intentional cranial modification from the Houtaomuga Site in Jilin, China: Earliest evidence and longest in situ practice during the Neolithic Age[END_REF]. The ACMs were performed via the implementation of a cranial device upon a child's skull from an early age so that cranial growth was prevented in certain directions [START_REF] Moss | The pathogenesis of artificial cranial deformation[END_REF][START_REF] Antón | Artificial cranial deformation and fossil Australians revisited[END_REF][START_REF] Tiesler | The bioarchaeology of artificial cranial modifications new approaches to head shaping and its meanings in pre-Columbian Mesoamerica and beyond[END_REF]. This results in a specific modification of the skull's shape that depends on the nature of the cranial device employed, its location upon the infant's skull, as well as the magnitude of pressure applied. The initiation time and the duration of the procedure are two other factors that likely account for the variation observed among cranial shapes (e.g., [START_REF] Ambialet | La déformation artificielle de la tête dans la région toulousaine[END_REF][START_REF] Ewing | Hyperbrachycephaly as influenced by cultural conditioning[END_REF][START_REF] Blackwood | A study of artificial cranial deformation in New Britain[END_REF][START_REF] Lieberman | Basicranial influence on overall cranial shape[END_REF][START_REF] Hutchison | Plagiocephaly and brachycephaly in the first two years of life: a prospective cohort study[END_REF][START_REF] Graham | Deformational brachycephaly in supine-sleeping infants[END_REF][START_REF] Rogers | Deformational plagiocephaly, brachycephaly, and scaphocephaly. Part I: terminology, diagnosis, and etiopathogenesis[END_REF][START_REF] Tiesler | The bioarchaeology of artificial cranial modifications new approaches to head shaping and its meanings in pre-Columbian Mesoamerica and beyond[END_REF]. The cranial devices employed in ACM are manifold and can consist of rigid tablets (e.g., [START_REF] Dembo | Deformaciones intencionales del cuerpo humano de carácter étnico[END_REF][START_REF] Romano | Estudio morfológico de la deformación craneana en Tamuín[END_REF][START_REF] Tiesler | The bioarchaeology of artificial cranial modifications new approaches to head shaping and its meanings in pre-Columbian Mesoamerica and beyond[END_REF], systems made of bands or chords (e.g., [START_REF] Dembo | Deformaciones intencionales del cuerpo humano de carácter étnico[END_REF][START_REF] O'brien | Boards and cords: discriminating types of artificial cranial deformation in prehispanic South Central Andean populations[END_REF], headdresses or caps (e.g., [START_REF] Ambialet | La déformation artificielle de la tête dans la région toulousaine[END_REF][START_REF] Hatt | Artificial moulding of the infant's head among the Scandinavian Lapps[END_REF], or cradle systems integrating constraining elements (e.g., [START_REF] Romano | Deformación cefálica intencional[END_REF][START_REF] Piper | The morphology of prehispanic cradleboards: form follows function[END_REF][START_REF] Tiesler | The bioarchaeology of artificial cranial modifications new approaches to head shaping and its meanings in pre-Columbian Mesoamerica and beyond[END_REF]. The modification of the cranial shape could also have been reached via the performance of daily head massages, so the skull is molded to fit a particular shape [START_REF] Hatt | Artificial moulding of the infant's head among the Scandinavian Lapps[END_REF][START_REF] Dingwall | Artificial cranial deformation. A contribution to the study of ethnic mutilations[END_REF][START_REF] Romano | Deformación cefálica intencional[END_REF][START_REF] Motte-Florac | La fontanelle chez les P'urhépecha et dans le centre du Mexique; du microcosme au macrocosme, de l'homme à dieu[END_REF][START_REF] Tiesler | La costumbre de la deformación cefálica entre los antiguos mayas: aspectos morfológicos y culturales[END_REF][START_REF] Yon | Modelar la cabeza: una tradición mesoamericana milenaria desde el Preclásico hasta la actualidad[END_REF].

Modified heads have been associated with various cultural meanings such as indicating social status (e.g., [START_REF] Marcus | The coevolution of ritual and society: New 14C dates from ancient Mexico[END_REF][START_REF] Ricci | Evidence of artificial cranial deformation from the later prehistory of the Acacus Mts.(Southwestern Libya, Central Sahara)[END_REF][START_REF] Geller | Getting a head start in life: Pre-Columbian Maya cranial modification from infancy to ancestorhood[END_REF][START_REF] Khudaverdyan | Trepanation and artificial cranial deformations in ancient Armenia[END_REF][START_REF] Sharapova | Skull Deformation during the Iron Age in the Trans-Urals and Western Siberia[END_REF][START_REF] Okumura | Differences in types of artificial cranial deformation are related to differences in frequencies of cranial and oral health markers in pre-Columbian skulls from Peru. Boletim do Museu Paraense Emílio Goeldi[END_REF], or an ethnic identity (e.g., [START_REF] Özbek | Cranial deformation in a subadult sample from Degirmentepe (Chalcolithic, Turkey)[END_REF][START_REF] Torres-Rouff | Cranial Vault Modification and Ethnicity in Middle Horizon San Pedro de Atacama, Chile[END_REF][START_REF] Blom | Embodying borders: human body modification and diversity in Tiwanaku society[END_REF][START_REF] Ricci | Evidence of artificial cranial deformation from the later prehistory of the Acacus Mts.(Southwestern Libya, Central Sahara)[END_REF][START_REF] Hakenbeck | Hunnic'modified skulls: physical appearance, identity and the transformative nature of migrations[END_REF][START_REF] Lozada | Marking ethnicity through premortem cranial modification among the Pre-Inca Chiribaya, Perú[END_REF][START_REF] Tiesler | The bioarchaeology of artificial cranial modifications new approaches to head shaping and its meanings in pre-Columbian Mesoamerica and beyond[END_REF][START_REF] Mayall | Migrating Huns and modified heads: Eigenshape analysis comparing intentionally modified crania from Hungary and Georgia in the Migration Period of Europe[END_REF][START_REF] Veeramah | Population genomic analysis of elongated skulls reveals extensive female-biased immigration in Early Medieval Bavaria[END_REF][START_REF] Fernandes | Cranial deformation and genetic diversity in three adolescent male individuals from the Great Migration Period from Osijek, eastern Croatia[END_REF][START_REF] Mayall | A review of the practice of intentional cranial modification in Eurasia during the Migration Period (4th-7th c AD)[END_REF], denoting religious faith (e.g., [START_REF] Houston | The memory of bones body, being, and experience among the classic Maya[END_REF][START_REF] Fletcher | The Manipulation of Social and Physical Identity in the Pre-Pottery Neolithic: Radiographic Evidence for Cranial Modification at Jericho and its Implications for the Plastering of Skulls[END_REF][START_REF] Tiesler | La deformación craneana como emblema de identidad, etnicidad y reproducción cultural entre los mayas del Clásico[END_REF][START_REF] García | El aspecto físico de los dioses mayas: modelado cefálico y otras marcas corporales[END_REF]), healthcare beliefs (e.g., Icart, 1784;[START_REF] Delisle | Contribution à l'étude des déformations artificielles du crâne[END_REF]Ambialet, 1893, p. 19;[START_REF] Hatt | Artificial moulding of the infant's head among the Scandinavian Lapps[END_REF][START_REF] Motte-Florac | La fontanelle chez les P'urhépecha et dans le centre du Mexique; du microcosme au macrocosme, de l'homme à dieu[END_REF][START_REF] Logan | Cranial modification among 19th century Osages: Admixture and loss of an ethnic marker[END_REF][START_REF] Duncan | Why the head? Cranial modification as protection and ensoulment among the Maya[END_REF] or simply for esthetic considerations (e.g., [START_REF] Hatt | Artificial moulding of the infant's head among the Scandinavian Lapps[END_REF][START_REF] Dingwall | Artificial cranial deformation. A contribution to the study of ethnic mutilations[END_REF][START_REF] Lorentz | Cultures and Physical Modifications: Child Bodies in Ancient Cyprus[END_REF].

A child's head, and the way various anatomical regions grow and develop, is central to the world view of many Mesoamerican populations (Ruiz de [START_REF] Ruiz De Alarcón | Tratado de las supersticiones de los naturales de esta Nueva España[END_REF][START_REF] Motte-Florac | La fontanelle chez les P'urhépecha et dans le centre du Mexique; du microcosme au macrocosme, de l'homme à dieu[END_REF]López Austin, 2004, pp. 224-225;[START_REF] Ponce | Breve relación de los dioses y ritos de la gentilidad[END_REF]Tiesler, 2014, p. 143). For example, among the Nahuas, an individual's spirit was thought to reside in the head. Therefore, the fontanelles of infants were considered as possible exit points through which the spirit may escape [START_REF] López Austin | Cuerpo humano e ideología: las concepciones de los antiguos Nahuas[END_REF]. Protecting the spirit from leaving the body of the infant via these openings was a major concern of the Nahua's belief system. For this reason, some authors have proposed that the action of modifying the shape of a skull should be considered as a complex cultural process that originates from different yet complementary intentions. They suggest that to fully understand the cultural complexity of ACM it is essential to distinguish the underlying intentions behind the process, whether these relate to childcare (López Austin, 2004, p. 212;Tiesler, 2014, p. 143) or proclaiming an ethnic identity, hierarchical status or any other cultural statements [START_REF] Duncan | Cranial modification among the Maya: Absence of evidence or evidence of absence[END_REF][START_REF] Duncan | Sellamiento ritual, envoltura y vendaje en la modificación cefálica Mesoamericana[END_REF]. Therefore, assessing and characterizing reliably the various forms of ACM is an important concern because this may inform us of the societal structure and relationships within and between populations in pre-Hispanic Mesoamerica (e.g., [START_REF] Tiesler | The bioarchaeology of artificial cranial modifications new approaches to head shaping and its meanings in pre-Columbian Mesoamerica and beyond[END_REF][START_REF] Alvarado Viñas | Modificación cultural de la cabeza. Los casos de Teopancazco, Teotihuacan[END_REF][START_REF] Pereira | Dinámicas poblacionales y modificación cefálica artificial en el Michoacán prehispánico[END_REF].

The identification and classification of marked forms of ACM among pre-Hispanic populations is generally addressed using the typological system developed by [START_REF] Dembo | Deformaciones intencionales del cuerpo humano de carácter étnico[END_REF]. The system is specifically designed so that ACM variants among pre-Hispanic populations could be differentiated. The method consists of examining several Other studies employ morphometrics such as linear measurements and angles in order to identify and differentiate ACMs (e.g., [START_REF] Dembo | Deformaciones intencionales del cuerpo humano de carácter étnico[END_REF][START_REF] Falkenburger | Recherches anthropologiques sur la déformation artificielle du crâne[END_REF][START_REF] Romano | Estudio morfológico de la deformación craneana en Tamuín[END_REF][START_REF] Comas | Crânes déformés de l'île de Sacrificios (État de Veracruz, Mexique)[END_REF][START_REF] Romano | Deformación cefálica intencional[END_REF][START_REF] Clark | Identifying artificially deformed crania[END_REF][START_REF] Pomeroy | A metric study of three types of artificial cranial modification from north-central Peru[END_REF][START_REF] O'brien | Boards and cords: discriminating types of artificial cranial deformation in prehispanic South Central Andean populations[END_REF]. For almost four decades, the rise of geometric morphometrics techniques has provided efficient tools for analyzing variation in biological shape [START_REF] Bookstein | Morphometric tools for landmark data: geometry and biology[END_REF][START_REF] Slice | Modern morphometrics in physical anthropology[END_REF]. Geometric morphometrics has also been applied to identify and characterize ACM shapes. It has been demonstrated to be efficient in differentiating variants even in the case of subtle ACM [START_REF] Cheverud | Effects of frontooccipital artificial cranial vault modification on the cranial base and face[END_REF][START_REF] Kohn | Asymmetric vault modification in Hopi crania[END_REF][START_REF] Friess | Exploring artificial cranial deformation using elliptic Fourier analysis of Procrustes aligned outlines[END_REF][START_REF] Manríquez | Deformación intencional del cráneo en poblaciones arqueológicas de Arica, Chile: análisis preliminar de morfometría geométrica con uso de radiografías craneofaciales[END_REF][START_REF] Gómez-Valdés | Morfometría geométrica aplicada al estudio de la deformación cefálica intencional[END_REF][START_REF] Perez | Artificial cranial deformation in South America: a geometric morphometrics approximation[END_REF][START_REF] Perez | Deformaciones artificiales del cráneo en cazadores-recolectores del Holoceno medio-tardío del noroeste de Patagonia[END_REF][START_REF] Bucchi | Artificial Cranial Modification in San Pedro de Atacama and the Loa Basin: A Quantitative Approach to Its Role as a Marker of Social Identity[END_REF][START_REF] Kuzminsky | The application of 3D geometric morphometrics and laser surface scanning to investigate the standardization of cranial vault modification in the Andes[END_REF][START_REF] Mayall | Migrating Huns and modified heads: Eigenshape analysis comparing intentionally modified crania from Hungary and Georgia in the Migration Period of Europe[END_REF][START_REF] Mayall | Generalized Procrustes analysis of an ontogenetic series of modified crania: Evaluating the technique of modification in the Migration Period of E urope (4th-7th century AD)[END_REF]Alejandro et al., 2019;[START_REF] Natahi | Neurocranial shape variation among Tarascan populations: Evidence for varying degrees in artificially modified crania in pre-Hispanic West Mexico (1200-1400 AD)[END_REF].

However, multiple cranial alterations, unrelated to any cultural practices, can originate from ante-mortem conditions (e.g., pathological conditions or occupational causes such as the use of tumplines for carrying heavy loads; [START_REF] Gervais | Déformations artificielles de crânes préhispaniques au Guatemala et au Mexique[END_REF][START_REF] Tiesler | Rasgos bioculturales entre los antiguos mayas: aspectos arqueológicos y sociales[END_REF][START_REF] Gervais | El uso del mecapal en Guatemala y sus consecuencias sobre la columna cervical (primeras observaciones)[END_REF], and/or postmortem ones (e.g., taphonomic processes or biases related to the restoration process; [START_REF] Shipman | Life history of a fossil: an introduction to taphonomy and paleoecology[END_REF][START_REF] Lyman | Vertebrate taphonomy[END_REF][START_REF] Ricci | Evidence of artificial cranial deformation from the later prehistory of the Acacus Mts.(Southwestern Libya, Central Sahara)[END_REF][START_REF] Arbour | Analyzing taphonomic deformation of ankylosaur skulls using retrodeformation and finite element analysis[END_REF][START_REF] Tiesler | The bioarchaeology of artificial cranial modifications new approaches to head shaping and its meanings in pre-Columbian Mesoamerica and beyond[END_REF] and this can substantially complicate the recognition and characterization of ACMs. In some contexts, the overlying sediments may exert compression forces on the skull causing distortions and discontinuities between and within certain cranial elements [START_REF] Laitman | The basicranium of Plio-Pleistocene hominids as an indicator of their upper respiratory systems[END_REF][START_REF] Franciscus | Nasal morphology and the emergence of Homo erectus[END_REF][START_REF] Gunz | Principles for the virtual reconstruction of hominin crania[END_REF][START_REF] Weber | Virtual anthropology: a guide to a new interdisciplinary field[END_REF][START_REF] Tiesler | The bioarchaeology of artificial cranial modifications new approaches to head shaping and its meanings in pre-Columbian Mesoamerica and beyond[END_REF][START_REF] Jurda | The Post-Mortem Pressure Distortion of Human Crania Uncovered in an Early Medieval Pohansko (Czech Republic) Graveyard[END_REF] that can be subsequently mistaken for ACMs. In others, the soil characteristics (e.g, acidity or alkalinity) can severely affect the bone leading to its degradation and destruction, making the identification and characterization of ACMs extremely difficult [START_REF] Emery | Maya Zooarchaeology: New Directions in Method and Theory[END_REF]. Therefore, under certain conditions a skull may only be represented by a few usable cranial elements, hindering reliable and in-depth investigations of ACM practices (Tiesler, 2014, p. 70;[START_REF] Hernández | Deformación Craneal en el Occidente Mesoamericano. Nuevas evidencias e interpretaciones sobre esta práctica cultural[END_REF][START_REF] Montiel Mendoza | La modificación cefálica en la Huaxteca prehispánicas[END_REF]. Currently, assessing the degree of ACM and differentiating the form variants based on isolated calvaria bone fragments is challenging and may lead to serious biases and misinterpretations.

Some authors have proposed that the combination of certain morphological criteria, found on individual calvaria, can be utilized as reliable indicators for diagnosing ACM [START_REF] Magitot | Essai sur les mutilations ethniques[END_REF][START_REF] Goldstein | Cranial deformation among Texas Indians[END_REF][START_REF] Stewart | Are supra-inion depressions evidence of prophylactic trephination?[END_REF][START_REF] Weiss | La trepanación ritual suprainiana[END_REF][START_REF] Holliday | Occipital lesions: a possible cost of cradleboards[END_REF][START_REF] Antón | Artificial cranial deformation and fossil Australians revisited[END_REF]Tiesler, 2012a[START_REF] Tiesler | Transformarse en maya: el modelado cefálico entre los mayas prehispánicos y coloniales[END_REF][START_REF] Tiesler | The bioarchaeology of artificial cranial modifications new approaches to head shaping and its meanings in pre-Columbian Mesoamerica and beyond[END_REF][START_REF] Tiesler | Términos y taxonomía empleados en las modificaciones cefálicas[END_REF][START_REF] Natahi | Neurocranial shape variation among Tarascan populations: Evidence for varying degrees in artificially modified crania in pre-Hispanic West Mexico (1200-1400 AD)[END_REF]. However, to date, the potential of using isolated calvaria bones to identify and differentiate ACMs has never been systematically investigated.

Although various authors have reported the expression of ACM techniques in western and central Mesoamerica (e.g., [START_REF] Hulse | Appendix III: Skeletal Material[END_REF][START_REF] Stewart | The true form of the cranial deformity originally described under the name "tête trilobée[END_REF][START_REF] Hurtado | La deformación craneana entre los tlatelolcas[END_REF][START_REF] Hurtado | Las deformaciones corporales entre los Mexica[END_REF][START_REF] Meighan | Excavations at Tizapan el Alto, Jalisco[END_REF][START_REF] Romano | Deformación craneana en Tlatilco, México[END_REF][START_REF] Gill | Cultural implications of artificially modified human remains from Northwestern Mexico[END_REF][START_REF] Bautista | Los antiguos pobladores de Coyoacán, DF Estudio osteológico y cultural[END_REF][START_REF] Lagunas Rodríguez | Los antiguos habitantes de Cholula: Prácticas osteoculturales[END_REF]; Uruñuela y Ladron de [START_REF] Uruñuela Y Ladron De Guevara | Analisis de los restos oseos de los entierros del fraccionamiento San Juan, Atoyac, Jalisco[END_REF][START_REF] Acosta | L'ensemble funéraire du site de Caseta[END_REF][START_REF] Bautista | Catálogo de los cráneos aislados de la Colección Solórzano[END_REF][START_REF] Pereira | Dinámicas poblacionales y modificación cefálica artificial en el Michoacán prehispánico[END_REF][START_REF] Serrano Sánchez | El modelado cefálico intencional en la Cuenca de México hacia el Posclásico Final[END_REF][START_REF] Natahi | Neurocranial shape variation among Tarascan populations: Evidence for varying degrees in artificially modified crania in pre-Hispanic West Mexico (1200-1400 AD)[END_REF], the preservation state of bone limited some studies where fragmented or poorly preserved material reduced substantially the size of the sample considered (e.g., Jácome Hernández, 2012, p. 315;Jácome Hernández et al., 2018, p. 690). In order to improve the possibility of diagnosing ACMs and differentiating variants relying on fragmentary cranial remains, we investigate how informative the bones of the calvaria can be for the identification and the differentiation of ACM variants. Using 3D geometric morphometrics, we aim to quantify shape variation of isolated calvaria bones within and among different groups composed of unmodified individuals (i.e., the control group) as well as groups consisting of individuals with known diverse ACM variants.

MATERIALS AND METHODS

Sample composition

Our sample includes a group of 49 archeological individuals all in an excellent state of preservation. In order to avoid mixing the shape signal related to the ACMs with shape signals due to interpopulation differences, we have only considered pre-Hispanic individuals coming from archaeological excavations carried out in western and central Mesoamerica, specifically in three nearby Mexican states: the states of Guanajuato, México and Michoacán (Figure 1). The archaeological sites are located in five different regions: the valleys of Acámbaro and Zamora-Jacona and the basins of Zacapu, Pátzcuaro and México (Figure 1;

Table 1). The individuals from Early and Middle Formative are respectively coming from the sites of El Opeño (Jacona-Zamora Valley; [START_REF] Oliveros | Hacedores de tumbas en el Opeño, Jacona, Michoacán[END_REF] and El Arbolillo (México basin; [START_REF] Vaillant | Excavations at El Arbolillo. nthropol Pap[END_REF]. The individuals from the sites JR24 (in the Acámbaro valley; [START_REF] Darras | Chupícuaro, entre el Occidente y el Altiplano central. Un balance de los conocimientos y las nuevas aportaciones[END_REF], Loma Alta (Zacapu basin; [START_REF] Arnauld | Arqueología de las Lomas en la cuenca lacustre de Zacapu[END_REF][START_REF] Carot | Le site de loma alta, lac de zacapu, michoacan (Mexique)[END_REF][START_REF] Pereira | Potrero de Guadalupe : anthropologie funéraire d'une communauté prétarasque du nord du Michoacan, Mexique[END_REF] and Ticomán (México basin; [START_REF] Vaillant | Excavations at Ticoman[END_REF] date back to the Late Formative (400 BC -300 AD). One individual from the site of Guadalupe dates to the Epiclassic period (600 -900 AD; [START_REF] Pereira | Potrero de Guadalupe : anthropologie funéraire d'une communauté prétarasque du nord du Michoacan, Mexique[END_REF][START_REF] Pereira | Arqueología de un lugar de pasaje hacia el inframundo[END_REF]. Individuals from El Palacio [START_REF] Lumholtz | Marked human bones from a prehistoric Tarasco Indian burial place in the State of Michoacan, Mexico[END_REF][START_REF] Lumholtz | Unknown Mexico: A record of five years' exploration among the tribes of the western Sierra Madre[END_REF] and Malpaís Prieto [START_REF] Pereira | Ephemeral cities? The longevity of the Postclassic Tarascan urban sites of Zacapu Malpaís and its consequences on the migration process[END_REF] for the Middle Postclassic (1200 -1400 AD; [START_REF] Pereira | Ephemeral cities? The longevity of the Postclassic Tarascan urban sites of Zacapu Malpaís and its consequences on the migration process[END_REF], two other sites of the Zacapu basin, were also included. For the Pátzcuaro basin, all the individuals come from Angamuco [START_REF] Fisher | A Typology of Ancient Purépecha (Tarascan) Architecture from Angamuco, Michoacán, Mexico[END_REF] and belong to the Late Postclassic -Early Colonial period (1200 -1600 AD; [START_REF] Fisher | Interim Report: Legados de la resiliencia: La Cuenca de Pátzcuaro Proyecto Arqueológico (Proyecto LORE LPB)[END_REF][START_REF] Cohen | Creating an Empire: Local Political Change at Angamuco[END_REF].

Individuals have been classified into five groups: four of them show the distinct forms of ACM mainly expressed in western and central Mesoamerica [START_REF] Pereira | Dinámicas poblacionales y modificación cefálica artificial en el Michoacán prehispánico[END_REF][START_REF] Serrano Sánchez | El modelado cefálico intencional en la Cuenca de México hacia el Posclásico Final[END_REF]. They have been differentiated according to the typology of [START_REF] Dembo | Deformaciones intencionales del cuerpo humano de carácter étnico[END_REF] i.e., the Fronto-Obelionic or FO type; the Tabular Erect Fronto-Occipital and Plano-Lambdoid variants, respectively TEFO and TEPL; the Tabular Oblique or TO type; Figure 2). A group of unmodified individuals was used as a control group (Table 1). Individuals were assigned to the control group based on the results of [START_REF] Natahi | Neurocranial shape variation among Tarascan populations: Evidence for varying degrees in artificially modified crania in pre-Hispanic West Mexico (1200-1400 AD)[END_REF].

All control group individuals were from El Palacio and Malpaís Prieto and their shape fall within the 95% confidence ellipse of a group composed of unmodified Mexican Indians and French medieval individuals from [START_REF] Natahi | Neurocranial shape variation among Tarascan populations: Evidence for varying degrees in artificially modified crania in pre-Hispanic West Mexico (1200-1400 AD)[END_REF]. All the individuals considered in the study were adults, except one (the individual Tarascan 153 from El Palacio). The age at death for this immature individual was estimated, from dental mineralization and eruption stages [START_REF] Moorrees | Age variation of formation stages for ten permanent teeth[END_REF][START_REF] Demirjian | A new system of dental age assessment[END_REF][START_REF] Ubelaker | Human skeletal remains: excavation, analysis, interpretation[END_REF][START_REF] Alqahtani | Brief communication: the London atlas of human tooth development and eruption[END_REF], as being between 10-20 years. This age-at-death overlaps with lower-bound for neurocranial maturity (as documented by [START_REF] Bastir | Craniofacial levels and the morphological maturation of the human skull[END_REF],

and as such we have included this individual in our analyses.

Data acquisition

The individuals from the JR24, Angamuco, El Palacio, Guadalupe, Loma Alta and Malpaís

Prieto have been all scanned using medical computed tomography (Mount Sinai Radiology, New York, United States of America; CT Scanner del Sur, Ciudad de México, México; with slice intervals varying from 0.5mm to 0.625mm and pixel sizes ranging from 0.38 to 0.56mm

; SI Table 1). Each surface has been generated using the HMH segmentation procedure (Half Maximum Height ; [START_REF] Spoor | Linear measurements of cortical bone and dental enamel by computed tomography: applications and problems[END_REF]. Subsequent corrections were applied manually in the Avizo software (Avizo Lite 8.0; Thermo Fisher Scientific). The rest of the sample (i.e., all individuals from El Opeño, El Arbolillo and Ticomán) has been scanned via surface laser scanning (i.e., with a NextEngine laser scanner, 3D Scanner Ultra HD, NextEngine, Inc.) with resolution parameters identical to those described in [START_REF] Natahi | Neurocranial shape variation among Tarascan populations: Evidence for varying degrees in artificially modified crania in pre-Hispanic West Mexico (1200-1400 AD)[END_REF].

From each scanned cranium the shape of three calvaria bones have been analyzed in isolation:

the frontal squamous part, the parietal and the posterior part of the occipital bone. The complete ectocranial surface of each bone was analyzed except for the occipital (Figure 3).

The signal describing the shape of the occipital bone was restricted to the occipital squama and the posterior part of the occipital base (i.e., the anatomical regions where the posterior elements of the cranial devices employed in ACM are usually arranged). The first structure is delimited anteriorly and superiorly by the two parietal bones (i.e., the lambdoid sutures) and laterally and inferiorly by the two petrous parts of the temporal bones. The limits of the second structure are defined by (from the anterior and median to the lateral parts): the posterior margin of the foramen magnum, the posterior margins of the posterior condylar foramina, the paracondylar processes and the occipitomastoid suture laterally.

As mentioned in [START_REF] Gunz | Semilandmarks: a method for quantifying curves and surfaces[END_REF], the calvaria has relatively few homologous anatomical structures which complicates any shape fine shape quantification relying only on traditional craniometric landmarks. Therefore, we have included semilandmarks in order to capture the three-dimensional shape of each calvaria bone [START_REF] Bookstein | Landmark methods for forms without landmarks: morphometrics of group differences in outline shape[END_REF][START_REF] Gunz | Semilandmarks in three dimensions[END_REF]. A 3D-template of 463 landmarks and semilandmarks was specifically digitized on the entire calvaria (Figure 3, center; Table 2). The latter has been warped onto each skull using the software Viewbox (dHAL software, Kifissia, Greece).

The missing data do not account for more than 4.3% of information loss for an individual (i.e., no more than 20 missing landmarks for the entire calvaria). If missing, their coordinates have been estimated in accordance with the standard protocol developed by [START_REF] Gunz | Statistical and geometric reconstruction of hominid crania: reconstructing australopithecine ontogeny[END_REF] and [START_REF] Gunz | Principles for the virtual reconstruction of hominin crania[END_REF]. In order to analyze the shapes of each four calvaria bones separately, seven semilandmark curves have been digitized: along the left and right sphenofrontal sutures, squamous sutures, lambdoid sutures and along the sagittal suture (Figure 3, green dots). When using the minimization of the bending energy as criterion to perform the sliding of the semilandmarks (see below), the anatomical landmarks and curve semilandmarks constrain the displacements of the surface semilandmarks, guaranteeing that no surface semilandmarks slide beyond the limits of the surface of interest [START_REF] Gunz | Semilandmarks: a method for quantifying curves and surfaces[END_REF]. Therefore, in the subsequent analyses we have defined five sliding groups (i.e., subset of landmarks and semilandmarks;

Table 2) as follows: one for the frontal, one for the left parietal, one for the right parietal and one for the occipital. After digitization and warping, using the R "Morpho" package [START_REF] Schlager | Morpho and Rvcg -Shape Analysis in R: R-Packages for Geometric Morphometrics, Shape Analysis and Surface Manipulations[END_REF], the 3D semilandmarks of the five subsets were independently allowed to slide along curves and surfaces in order to minimize the bending energy of the Thin-Plate Spline (TPS) interpolation function that is computed between each specimen calvaria bone configuration and the respective sample Procrustes average [START_REF] Bookstein | Landmark methods for forms without landmarks: morphometrics of group differences in outline shape[END_REF][START_REF] Gunz | Semilandmarks in three dimensions[END_REF].

High degrees of neurocranium asymmetry have been observed in individuals expressing different ACM types [START_REF] Neumann | Types of artificial cranial deformation in the eastern United States[END_REF][START_REF] Romano | Deformación cefálica intencional[END_REF][START_REF] Kohn | Asymmetric vault modification in Hopi crania[END_REF][START_REF] Tiesler | La costumbre de la deformación cefálica entre los antiguos mayas: aspectos morfológicos y culturales[END_REF][START_REF] Clark | Identifying artificially deformed crania[END_REF][START_REF] Pomeroy | A metric study of three types of artificial cranial modification from north-central Peru[END_REF][START_REF] Natahi | Neurocranial shape variation among Tarascan populations: Evidence for varying degrees in artificially modified crania in pre-Hispanic West Mexico (1200-1400 AD)[END_REF]. The quantification of asymmetry being not relevant to our study, the symmetric component of shape variation was used in the subsequent analyses [START_REF] Klingenberg | Shape Analysis of Symmetric Structures: Quantifying Variation among Individuals and Asymmetry[END_REF]. The entire calvaria, the frontal bone, the occipital bone all display an internal symmetry plane so their symmetric configuration has been computed as the average of their respective original and reflected relabeled configurations [START_REF] Mardia | Statistical assessment of bilateral symmetry of shapes[END_REF][START_REF] Klingenberg | Shape Analysis of Symmetric Structures: Quantifying Variation among Individuals and Asymmetry[END_REF][START_REF] Savriama | Beyond bilateral symmetry: geometric morphometric methods for any type of symmetry[END_REF][START_REF] Klingenberg | Analyzing fluctuating asymmetry with geometric morphometrics: concepts, methods, and applications[END_REF]. In order to evaluate the shape changes related to the parietal bone only, we have proceeded differently and chosen to consider it with a matching symmetry (i.e., right and left parietal bones are mirror images of each other). Right configurations were reflected by changing the sign of the x coordinates [START_REF] Klingenberg | Shape Analysis of Symmetric Structures: Quantifying Variation among Individuals and Asymmetry[END_REF][START_REF] Zelditch | Geometric morphometrics for biologists: a primer[END_REF].

Subsequently, the two configurations of each individual were superimposed in pairs via a Procrustes fit in order to compute their respective mean shape. After the sliding, the semilandmarks were treated as homologous points and combined with traditional landmarks so they can be transformed into Procrustes shape coordinates via a Generalized Procrustes Analysis (GPA; [START_REF] Rohlf | Extensions of the Procrustes method for the optimal superimposition of landmarks[END_REF][START_REF] Bookstein | Biometrics, biomathematics and the morphometric synthesis[END_REF]Mitteroecker & Gunz, 2009). Each configuration is scaled to have a unit Centroid Size (CS: square root of the summed squared Euclidean distances from all semilandmarks to their centroid; [START_REF] Dryden | Statistical shape analysis[END_REF]. Then all configurations are translated and rotated to minimize the overall sum of the squared distances between the corresponding landmarks and semilandmarks.

Analyses of shape variation

In order to explore the informative potential of calvaria bones shapes in the identification and differentiation of ACM, we have evaluated their morphological differences within and between the five aforementioned groups (i.e., an Unmodified group used as control, a group composed of individuals with FO ACM, one with TEFO ACM, one with TEPL ACM and one with TO ACM). The morphological differences within and between group were measured following [START_REF] Stelzer | Using the covariation of extant hominoid upper and lower jaws to predict dental arcades of extinct hominins[END_REF]. This consisted of computing Procrustes distances pairwise for all possible combinations within a group (except for the TO group which is represented by one individual) and between groups. The within variation of the TO group could not been explored since the sample size limited to one individual.

Visualization patterns of shape variation

In order to provide morphological elements that can help identifying a form based on isolated bones, we have observed the morphological variations between each group mean shape through the displacements of their corresponding landmarks. We have also generated 3D digital meshes of the three calvaria bones. They have been respectively warped towards the mean shapes of our five groups for each calvaria bone. We have used the landmarks displacements and the generated meshes to visualize and describe the shape changes that characterize an ACM in comparison to another on one isolated bone.

RESULTS

Figure 4 displays the within and between group variation for the Unmodified group used as control and the different types of ACM that we identified via visual examinations. SI Table 2 describes the summary statistics of the within and between group comparisons. This group displays a bimodal distribution when compared to the Unmodified one since part of its variation lies in the within-group range of variation of the Unmodified individuals. The other part displays the highest Procrustes distances values (SI Table 2a). The variation of the occipital bone within the Unmodified group is close to that calculated for the Unmodified -FO and Unmodified -TEPL comparisons (Figure 4.c). The Unmodified -TO is distinct from the within-group variation of the Unmodified individuals. The variation observed for the Unmodified -TEFO comparison is bimodal with one section overlapping the Unmodified within-group variation while the other shows the highest values.

Within and between group variations

The within and between group variation of the Unmodified group

The within and between group variation of the Fronto-Obelionic group

The frontal bone morphological differences we observe among the individuals with a FO ACM differ slightly from the variation measured for FO -TEFO, SI Table 2a). The highest differences are those calculated for the FO -Unmodified comparison. The FO within-group variation for the parietal bone, expresses values close to all comparison groups except part of the FO -TEFO variation for which the highest Procrustes distances are observed (Figure 4.e; SI Table 2b). The comparisons of the occipital morphological differences for the FO group reveals that the FO within-group variation is close to the variation computed for the FO -Unmodified comparison (Figure 4.f).

The FO -TEFO group shows a flattened distribution with some values located in the FO within-group distribution whereas some exceed it and are much higher (with a 3 rd quartile of the Procrustes distances of 0.153; SI Table 2c). The FO -TEPL comparison yields a widespread distribution with most of the variation located in the same variation range as the FO -Unmodified distribution. The FO -TO group displays important morphological differences that clearly separate its distribution from that of the FO within-group.

The within and between group variation of the Tabular Erect Fronto-Occpital group

The TEFO within-group variation for the frontal bone is comparable to all groups except that of the TEFO -Unmodified one (Figure 4.g; SI Table 2a). This latter group exhibits a bimodal distribution with some values laying in the TEFO within-group variation and others exceeding the variation range of the other groups. The variation measured for the parietal bone in the TEFO within group is very important (i.e., a Procrustes distances mean of 0.120) and expresses a bimodal pattern where some values are low and others high (Figure 4.h; SI Table 2b). The variation of this group exceeds the variation displayed by the other groups except the TEFO -FO and the TEFO -Unmodified groups (the latter expressing a bimodal distribution and a Procrustes distances mean of 0.143). For the occipital bone (Figure 4.i), the TEFO within-group variation also shows a bimodal pattern of variation. Variation in this group is more important (i.e., a Procrustes distances mean of 0.160) than the ones computed for all other groups. Only the variation of the TEFO -TO group is higher than the TEFO withingroup variation (with a Procrustes distances means of 0.189).

The between group variation of the Tabular Erect Plano-Lambdoid group

The variation for the TEPL within-group overlaps in major part that of the TEPL -Unmodified group (Figure 4.j). It also overlays the other groups variation (i.e., TEPL -FO, TEPL -TEFO and TEPL -TO) but to lesser extents. Regarding the parietal bone (Figure 4.k), the within-group TEPL variation differs from the other groups, which present rather similar distributions except for the TEPL-TEFO group. When examining the occipital bone variation (Figure 4.l), the TEPL within-group expresses a large range of variation with some Procrustes distances showing low values whereas others are displaying high ones (SI Table 2c). The lowest values are similar to the ones observed in TEPL -FO, TEPL -TEFO and TEPL -Unmodified groups.

The within and between group variation of the Tabular Oblique group

The lowest variation registered for the frontal concerns the two groups TO -FO and TO -TEFO (Figure 4.m; SI Table 2a). TO -Unmodified and TO -TEPL express slightly higher amount of shape variation with respective Procrustes distances means of 0.107 and 0.091.

Considering the parietal bone (Figure 4.n), the between-group variations of the TO group are quite similar with the TO -FO and TO -TEPL comparisons displaying the lowest variations.

The TO -Unmodified and TO -TEFO show the highest variation with respectively unimodal and bimodal distributions. Regarding the occipital bone, all of the comparisons show a high amount of variation compared to any of the other comparisons measured (Figure 4.o; SI Table 2b). The TO -Unmodified, TO -FO and TO -TEPL groups overlap each other. The TO -TEFO group is the one showing the highest amount of variation and the highest values (Figure 4.o; SI Tables 2a and2c).

The shape variation computed within and between each group has revealed that some calvaria bones can be informative in the identification and characterization process of ACM.

The challenge of identifying and differentiating ACM using isolated calvaria bones

Firstly, we have shown that the variation observed between the Unmodified individuals and the individuals belonging to other groups always exceeded that of the within-group composed of the Unmodified individuals (SI Table 2). It suggests that regardless of the type of ACM to which it belongs, an isolated calvaria bone of an individual with ACM expresses in most instances morphological differences greater than the physiological variation (i.e., the variation within the Unmodified group) and can be dissociated from it.

Figure 5 describes the calvaria bones' mean shape of each ACM variant (except for the TO variant, which is represented by one individual). Figures 6 and7 and SI Figures 1, 2 and3 illustrate the calvaria bones' shape changes between groups. For the frontal bone, the flattening degree of the frontal squama distinguishes ACM from the Unmodified group (Figure 5). However, in the case of TEPL ACM, the morphological differences of the frontal bone observed between the Unmodified and the TEPL groups are more tenuous (Figure 4.a). Thus, some difficulties can be encountered when looking to differentiate those forms from the physiological variation if the analyses are exclusively based on visual examinations. When comparing the parietal bones of every ACM variant to the Unmodified group (Figures 5 and6), the important protrusion of the lateral parietal region is a pattern shared among all types.

For all ACM variants, the parietal bosses move backward and laterally when compared to the Unmodified group (Figure 6). Furthermore, ACM affects the lambdoid suture and its surroundings, and is characterized by their stretching laterally and inferiorly. The occipital bone of the Unmodified group (Figure 5) has a narrower and rounder shape than that of all ACM types, which shows a certain amount of bone flattening (differentially localized according to the ACM variant considered) associated with a broadened shape (Figure SI 3). FIGURE 6 Morphological differences between the frontal, parietal and occipital mean shapes of the Unmodified group and each ACM type. The differences are illustrated as landmarks displacements. The arrows represent the displacements from a mean shape (column) to another (row). Arrows with small lengths and cold colors indicate low morphological differences. Arrows with large lengths and warm colors indicate large morphological differences. The magnitude of the heatmaps (i.e., the minimum and maximum values) have been standardized on the minimal and maximal Procrustes distances observed when comparing the mean shapes of the five groups for each bone separately.

FIGURE 7

Morphological differences between the frontal (for the Fronto-Obelionic group), the parietal (for the Tabular-Erect Plano-Lambdoid group) and the occipital (for the Tabular Oblique group) mean shapes and all other groups. The differences are illustrated as landmarks displacements. The arrows represent the displacements from a mean shape (column) to another (row). Arrows with small lengths and cold colors indicate low morphological differences. Arrows with large lengths and warm colors indicate large morphological differences. The magnitude of the heatmaps (i.e., the minimum and maximum values) have been standardized on the minimal and maximal Procrustes distances observed when comparing the mean shapes of the five groups for each bone separately.

In some cases, certain bones exhibit shape features specific to some types of ACM and allow their differentiation from the other ACM variants. The within-group variation observed for the frontal bone of the FO group indicates a distinct shape when compared to the other groups.

The frontal bone of the FO ACM displays a marked flattening, a shortened length of the frontal squama associated with a more retracted position of the glabellar region and the orbital rims (Figure 7). These features distinguish FO ACM from the Unmodified group and the TEPL ACM, which show a rounded frontal squama and a more protruding glabellar region (Figures 5 and7). The differences are more subtle in regards with the two other types of ACM that both involve a flattening of the frontal bone. The evaluation of the shape differences between the FO and the TO ACMs demonstrates that the degree of flattening is lower for the FO group than for the TO one. In comparison with the TEFO group, the FO one shares a similar flattened morphology. Compared to the TEFO and TO groups, the FO one is mainly characterized by an important degree of lateral protrusion that affects the region of the temporal lines and the lateral sections of the coronal suture combined with a reduced height of the frontal squama (Figure 5 and7).

The measures of morphological differences (SI Table 2b) and the distribution pattern of variation within the TEPL variant for the parietal bone (Figure 4.k), also point to specific shape features. First, the parietal shape is broadened (Figure 5); likewise the other individuals belonging to any ACM groups. Yet, they differ from the FO and TO parietal mean shapes because the bulging of the TEPL mean shape is less prominent than these two groups (Figure 7). The TEPL also shows higher parietal bosses oriented more anteriorly than these two groups. Finally, the differences between the TEPL and the TEFO are subtle, as they seem to relate to small variations in the lateral protrusion of the parietal bone (Figure 7). When compared to the Unmodified group, the morphological differences concern similar regions. However, they express this characteristic with lower intensity among the TEPL group.

Differentiating those forms via a visual examination is a difficult process that should be addressed using complementary analyses (e.g., using linear measurements).

The internal variation of the TO group could not be investigated because of its sample size of one individual. Nevertheless, when compared to individuals belonging to other groups the TO individual displays a specific occipital shape that is not reported in the other comparisons. The TO occipital shows a very high degree of specificity as evidenced by its unique morphology (Figure 5) and by its important amount of shape variation when it is compared to occipital bones from other ACM groups (no mean Procrustes distance is less than 0.14; SI Table 2c; In combination with these characteristic features, we also observe that the superior part of the occipital squama is reduced substantially, and the occipital eminence occupies a much higher position, closer to lambda (Figure 7). A downward motion of the asterionic region is also observed and results in its displacement inferiorly and anteriorly.

DISCUSSION

This study has provided, for the first time, information on the shape features of isolated calvaria bones that pertain to instances of ACM. Besides evaluating the potential of using isolated calvaria bones to identify and differentiate ACM, it also reveals valuable information relative to the techniques employed to produce certain ACM variants. These results question the homogeneity of one specific group: the Tabular Erect Fronto-Occipital variant.

Our results demonstrate that isolated bones may provide valuable information that can help to identify individuals with ACM from those that have never undergone any form of ACM during their lifetime. Calvaria bones that have undergone ACM exhibit characteristic flattening and broadening morphology, when compared to the natural shape variation of the Unmodified group. In addition, under certain conditions our results support the assumption, that some ACM variants can be characterized based on isolated calvaria bones.. The frontal bone is the most informative element to characterize the Fronto-Obelionic (FO) type. The combination of a flatter and broader morphology seems to be specific to this variant. The Tabular Erect Plano-Lambdoid (TEPL) type displays a parietal shape that can be distinguished from the other variants through the identification of laterally expanded parietal bosses as well as via their anterior position. Finally, the elongated shape of the nuchal portion of the occipital bone, characterizes the Tabular Oblique (TO) type. This morphology is highly specific to this type and has never been observed in any of the other ACM variants considered here. These results are important for the context of western and central Mesoamerican archaeology where in-depth investigations on the evolution and diversity of ACM practices are sometimes limited by bone preservation. However, the methodological framework presented here could easily be applied to other archeological contexts across the Americas.

Such research would permit a clearer understanding of the spread and evolution of ACM practices on a continental scale. For example, the technique outlined here may be extremely valuable when applied to the archeology of the Maya area, where poor bone preservation has substantially limited the study of ACM (e.g., [START_REF] Danforth | Stature change in prehistoric Maya of the Southern Lowlands[END_REF][START_REF] Wright | Biological perspectives on the collapse of the Pasión Maya[END_REF][START_REF] Cucina | Sex differences in oral pathologies at the Late Classic Maya site of Xcambó, Yucatán[END_REF].

While the patterns of variation within and between groups have revealed some specificities among certain variants, they have also brought information on standardization of ACM techniques and the manner in which they were performed. The FO variant shows within-group values similar to that of the control group for the three calvaria bones considered in this study. This reinforces that this technique was standardized [START_REF] Natahi | Neurocranial shape variation among Tarascan populations: Evidence for varying degrees in artificially modified crania in pre-Hispanic West Mexico (1200-1400 AD)[END_REF]. When comparing the occipital shape differences within the FO group to those quantified between groups, the weakest differences were recorded for the FO -Unmodified comparison and the highest for the FO -TEFO comparison. This suggests that the shape of the occipital bone in individuals with FO ACM is closer to that of individuals with no modification than to any of the ACM groups. The occipital shape variation observed for the Unmodified -FO comparison differs slightly from the variation recorded for the FO within-group. These results show that the occipital bone underwent a modification process important enough to distinguish it from the physiological variation; yet not as marked as the reported case of TO ACM. Therefore, it strengthens the assumption of [START_REF] Pereira | Potrero de Guadalupe : anthropologie funéraire d'une communauté prétarasque du nord du Michoacan, Mexique[END_REF] that FO variant is distinct from the two major types (i.e., Tabular Erect and Tabular Oblique) usually encountered in the context of Mesoamerican archaeology [START_REF] Romano | Deformación cefálica intencional[END_REF][START_REF] Tiesler | The bioarchaeology of artificial cranial modifications new approaches to head shaping and its meanings in pre-Columbian Mesoamerica and beyond[END_REF][START_REF] Tiesler | Modificaciones cefálicas culturales en Mesoamérica[END_REF]. Moreover, it proves that an element of the cranial device (e.g., such as a pad or a bandage) had also exerted a constraint with lower intensity on the nuchal part of the occipital bone for this variant. Consequently, these lines of evidence are consistent with the conclusions reached by [START_REF] Pereira | Potrero de Guadalupe : anthropologie funéraire d'une communauté prétarasque du nord du Michoacan, Mexique[END_REF][START_REF] Pereira | Dinámicas poblacionales y modificación cefálica artificial en el Michoacán prehispánico[END_REF] that such a modification process would be obtained through the implementation of constraining elements localized on the frontal squama and in the obelionic and nuchal regions.

The TEPL variant results from the implementation of a constraining element in the posterior section of the occipital bone, which prevents brain growth in that direction. While barely noticeable via a visual examination, we have demonstrated here that the frontal bone for this variant presents a shape that differs slightly from the Unmodified group. This information is valuable regarding the nature of the cephalic device employed to produce this variant. The TEPL variant is thought to be induced by the process of cradleboarding (e.g., [START_REF] Dembo | Deformaciones intencionales del cuerpo humano de carácter étnico[END_REF][START_REF] Tiesler | The bioarchaeology of artificial cranial modifications new approaches to head shaping and its meanings in pre-Columbian Mesoamerica and beyond[END_REF]. [START_REF] Dembo | Deformaciones intencionales del cuerpo humano de carácter étnico[END_REF] have identified forms similar to ours since they have observed both anterior and posterior compression planes among individuals exhibiting it. More specifically, they proposed that the head of the newborn was maintained by a system tying the frontal bone back to the cradleboard. Such a system, as documented for the southwest of the United States of America (e.g., [START_REF] Piper | The morphology of prehispanic cradleboards: form follows function[END_REF] would result in a slightly modified curvature of the frontal squama and would explain the variation we have documented here.

The TEPL group considered here expresses a within-group variation distribution and values similar to that of the control group for the frontal and parietal bones. However, the group variation for the occipital bone is bimodal with very high Procrustes distances. It indicates that very different occipital shapes co-exist within that cluster and questions whether or not this practice was standardized. Such a result is consistent with the hypothesis that these variants were produced via cradleboarding. Random phenomena such as the infant's head movements are likely to occur daily and may explain the discrepancies of occipital shapes observed here. The consistency of the within-group variation for the parietal bone compared to the bimodal distribution of the occipital variation is of interest. It suggests that the parietal shapes within this group are similar while the occipital ones differ greatly. This result implies that differential constraints localized in the posterior part of the skull can result in similar responses in other region (i.e., the parietal bones). Whether those forms have been produced by different cradleboarding techniques or by random events that occurred during the life of the infant (e.g., head movements, sleep position), is currently unknown. However, future studies could compare the occipital shape variation of the TEPL type to that of children with positional plagiocephaly (with a specific focus on the lateralization) in order to decipher the underlying causes of such shape variation .

The within-group variations of the frontal, parietal and occipital bones observed for the Tabular Erect Fronto-Occipital (TEFO) group exhibit a bimodal distribution. Furthermore, several comparisons with other groups have also shown a bimodal distribution. Except for the variation measured between the TEFO and the TO individual for the occipital bone and the variation between the TEFO and the Unmodified groups for the parietal bone, the withingroup variation of the TEFO group is always roughly equal to or greater than the between group variation.

These results indicate important shape differences within this group. It is composed of four individuals, one of which expresses a different shape to the others. This questions the homogeneity of the technique employed to produce their forms and highlights the limitations that current classification systems have to face. Future work, encompassing larger sample sizes, should focus on the variation recorded within each variant in order to disentangle whether cases like the TEFO variant actually forms a homogenous class ensuing from similar techniques of ACM.

The purpose of this study was to investigate the shape variation of the calvaria bones among individuals with ACM independent of how asymmetric they are, as the asymmetric component of all landmark configurations was removed. Nevertheless, ACM is reported to cause important amount of asymmetry in the entire cranium [START_REF] Neumann | Types of artificial cranial deformation in the eastern United States[END_REF][START_REF] Romano | Deformación cefálica intencional[END_REF][START_REF] Kohn | Asymmetric vault modification in Hopi crania[END_REF][START_REF] Tiesler | La costumbre de la deformación cefálica entre los antiguos mayas: aspectos morfológicos y culturales[END_REF][START_REF] Clark | Identifying artificially deformed crania[END_REF][START_REF] Pomeroy | A metric study of three types of artificial cranial modification from north-central Peru[END_REF]. Some authors have identified that in certain ACM cases, flattening can affect separately the right or left posterior portions of the skull [START_REF] Kohn | Asymmetric vault modification in Hopi crania[END_REF][START_REF] Tiesler | La costumbre de la deformación cefálica entre los antiguos mayas: aspectos morfológicos y culturales[END_REF][START_REF] Natahi | Neurocranial shape variation among Tarascan populations: Evidence for varying degrees in artificially modified crania in pre-Hispanic West Mexico (1200-1400 AD)[END_REF]. As asymmetry was excluded here, further studies should evaluate the extent to which it can complicate the assessment of ACMs based only on calvaria bones.

  morphological features among which the most significant are flattening and broadening of specific bones. The authors have defined three major categories of cranial modifications, each corresponding to the cephalic devices used. The annular forms, with symmetric circular constrictions are associated with devices composed of bandages, chords, or headdresses. The tabular erect types, display two parallel constriction planes oriented postero-superiorly, which are usually thought to result from infant cradleboarding practices. Finally, the tabular-oblique form refers to individuals exhibiting non-parallel constriction planes that affect the anterior and posterior parts of the vault. The two tabular forms utilize mostly rigid tablets to achieve the desired ACM. Each one of these forms (annular, tabular erect and tabular oblique) are further subdivided into different variants; indicating various ACM techniques throughout the Americas.

FIGURE 1

 1 FIGURE 1 Locations of the archaeological sites.

FIGURE 2

 2 FIGURE 2 Unmodified cranium and four different artificial cranial modifications types preferentially expressed in western and central Mesoamerica: (a) Unmodified cranium, (b) the Fronto-Obelionic type (FO), (c) the Tabular-Erect Fronto-Occipital type (TEFO), (d) the Tabular-Erect Plano-Lambdoid type (TEPL) and (e) the Tabular Oblique type (TO). Modified from Pereira (2018).

FIGURE 3

 3 FIGURE 3Landmark template, with the four groups of landmarks and semilandmarks considered. The red, green and blue dots represent respectively the anatomical landmarks, the curve semilandmarks and the surface semilandmarks.

FIGURE 4

 4 FIGURE 4Distribution of the Procrustes distances for all pairwise combinations of calvarial bones within and between the five groups: the Unmodified group, the Fronto-Obelionic group (FO), the Tabular Erect Fronto-Occipital group (TEFO), the Tabular Erect Plano-Lambdoid group (TEPL) and the Tabular Oblique group (TO) composed of one individual.

Figure 4 .

 4 Figure 4.a shows that the within group variation for the frontal bone of the Unmodified group overlaps that of the Unmodified -TEPL (i.e. Tabular Erect Plano-Lambdoid) and part of Unmodified -TEFO (i.e., Tabular Erect Fronto-Occipital) comparison. The other part of the variation observed for the Unmodified -TEFO group ranges outside the variation of the Unmodified individuals. The Unmodified -TO (i.e., Tabular Oblique) and Unmodified -FO (Fronto-Obelionic) groups differ clearly from the variation within the Unmodified cluster. When considering the parietal bone (Figure 4.b), the highest values of the within variation for the Unmodified group intersects that of all groups except that of Unmodified -TEFO group.

FIGURE 5

 5 FIGURE 5Mean shapes of each group for the frontal, parietal and occipital bones.

Figure 4

 4 Figure 4.o). Important increases in length and flattening of the nuchal area are the most noticeable criteria accounting for the specific occipital shape of this variant (Figure 5 and 7).

TABLE 1

 1 List of individuals.

TABLE 2

 2 List of landmarks, curve and surface semilandmarks.

	No	Anatomical	Unilateral/Bilateral	Comments
		landmarks
	1	Nasion	Unilateral
	2	Glabella	Unilateral
	3	Bregma	Unilateral
	4	Lambda	Unilateral
	5	Inion	Unilateral
	6	Opisthion	Unilateral
	7	Basion	Unilateral
	8, 9	Frontomalare	Bilateral
		temporal
	10, 11	Frontomalare	Bilateral
		orbital
	12, 13	Porion	Bilateral
	14, 15	Mastoid notch	Bilateral
	12,18	Asterion	Bilateral
	13,19	Pterion	Bilateral
		Curve
		semilandmarks
	20:25,	Inferior orbital	Bilateral	Rim of the orbital opening to frontomalare
	26:31	margin		orbital
		(n= 6 x 2)
	32:36,	Sphenofrontal	Bilateral	Cranial suture between sphenoid and
	37:41	suture		frontal bone
		(n= 5 x 2)
	42:49,	Coronal suture	Bilateral	Cranial suture separating the frontal from
	50:57	(n= 8 x 2)		the two parietal bones
	42:49,	Squamosal	Bilateral	Cranial suture separating the temporal
	50:57	suture		squama from the two parietal bones
		(n= 13 x 2)
	84:89,	Lambdoid	Bilateral	Cranial suture separating the occpital from
	90:95	suture		the two parietal bones
		(n= 6 x 2)
	96:103	Sagittal suture	Bilateral	Cranial suture expanding from bregma to
		(n= 8)		lambda
		Surface
		semilandmarks
	104:154,	Frontal patch	Bilateral
	284:334	(n= 51 x 2)
	155:253,	Parietal vault	Bilateral
	335:433	patch
		(n= 99 x 2)
	254:283,	occipital vault	Bilateral
	434:463	patch
		(n= 30 x 2)

ACKNOWLEDGEMENTS

We would like to acknowledge the Centro francés de Estudios Mexicanos y Centroamericanos (CEMCA) for facilitating the access to the archaeological material and providing the logistic facilities that enabled the acquisition of CT data. We are also deeply grateful to Isaac Barrientos Juárez and Osiris Quezada Ramírez for their valuable assistance in the transportation of the skulls of the CEMCA collections. We would like to thank the Division of Anthropology Loan Committee from the American Museum of Natural History for having allowed the CT scanning of part of the Lumholtz collection. We are thankful to Gisselle Garcia and Kristen Mable for their help in preparing the skulls so they could be safely transported. We are grateful to Jeffrey T. Laitman for having facilitated the CT scanning and having provided a storage location for the skulls. Thanks to Juan-Manuel Argüelles for having provided an access to the collections of the Dirección de Antropología Física. We also thank the two anonymous reviewers for their insightful comments and suggestions. We are grateful to Adam van Casteren and Thomas Davies for proofreading the article. We acknowledge the LascArBx: Cluster of Excellence in Archaeological Sciences of Bordeaux (ANR-10-LABX-52) for granting SN a PhD fellowship. Finally, we also thank the ANR MESOMOBILE (ANR-14-CE31-0016), the LascArBx: Cluster of Excellence in Archaeological Sciences of Bordeaux (ANR-10-LABX-52) and the CEMCA for having funded the analyses and the mobility of SN.