Jérémie Bardin
email: jeremie.bardin@upmc.fr

Isabelle Rouget

Fabrizio Cecca

ONTOGENY IN PHYLOGENIES Ontogenetic data analyzed as such in phylogenies

Keywords: phylogeny, cladistics, ontogeny, development, ammonite, Amaltheidae, Jurassic, Pliensbachian

Ontogeny is rarely included in phylogenetic analyses of morphological data.

When used, the ontogenetic information is reduced to one character for two or three different ontogenetic stages. Several examples show that current methods miss a major part of the information. We here propose a new method for including the ontogenetic dimension in coding schemes of phylogenetic analyses. Our goal was to maximise the phylogenetic information extracted from ontogenetic trajectories. For discrete features, we recommend including precise timings of transformation(s) from one state to another in the ontogenetic trajectories. For continuously varying features, growth laws are modelled on raw data using least-square regressions. Then, parameters of models are included in the coding scheme as continuous characters. This method is employed to reconstruct phylogenetic relationships using the ammonite family Amaltheidae as a test subject. Based on the same data set, a second analysis has been performed only for characters of the adult stage. Comparisons of retention index, bootstrap support and stratigraphic congruence between the two analyses show that the inclusion of ontogeny yields better phylogenetic reconstruction. Morphological traits in ammonites which are usually the most homoplastic show a better fit to most parsimonious trees by including the ontogenetic dimension. In several cases, growth rates and patterns of growth have better fit to phylogeny than adult shapes, implying that paths of ontogeny can be more relevant than its products.

INTRODUCTION

The interface between ontogeny and phylogeny, recently called "evo-devo", is a classical topic in evolutionary biology (e.g., [START_REF] Gould | Ontogeny and Phylogeny[END_REF][START_REF] Alberch | Size and shape in ontogeny and phylogeny[END_REF][START_REF] Fink | The conceptual relationship between ontogeny and phylogeny[END_REF][START_REF] Humphries | Ontogeny and systematics[END_REF][START_REF] Mabee | Phylogenetic interpretation of ontogenetic change: Sorting out the actual and artefactual in an empirical case study of centrarchid fishes[END_REF][START_REF] Mcnamara | Evolutionary change and heterochrony[END_REF][START_REF] Raff | The shape of life[END_REF][START_REF] Futuyma | Evolutionary biology[END_REF][START_REF] Rohlf | On applications of geometric morphometrics to studies of ontogeny and phylogeny[END_REF][START_REF] Wiens | Can incomplete taxa rescue phylogenetic analyses from long-branch attraction?[END_REF][START_REF] Germain | Evolution of ossification sequences in salamanders and urodele origins assessed through event-pairing and new methods[END_REF][START_REF] Laurin | Developmental characters in phylogenetic inference and their absolute timing information[END_REF][START_REF] Wolfe | Testing the phylogenetic position of Cambrian pancrustacean larval fossils by coding ontogenetic stages[END_REF]. One of the main cutting edges of evo-devo is that emergent properties appear from the study of both ontogeny and evolution together [START_REF] Hall | Evo-devo or devo-evo -does it matter?[END_REF]. Thus, a major goal in this field is to represent and use ontogenetic data in phylogenies.

Several attempts have been made to include ontogenetic data in phylogenetic analyses [START_REF] Mabee | Coding polymorphic data: examples from allozymes and ontogeny[END_REF][START_REF] Smith | Integration of craniofacial structures during development in mammals[END_REF][START_REF] Velhagen | Analyzing developmental sequences using sequences units[END_REF][START_REF] Steyer | Ontogeny and phylogeny in temnospondyls: a new method of analysis[END_REF]Jeffery, Bininda-Emonds, et al. 2002;Jeffery, Richardson, et al. 2002;[START_REF] Germain | Evolution of ossification sequences in salamanders and urodele origins assessed through event-pairing and new methods[END_REF][START_REF] Laurin | Developmental characters in phylogenetic inference and their absolute timing information[END_REF][START_REF] Wolfe | Testing the phylogenetic position of Cambrian pancrustacean larval fossils by coding ontogenetic stages[END_REF] and most of these studies showed that ontogenetic data contain phylogenetic signals and that their inclusion outperforms classic analyses. We briefly review current methods and some of their limitations, illustrating them with an ammonite example. These methods used ontogeny of features as discrete characters based on their shape and/or their timing or duration. However, many ontogenetic changes of morphology are continuous or vary continuously both in shape and time. Ontogeny can be regarded as the covariation of size, shape and age; so far the best way to represent it, is the ontogenetic trajectory formalized with continuous allometric growth models (e.g. [START_REF] Gould | Allometry and size in ontogeny and phylogeny[END_REF][START_REF] Alberch | Size and shape in ontogeny and phylogeny[END_REF]). We present a new approach based on these trajectories where ontogenetic data are used as such in phylogenies. This formal approach can be applied both to represent data on a given phylogeny and, in phylogenetic analyses, to increase the use of ontogenetic information. Our method avoids artificial sequencing into discrete units and codes ontogeny itself rather than its products. We assess the relevance of the method by comparing the results of two parsimony analyses: with and without including the treatment of ontogeny. The group under study is the Amaltheidae, a Pliensbachian (Early Jurassic) ammonite family which is well-known as a central model for ontogenetic studies of ammonoids [START_REF] Mattéi | Application de méthodes d'analyse globale à l'étude des Amaltheidae du bassin sédimentaire des Causses (Carixien supérieur et Domérien)[END_REF][START_REF] Meister | Ontogenèse et évolution des Amaltheidae (Ammonoidea)[END_REF]. Ammonoids are a well-suited model for the study of ontogeny in relation to phylogeny because their conch records an important part of their ontogeny. Several studies emphasized how one can take advantage of the ontogeny for phylogenetic purposes (e.g. [START_REF] Korn | Quantification of ontogenetic allometry in ammonoids[END_REF][START_REF] Knauss | Geographic Information Systems technology as a morphometric tool for quantifying morphological variation in an ammonoid clade[END_REF].

Review of methods dealing with ontogenetic characters

Since Haeckel's famous adage rebuttal, several methods were proposed to include ontogenetic variation of characters in phylogenetic reconstructions. In the literature, a large terminology exists to discretize ontogeny (e.g., for butterfly: egg, caterpillar, chrysalis and adult butterfly). Most of the phylogenetic analyses using ontogenetic information are based on these traditional ontogeny discretizations. The method proposed by [START_REF] Steyer | Ontogeny and phylogeny in temnospondyls: a new method of analysis[END_REF] separates characters for different ontogenetic stages (e.g. larval, juvenile and adult in its analysis) resulting in several matrices. An analysis is performed for each dataset. The resulting trees, called ontotrees, are compared and combined. [START_REF] Wolfe | Testing the phylogenetic position of Cambrian pancrustacean larval fossils by coding ontogenetic stages[END_REF] proposed a somewhat different method in which each ontogenetic stage is coded as an OTU in the matrix. These methods characterize evolutionary dynamics between ontogenetic stages. However, a major limitation is that all characters have to be coded on the same divisions of ontogenetic stages. Why should we consider that all characters change at the same time during ontogeny? Some works (e.g. [START_REF] Minelli | From embryo to adult-beyond the conventional periodization of arthropod development[END_REF] for arthropods) have shown that conventional periodization (i.e. the categorization of ontogeny into discrete intervals) used to describe ontogeny may not illustrate accurately the evolution of the group. The transformation of different characters can occur at different times during ontogeny. This is illustrated in figure 1 where trajectories of three ammonites (amaltheid taxa) are plotted for two morphological traits: the umbilical width (Uw = U/D) and the tuberculation. Ontogenetic trajectories of Uw follow a saturating growth law [START_REF] Alberch | Size and shape in ontogeny and phylogeny[END_REF] according to which the shape tends to reach a constant when approaching adult size. The tuberculation develops two stages: the first one called the Perlatum stage is characterized by small tubercles on each rib (black on Fig. 1), the second one called the Gibbosum stage is characterized by bigger tubercles which develop on every few ribs (grey on Fig. 1).

The Uw ontogenetic trajectory of A. salebrosus is more curved than the one of A. gibbosus, this difference expresses during the whole ontogeny and is especially easy to observe at the beginning of the trajectories. The Perlatum stage is the same in both taxa whereas the Gibbosum stage has a different offset between the two species.

Comparison of these ontogenetic trajectories shows that shifts of the two characters can occur in distinct parts of the ontogeny. Moreover, this example shows that ontogenetic trends can be different for each character, as Uw is peramorphic for A. salebrosus in comparison to A. gibbosus, whereas the offset of the Gibbosum stage is paedomorphic. The third ontogenetic trajectory presents the tuberculation for P. bechteri (Fig. 1); it has the same offset but a different onset for the Gibbosum stage.

This example shows that timings can be independent between several events in the ontogenetic trajectory of one given morphological trait, thus constituting several characters. Such examples have been described in birds. This concept is known as "mosaic heterochrony" or "dissociated heterochrony" (see review in [START_REF] Klingenberg | Heterochrony and allometry: the analysis of evolutionary change in ontogeny[END_REF]. Despite being well-known in the field of morphometrics, the possibility for the characters to evolve independently in the ontogeny has never been formalized for phylogenetic inference. Indeed, the above-mentioned methods do not precisely take into account the different timings in morphological changes.

The central question of the recognition of ontogenetic stages and their comparison between OTUs has led to the development of a suite of methods aimed at treating the order of suggested events and including it in phylogenetic analysis: mainly "event-pairing" [START_REF] Smith | Integration of craniofacial structures during development in mammals[END_REF][START_REF] Velhagen | Analyzing developmental sequences using sequences units[END_REF] and "event-pair cracking" (Jeffery, Bininda-Emonds, et al. 2002;Jeffery, Richardson, et al. 2002;[START_REF] Jeffery | A new technique for identifying sequence heterochrony[END_REF]. A characteristic of these methods is that they do not need a measure of age or time. This has been viewed as an advantage as the use of proxies for age has been discarded in some works (e.g. [START_REF] Smith | Heterochrony revisited: the evolution of developmental sequences[END_REF][START_REF] Koenemann | The limitations of ontogenetic data in phylogenetic analyses[END_REF]. Sequencebased methods can only detect and use ontogenetic variations which make some events to change their order of appearance. This is an important intrinsic limitation.

To us, these methods should only be used when time or its proxies are too dubious to be used. [START_REF] Germain | Evolution of ossification sequences in salamanders and urodele origins assessed through event-pairing and new methods[END_REF] proposed the continuous analysis which uses age and further showed [START_REF] Laurin | Developmental characters in phylogenetic inference and their absolute timing information[END_REF] that the use of time rather than sequences could extract additional reliable information for phylogenetic reconstruction.

The terms "development" and "ontogeny" are often used in very different ways. [START_REF] Gould | Ontogeny and Phylogeny[END_REF] recalls that ontogeny is the life history of an individual, whereas development is differentiation or any change in shape during ontogeny. Thus, development is included within the concept of ontogeny, together with maturity and growth. Most of the methods above-mentioned are presented as treating developmental data, whereas they usually use sexual maturity or increase in size (growth). Thus, we should use the term "ontogeny" for these purposes. Developed by [START_REF] Alberch | Size and shape in ontogeny and phylogeny[END_REF], the ontogenetic trajectory consists in representing the expression of a given trait during the lifespan of an organism. Keeping this in mind, we realize that all the above-mentioned methods compare the results of ontogeny at different stages, rather than ontogeny itself (i.e. the trajectory). This is mainly due to discretization both in the time (e.g. hatching, sexual maturity) and/or shape dimensions (e.g. discretization of continuous traits). When the three dimensions of ontogeny (i.e., growth, development, maturity) are available, they should all three be used and this is what we propose with our method. Referring to Gould's concepts, coding differences between modelled ontogenetic trajectories corresponds to coding dissociations between ontogenetic trajectories in these three dimensions as precisely and accurately as possible. This can be illustrated by deciphering the differences between the three ontogenetic trajectories of the character Uw provided in figure 2.

First of all, histograms of distributions show that expressed values of Uw are overlapping for the three taxa and that distributions of A. talrosei and P. solare are very similar to each other. Then, having a look at the tendencies of the character in the ontogeny, the trajectories of A. gibbosus and A. talrosei decrease while that of P. solare increases. This would be an argument to group A. gibbosus and A. talrosei. To go further, A. gibbosus and P. solare share a curved ontogenetic trajectory while A. talrosei has a linear one. Exploiting more accurately these ontogenetic trajectories leads to an important additional source of characters. This recalls what some phylogenists did by including changes of derivatives of traits against ontogeny (e.g., [START_REF] Wagner | The utility of fossil data in phylogenetic analyses: a likelihood example using Ordovician-Silurian species of the Lophospiridae (Gastropoda: Murchisoniina)[END_REF]. This is the information we propose to capture with the approach presented in this paper which aims at exploiting the ontogeny itself without any a priori discretization of the timing and of the ontogeny.

The Method

The objective is to code ontogenetic variation as characters and character states. We choose the theoretical framework of [START_REF] Alberch | Size and shape in ontogeny and phylogeny[END_REF] for the description of the ontogenetic trajectories. It consists of representing the expression of a morphological feature during the life of an individual or a population. This formalism can be applied to all different types of characters used in phylogenetic analysis. For binaries (Fig. 3a), the ontogenetic trajectory is determined by a time of onset (α) and a time of offset (β). For multistates (Fig. 3b), several onset and offset times are introduced depending on the number of states developed in the ontogenetic trajectories. In addition to onset and offset times, growth curves of continuous characters (Fig. 3c) are determined by a growth rate (k). The latter can be involved in different growth laws (e.g., a saturating growth law in Fig. 3c). Basically, our method consists of identifying and coding homologous ontogenetic stages for each character. We discuss dependences between ontogenetic stages which can be complex and have to be integrated into the coding scheme. Steps involved in this method for coding ontogeny are summarized in figure 4.

Ontogenetic Stage Comparisons -Differences between ontogenetic trajectories can be of two types: novelties on the one hand, changes in rates and timings of parts of ontogenetic trajectories on the other, the so-called heterochronies. In organisms with complex ontogenies, the analysis of these differences requires precise description of the ontogenetic trajectories and the distinction of ontogenetic stages.

The ontogenetic stages constitute units that we want to compare in terms of rates and timing among taxa. The possibility of splitting and treating separately ontogenetic trajectories of different traits should be added to current phylogenetic methods. Alba (2002, p. 33-36) claims that ontogenetic trajectories have to be compared at homologizable stages. He considers that a developmental stage is a period between two homologous shape-independent developmental events. According to him, these events should be used to standardize ontogeny instead of absolute age. However, we consider that these events can also be subject to evolutionary variation in their timing in terms of absolute age and should be treated the same way as any other characters.

These homologous events define homologous stages which can be compared between taxa in terms of shape, growth-rate and timing. Stages can be identified by remarkable events in ontogenetic trajectories (e.g. appearance of a particular feature, break in trajectory for continuous characters). Sometimes the entire ontogenetic trajectory of a given character corresponds to a stage because no specific event can be identified. When several stages can be recognized, several criteria for recognizing between-taxa homologous stages can be used. The first criterion is the order of stages, considering that they most likely appear in the same order. The second criterion is the expression of the characters. For discrete characters it means sharing the same state. For continuous characters, it corresponds to values on shape axis (Y axis) and/or values of slope. The third criterion corresponds to similar timing/durations of some potentially identified homologous stages between ontogenetic trajectories of taxa. None of these criteria has special priority over the others.

at UPMC on June 20, 2016 http://sysbio.oxfordjournals.org/ Downloaded from Which Kind of Character? -The treatment of each stage depends on the type of character under study. Discrete characters provide the simplest case. During ontogeny, an OTU can change from one state to the other once or several times. In that context, the information to code is the absence/presence of the states and the timing of this (these) transformation(s) during growth. The latter corresponds to parameters α and β of [START_REF] Alberch | Size and shape in ontogeny and phylogeny[END_REF], respectively the onset and offset.

The case of continuous characters is more complex as the variation is continuous in the bivariate representation of an ontogenetic trajectory (Fig. 3c). Many studies based both on empirical data (e.g. [START_REF] Gould | Ontogeny and Phylogeny[END_REF]) and theoretical models [START_REF] Alberch | Size and shape in ontogeny and phylogeny[END_REF]) provide useful equations for describing ontogenetic trajectories.

In practice, ontogenetic trajectories are described with equations that fit the data. We propose to use parameters of the fitting models as continuous characters. Many methods exist to transform these raw parameters into code (e.g., gap-coding, segment-coding, gap-weighting). In their coding scheme, to a greater or lesser extent, all available methods reduce the information expressed in the raw data [START_REF] Wiens | Character analysis in morphological phylogenetics: Problems and solutions[END_REF][START_REF] Goloboff | Continuous characters analyzed as such[END_REF][START_REF] Bardin | Increasing the number of discrete character states for continuous characters generates well-resolved trees that do not reflect phylogeny[END_REF]. We favour methods that offer the highest resolution in continuous character treatment in order not to discard phylogenetic information, even minor, expressed from ontogenetic trajectories.

Dependences in the Coding Scheme -When entire trajectories are considered, this stage-by-stage approach leads to consider links between those stages which have initially been considered separately. Two different types of dependences have to be taken into account. The first one concerns the coding procedure itself and the other implies biological dependences.

When several stages have been recognized and coded separately, a part of the information is redundant (Fig. 3b). Two stages that follow each other share the same timing. The end of the first stage (β1) is identical to the beginning of the second stage (α2). These two parameters have to be coded only once in the matrix. Concerning continuous characters, these redundancies exist also for the shape axis (i.e. the σ1 of a first stage is identical to the σ0 of a second stage). Again, these two parameters have to be coded only once.

In phylogenetic inference, investigations about the dependences between characters is a central topic and has received much attention (e.g. [START_REF] Huelsenbeck | Effects of nonindependent substitution on phylogenetic accuracy[END_REF][START_REF] O'keefe | Inferring and testing hypotheses of cladistic character dependence by using character compatability[END_REF][START_REF] Maglia | Identifying Character Non-Independence in Phylogenetic Data Using Data Mining Techniques[END_REF]. Integrating important amounts of information from ontogeny forces us to investigate dependences about timing and rates. We distinguished two cases in which the coding scheme has to be adapted because of dependences. The first one concerns transformations in different characters which occur at the same age. One should investigate whether this similar timing could be due to the same causality. If such a hypothesis is supported with evidence, this same timing between the different characters has to be coded only once in the matrix. This case corresponds to several usual developmental events such as hatching, metamorphoses, sexual maturity.

The second one involves dependences that can be integrated under the concepts of modularity, fragmentation and integration (e.g. [START_REF] Schlosser | Introduction: The modularity concept in developmental and evolutionary biology[END_REF]). Definitions of a module are really diverse [START_REF] Eble | Morphological Modularity and Macroevolution: Conceptual and Empirical Aspects[END_REF]. Albeit in phylogenetic studies, we generally use what [START_REF] Eble | Morphological Modularity and Macroevolution: Conceptual and Empirical Aspects[END_REF] called "Variational Morphological Modules", that is to say, modules are groups of traits co-varying and thus units we want to use as characters in phylogenetic analyses. They are of great importance in phylogenetic analysis for coding independent characters. Integration occurs when several modules start to covary, while they had an independent behaviour in earlier evolutionary history. Fragmentation is the division of a module into several independent character sets. Integration and fragmentation can affect both shape and timing. Modules have to be recognized a priori and integrated in the coding scheme.

Extrinsic versus Intrinsic Time -By using ontogenetic trajectories, we represent shape/size (Y axis) vs age (X axis). Absolute age is called extrinsic time. In practice, it can be measured for living organisms but in wild specimens or fossils, this is rarely possible. Variables from organisms are thus selected to represent time; they are the so-called intrinsic time (e.g. [START_REF] Blackstone | Size and time[END_REF][START_REF] Reiss | The meaning of developmental time: a metric for comparative embryology[END_REF][START_REF] Hall | How do embryos measure time[END_REF][START_REF] Klingenberg | Individual variation of ontogenies: a longitudinal study of growth and timing[END_REF]. Size is one of the most successful variables for representing age [START_REF] Strauss | On allometry and relative growth in evolutionary studies[END_REF][START_REF] Strauss | Heterochronic variation in the developmental timing of cranial ossification in poecilid fishes (Cyprinodontiformes)[END_REF]McKinney and McNamara 1991: p. 41). Strauss (1987: p. 33) argued that overall body size is the best measure to standardize development of organisms. However, most of the authors who use size consider it to be an approximation of extrinsic age (e.g. [START_REF] Dommergues | Can ribs and septa provide an alternative standard for age in ammonite ontogenetic studies?[END_REF][START_REF] Mckinney | Classifying heterochrony: allometry, size, and time[END_REF][START_REF] Mckinney | Heterochrony: the Evolution of Ontogeny[END_REF]. [START_REF] Mckinney | Ecological causation of heterochrony: a test and implications for evolutionary theory[END_REF] introduced the term "allometric heterochrony" for transformation deduced from shape-size representations (i.e. size as standard for age). Several examples have been published demonstrating that size was incongruent with age [START_REF] Emerson | Heterochrony and frogs: the relationship of a life history trait to morphological form[END_REF][START_REF] Blackstone | Morphological variation in a colonial marine hydroid: a comparison of sizebased and age-based heterochrony[END_REF][START_REF] Klingenberg | Heterochrony and allometry: lessons from the water strider genus Limnoporus[END_REF][START_REF] Leigh | Ontogeny of body size variation in African apes[END_REF]. Determining whether size is a good proxy for age depends on the group under study and the taxonomic scale of the analysis.

For example, in ammonoids, size is generally approximated by the diameter of the shell. Ammonite shells have an accretionary growth, thus size (i.e. diameter) vs age is monotonous. As soon as their whorl expansion rate and growth rate is more or less constant, we can consider that size is a good standard for age. However, comparing phylogenetically distant ammonoid taxa with various whorl expansion rate and growth rate will make diameter unsuitable for providing a good standard for age.

The taxonomic scale of comparison is thus a major limitation of the use of size. [START_REF] Mckinney | Heterochrony: the Evolution of Ontogeny[END_REF] basic assumption was that size increases identically between taxa to be compared [START_REF] Klingenberg | Heterochrony and allometry: the analysis of evolutionary change in ontogeny[END_REF]. As the taxonomic breadth of the ingroup increases, size should become an increasingly poor proxy for age. [START_REF] Reiss | The meaning of developmental time: a metric for comparative embryology[END_REF] claimed that extrinsic time is not suitable for comparing developmental events because they are too dependent on several environmental parameters such as temperature as well as size itself. Thus, an intrinsic time closer to these phenomena should be selected to scale developmental events. In this paper, we are seeking to reconstruct evolutionary history through ontogeny using the parsimony criterion. By using extrinsic time, Reiss's criticism would correspond to detecting similarities due to environmental or size parameters. In cladistics, these correspond respectively to homoplasy and dependence. Concerning homoplasy, the power of cladistics is to find trees that minimize it. Dependence can be detected a priori or a posteriori to the analysis (O'Keefe and [START_REF] O'keefe | Inferring and testing hypotheses of cladistic character dependence by using character compatability[END_REF]. Thus, the main criticism against the use of extrinsic time could be avoided in the context of cladistics as well as of model-based methods. We highly recommend the use of extrinsic time.

When it is unavailable, one should select the least-biased proxy variable.

MATERIAL & METHODS

Taxa

The ingroup (Tab. 1) of our analysis is composed of all accepted species within the family Amaltheidae, following [START_REF] Howarth | A monograph of the ammonites of the liassic family Amaltheidae in Britain[END_REF] and [START_REF] Meister | Ontogenèse et évolution des Amaltheidae (Ammonoidea)[END_REF]. Some additional comments on taxa are available from online appendix 1 (http://dx.doi.org/10.5061/dryad.0c1p0). The ingroup covers the entire morphological diversity of the family. Some species have been grouped into a single OTU when they were indistinguishable morphologically. The morphological analysis is based on a thorough survey of the literature (mainly [START_REF] Howarth | A monograph of the ammonites of the liassic family Amaltheidae in Britain[END_REF][START_REF] Tintant | Les Amalthéidés de Côte-d'or et leur répartition stratigraphique[END_REF][START_REF] Efimova | Field atlas of the Jurassic fauna and flora of the North-East of the USSR[END_REF][START_REF] Mattéi | Application de méthodes d'analyse globale à l'étude des Amaltheidae du bassin sédimentaire des Causses (Carixien supérieur et Domérien)[END_REF][START_REF] Meister | Ontogenèse et évolution des Amaltheidae (Ammonoidea)[END_REF][START_REF] Morard | Les événements du passage Domérien-Toarcien entre Téthys occidentale et Europe du Nord-Ouest[END_REF][START_REF] Bardin | Late Pliensbachian (Early Jurassic) ammonites from Lac de Charmes (Haute-Marne, France): Systematic, biostratigraphy and palaeobiogeography[END_REF]) in addition to some material available in the collections of University Pierre et Marie Curie (UPMC) and of the Muséum National d'Histoire Naturelle, in Paris (MNHN) (online appendix 2: http://dx.doi.org/10.5061/dryad.0c1p0).

Outgroup

In previous evolutionary scenarios, Oistoceras figulinum [START_REF] Simpson | The fossils of the Yorkshire Lias, described from nature[END_REF]) has been consensually viewed as the "ancestor" of the Amaltheidae [START_REF] Howarth | A monograph of the ammonites of the liassic family Amaltheidae in Britain[END_REF][START_REF] Meister | Ontogenèse et évolution des Amaltheidae (Ammonoidea)[END_REF]). We choose it as the outgroup to polarize characters of the analysis.

Oistoceras figulinum is morphologically close to the Amaltheidae and expresses very few autapomorphic states in our coding scheme.

Characters

Two data matrices are compiled:

-The first one (i.e. matrix a) includes ontogenetic information (online Appendix 3: http://purl.org/phylo/treebase/phylows/study/TB2:S16472?xaccess-code=2c3cb8ceba8b4a3fe755da29ff1e1713&format=html). It contains 33 characters, out of which 13 characters result from the analysis of ontogeny (three discrete ones and ten others resulting from coding of linear and saturating growth laws). To make the reading easier, this first matrix is called matrix a, is involved in analysis a and leads to tree a. Statistically significant parameters (i.e. from regressions explaining more than 95% of the variance) have been integrated into the matrix by using gap weighting [START_REF] Thiele | The holy grail of the perfect character: The cladistic treatment of morphometric data[END_REF][START_REF] Wiens | Character analysis in morphological phylogenetics: Problems and solutions[END_REF] with 1000 states (online appendices 3-4: http://purl.org/phylo/treebase/phylows/study/TB2:S16472?x-access-code=2c3cb8ceba8b4a3fe755da29ff1e1713&format=html); others have been coded as question marks. Ontogenetic trajectories of these characters are available from Morphobank website (online appendix 5: http://morphobank.org/permalink/?P1271).

Shape and Ornament of Ammonite Shells

In ammonoids, characters related to shell shape and ornaments are thought to be highly homoplastic but they may still be valuable if properly defined [START_REF] Yacobucci | Meta-analysis of character utility and phylogenetic information content in cladistic studies of ammonoids[END_REF]. Here, we consider some of the most common parameters in ammonoid descriptions: the umbilical width (Uw), whorl breadth against whorl height (WbWh), the ribbing frequency (Ribs) and the tuberculation. Refining their treatment in phylogenetic analyses in order to extract a reliable signal is a major goal. Some traits appear to be correlated; table 2 indicates features that have been combined to provide independent characters. Measurements have been made twice on each specimen, one at the smallest diameter available and the other at the greatest diameter. We measured numerous specimens for each taxon to take into account the intraspecific variation. An alternative approach is to measure few, well-preserved specimens, which is possible in ammonoids as their conchs preserve the whole ontogeny. The advantage is that the trajectories are complete and precise but the inconvenience is that these trajectories, even if constituting good representations of specimens are poor representations of the whole species.

Five characters have been coded for Uw. Ontogenetic trajectories follow a linear model for several taxa and a saturating growth law for the others. A challenge appears because ontogenetic trajectories of Uw have different shapes. Usually, shapes have to be similar to be comparable [START_REF] Klingenberg | Heterochrony and allometry: the analysis of evolutionary change in ontogeny[END_REF]. For the phylogenetic inference, we decided to code the different shape of the ontogenetic trajectories as binary character. Then, we have refined the coding scheme in including parameters of each model for the taxa involved. Thus the five characters were the type of growth, the slope, the growth rate (k) for the two types of models and the shape σ1 for SG law (Fig. 2). The coding scheme for the whorl breadth against whorl height (WbWh) is identical to that of Uw. We specify that the type of growth (i.e. linear or saturated) has been coded only once for Uw and WbWh.

For the coding of the ribbing frequency, we also used a saturating growth law in a number of ribs per half-whorl divided by the diameter against diameter. Thus, the y axis is a measure of ribbing frequency (i.e. how many ribs can be secreted on a given diameter); it constitutes a parameter of shape independent of the diameter. The selection of this model is motivated by [START_REF] Meister | Ontogenèse et évolution des Amaltheidae (Ammonoidea)[END_REF] claiming that the early and middle ontogeny of Amaltheidae was very polymorphic and that a stabilization occurred in the late ontogeny. We code the growth rate and the shape σ1 which corresponds to the ribbing frequency that specimens are tending towards.

Tubercles are part of the shell ornamentation which is well-developed and diversified within the Amaltheidae. Several characters have been coded to express this tuberculation through ontogeny (characters 17, 19 and 20). They consist of the offset diameter of the Perlatum stage, the type of complex tubercles which characterizes the Gibbosum stage and its expression (Fig. 1). The onset and offset of this stage is subject to covariation for some species but not all. We used a step matrix to code it. The detailed procedure is presented in the online appendix 6 (http://dx.doi.org/10.5061/dryad.0c1p0). Illustrations of every character are available from online appendix 5 (http://morphobank.org/permalink/?P1271).

Analyses

We choose parsimony as an optimality criterion even if this method to treat the ontogeny can also be used with model-based methods (e.g. Bayesian inference, maximum likelihood). Most parsimonious trees were sought using branch-andbound algorithm implemented in PAUP* version 4.0b10 [START_REF] Swofford | Phylogenetic Analysis Using Parsimony (*and Other Methods)[END_REF].

Trees indices -The level of homoplasy can be used to estimate the quality of the homology hypotheses. To compare phylogenies resulting from both analyses, we compute Consistency Index (CI), Retention Index (RI) and Rescaled Consistency Index (RC) which are usually calculated to quantify the rate of homoplasy [START_REF] Farris | The retention index and the rescaled consistency index[END_REF]). Node supports were evaluated by bootstrap procedure using 1000 replicates (Felsenstein 1985).

Stratigraphic congruence -Considering the high quality of the fossil record of the amaltheids [START_REF] Mattéi | Application de méthodes d'analyse globale à l'étude des Amaltheidae du bassin sédimentaire des Causses (Carixien supérieur et Domérien)[END_REF], stratigraphic congruence between phylogenetic tree and stratigraphic occurrences of the taxa is relevant to evaluate tree robustness [START_REF] Rouget | Reconstruction phylogénétique chez les ammonites : confrontation des approches cladistique et stratigraphique[END_REF]. Consistency indices have been created to assess the congruence between the tree and the occurrences of taxa in the fossil record. None of these indices has received unanimous support. We use the Stratigraphic Consistency Index [START_REF] Huelsenbeck | Comparing the straigraphic record to estimates phylogenetic analysis[END_REF] which has the advantage of being based on the relative position of occurrences of taxa in the fossil record rather than on absolute ages which were not available. SCI is affected by factors such as the inference accuracy, tree balance, sampling intensities and the taxonomic status of the OTUs [START_REF] Sidall | Stratigraphic Indices in the Balance: A Reply to Hitchin and Benton[END_REF][START_REF] Wagner | Age rank: clade rank metrics -sampling, taxonomy, and the meaning of "stratigraphic consistency[END_REF][START_REF] Lelièvre | Temporal information, fossil record and phylogeny[END_REF]). Here, we use it to compare the resulting trees of the two analyses (i.e. with and without ontogenetic information). We expect that the higher SCI indicates the best inference and thus if our new approach helps in resolving the phylogeny. To go further, we also compare two interpretations of cladograms consistent with stratigraphy by proposing ancestor-descendant relationships and counting gaps. This recalls stratocladistics [START_REF] Fisher | Stratocladistics: Integrating Temporal Data and Character Data in Phylogenetic Inference[END_REF]) as ancestor-descendant relationships are proposed to reduce stratigraphic debt. A major difference is that we do not use these relationships or stratigraphic debt to find most parsimonious trees but only to compare MPTs obtained with the two different analyses (i.e. with and without ontogenetic information). As it is impossible to estimate absolute ages of appearances of taxa, the unit of time is the ammonite subzone.

Testing dependences in amaltheids coding scheme

Detecting dependences between characters is a challenging investigation. In the literature, two approaches have been tried: before the analysis (e.g. O'Keefe and [START_REF] O'keefe | Inferring and testing hypotheses of cladistic character dependence by using character compatability[END_REF][START_REF] Maglia | Identifying Character Non-Independence in Phylogenetic Data Using Data Mining Techniques[END_REF]after (e.g. Felsenstein 1985b;[START_REF] Maddison | A method for testing the correlated evolution of two binary characters: Are gains or losses concentrated on certain branches of a phylogenetic tree?[END_REF][START_REF] Cheverud | The quantitative assessment of phylogenetic constraints in comparative analyses: Sexual dimorphism in body weight among primates[END_REF][START_REF] Abouheif | A method for testing the assumption of phylogenetic independence in comparative data[END_REF]. A covariation may be due either to common history and/or to a relation of dependence. The problem of addressing character dependences after conducting the analysis is that clades on the tree can be based on character dependences rather than on congruence of independent characters. In this case, investigating for dependence is fully biased. If dependence relationships are investigated before the analysis and no covariation is observed, no relation of dependences can be suspected between characters under consideration. If two characters are dependent, we expect them to covary highly. Thus, in every pair of characters coding ontogeny, we performed tests. For two discrete characters, we performed χ² tests; for two continuous characters, we used correlation tests and for cases of one continuous and one discrete character, we performed ANOVAs.

RESULTS & DISCUSSION

Are Ontogenetic Variations of Features Dependent or Not?

Over the 91 pairs of characters coding ontogeny, 50 tests could be performed by respecting assumptions of the tests. 17 pairs of characters over the 50 show a significant covariation (i.e. p-values < 0.05), this is more than would be expected if all characters were independent and only a few would have been correlated by chance alone. However, this result confirms that the different features mostly have independent variations in ontogeny and, thus, have to be coded separately. As noted by [START_REF] Maddison | The Unsolved Challenge to Phylogenetic Correlation Tests for Categorical Characters[END_REF], investigating correlation involving discrete characters is challenging because they usually evolved only a few times. Thus they are unsuitable for usual statistics (e.g. Pagel's test) which will conclude that a correlation between two traits exists whereas coincidence followed by co-inheritance may easily explain the pattern. Over the 17 pairs of characters showing significant covariation, only five pairs transform enough times (more than 4) to ensure that the dependence is meaningful. These five have been kept in the analysis because no hypotheses based on shell morphogenesis or any other a priori argument could explain these relationships. We assume that their covariations are based on shared evolutionary history.

As the problem of detecting whether a covariation results from congruence or dependence is still unresolved, we prefer a priori arguments which are independent of the dataset. Here for example, we investigated the relationship between starting and ending of the Gibbosum (table 2; online appendix 6: http://dx.doi.org/10.5061/dryad.0c1p0). The a priori study of these timings allowed us to conclude that starts and ends were dependent for several taxa but not for A.

bechteri. We built character 20 in order to express both variation between taxa and the changing relation of dependences between starting and ending of the Gibbosum stage. This coding scheme allows us to describe a fragmentation event of the module composed by these two parameters between nodes 14 and 15.

Does Including Ontogenetic Information Increase the Robustness of the Phylogeny of Amaltheidae?

The analysis with ontogenetic information (i.e. analysis a) results in three MPTs (Fig. 5a). The analysis without ontogenetic information results in one MPT (Fig. 5b). Both results are included in a biostratigraphic scheme based on the literature (Fig. 5). The two cladograms present several topological differences. The major one concerns relations between species between node 1 and 9 on both trees a and b.

Tree a has better indices (i.e. CI, RI and RC) than tree b (table 3), but the differences remain insufficient to conclude which is the more accurate of the ontogeny-derived matrices. For both trees a and b, bootstrap supports are relatively weak. However, mean support of tree a (i.e. 66.2) is higher than for tree b (i.e. 58.8).

The stratigraphic congruence is greater using ontogenetic information (SCI = 0.77) than without (SCI = 0.61). It could indicate that tree a is better than tree b even if both values are low. However, this index is sensitive to the tree balance [START_REF] Sidall | Stratigraphic Indices in the Balance: A Reply to Hitchin and Benton[END_REF][START_REF] Wagner | Age rank: clade rank metrics -sampling, taxonomy, and the meaning of "stratigraphic consistency[END_REF][START_REF] Lelièvre | Temporal information, fossil record and phylogeny[END_REF] which is different for trees a (4 balanced nodes) and b (6 balanced nodes). Thus, SCI of tree b decreases in comparison to tree a. Finally, tree a minimizes unsampled representative with a length of 6.5 subzones compared to tree b with 16 subzones (Fig. 6, Tab. 4). Tree a is thus much more consistent with stratigraphy. To conclude, even if all indices are quite close to each other, they are all better for tree a which displays a higher robustness in comparison to tree b. Thus, for the amaltheids our method improves the quality of the phylogenetic hypothesis.

The type of growth (i.e. saturated or linear) and the sign of the slope have a high RI suggesting that the ontogenetic pattern of variation of Uw and WbWh has a powerful phylogenetic signal (Tab. 5). However, refining the coding scheme of Uw with growth rate both for linear model and saturating growth law provided very low RIs. This could be due either to the model used which does not adequately fit the data, or to the lack of phylogenetic signal of these characters. Uw coded on the adult has a higher RI than the mean RI of all characters coding Uw with our method.

However, the character Uw σ1 which tries to code the same information as Uw adult has a greater RI than the latter. This shows that, even if only the adult stage needs to be coded, modelling ontogenetic trajectory and coding the σ1 is better than just calculating the mean of adult specimens' values.

The RI of the character WbWh in adults is very weak (Tab. 5). By including the ontogenetic dimension, RIs of the three characters (σ1, k SGL, k linear) are higher.

For this shape parameter, ontogeny has to be taken into account to extract a relevant phylogenetic signal.

Finally, ribbing frequency in adults (analysis b, Tab. 5) has a slightly higher RI than Ribs σ1 (analysis a, Tab. 5). However, the growth rate (Ribs k, analysis a, Tab.5) has a greater RI. This result suggests that concerning ribbing frequency, the phylogenetic signal is higher in the rate of expression during ontogeny rather than in absolute value of ribbing frequency. This emphasizes that trajectory can be more relevant than its products for phylogenetic reconstruction.

Heterochrony and the Evolution of Ontogeny

The method herein proposed is not disconnected from the classic formalisation of heterochronies (e.g. [START_REF] Gould | Ontogeny and Phylogeny[END_REF][START_REF] Alberch | Size and shape in ontogeny and phylogeny[END_REF][START_REF] Alba | Shape and Stage in Heterochronic Models[END_REF]. [START_REF] Alberch | Size and shape in ontogeny and phylogeny[END_REF] defined the different types of heterochronies and the relationships between these and the controlling parameter (see tab. 1 in [START_REF] Alberch | Size and shape in ontogeny and phylogeny[END_REF]). We propose here a similar table (Tab. 6) depicting how to recognize them on ontogenetic trajectories, that is to say not only the controlling parameter but also the potential inferred variation in all parameters used according to the two models in our study.

The evolution of tubercles exhibits several heterochronies (Fig. 7). Tubercles appear at node 9 which includes taxa usually included in Amaltheus margaritatus and Pleuroceras. It consists of small tubercles developed at the middle of each rib, the socalled Perlatum stage [START_REF] Frentzen | Ontogenie, Phylogenie und Systematik der Amaltheen des Lias Delta Südwestdeutschlands[END_REF]). This stage is expressed early during ontogeny (char. 17(1)). Starting from node 10, the Perlatum stage is followed by a second tuberculated stage which consists of strong tubercles (hypermorphosis, char. 18(1)) and extends up to an average diameter of 60 mm (char. 20(0)). We called this stage the Gibbosum stage [START_REF] Frentzen | Ontogenie, Phylogenie und Systematik der Amaltheen des Lias Delta Südwestdeutschlands[END_REF], even if our interpretation of secondary homology leads us to consider that the Gibbosum stage overlaps the Coronatum and Spinosum stages of [START_REF] Frentzen | Ontogenie, Phylogenie und Systematik der Amaltheen des Lias Delta Südwestdeutschlands[END_REF]. The relative strength of this stage changes through nodes 12 and 13. First, a cyclic pattern of strength appears with a period of approximately six ribs (char. 19(2)). Then, this pattern becomes stronger (node 13) and results in one strong tubercle every six ribs (char. 19(3)). At node 14, the Gibbosum stage extends through almost the entire ontogeny up to a diameter of 80 mm (char. 20(3)). After the extension of the Gibbosum stage, it will decrease at node 38 through a post-displacement leading to the beginning of the tuberculation at a diameter of 35 mm (char. 20( 4)). This post-displacement makes a clear disjunction between the stages Perlatum and Gibbosum stages. At node 16, the Gibbosum stage disappears (char. 18(0)) and the Perlatum stage extends further in the ontogeny (17(2)). Finally, the Perlatum stage extends into the entire ontogeny at node 18 (char.

16(3)).

Including Ontogeny Reveals New Clades and New Evolutionary History

Amaltheid phylogenetic relationships have been proposed in several works (e.g. [START_REF] Frentzen | Ontogenie, Phylogenie und Systematik der Amaltheen des Lias Delta Südwestdeutschlands[END_REF][START_REF] Howarth | A monograph of the ammonites of the liassic family Amaltheidae in Britain[END_REF][START_REF] Dagis | Late Pliensbachian ammonites (Amaltheidae) of the North Siberia[END_REF][START_REF] Mattéi | Application de méthodes d'analyse globale à l'étude des Amaltheidae du bassin sédimentaire des Causses (Carixien supérieur et Domérien)[END_REF][START_REF] Meister | Ontogenèse et évolution des Amaltheidae (Ammonoidea)[END_REF]. As in many ammonoid groups, relationships within the Amaltheidae have been produced using a stratophenetic approach. Only one tree formalized as a cladogram, but drawn by hand and poorly resolved, has been so far published [START_REF] Hardy | Distribution phylogénétique des extinctions dans le registre fossile: apports à la compréhension de la dynamique de la biodiversité[END_REF]. agreement with paleobiogeographic reconstruction between provinces in the Pliensbachian [START_REF] Dera | Ammonite paleobiogeography during the Pliensbachian-Toarcian crisis (Early Jurassic) reflecting paleoclimate, eustasy, and extinctions[END_REF]. The Boreal domain is isolated from the NW European one during the Spinatum Zone, leading to the differentiation of the Arctic province. The monophyly of the Siberian species confirms that amaltheids were cosmopolitan during the Margaritatus Zone, and then evolved independently in the Boreal and NW European domains.

CONCLUSION

Both theoretical and empirical arguments support the idea of including ontogenetic data as accurately as possible in phylogenies and avoiding artificial discretization of ontogeny. The results showed that our method results in a tree with better retention index, bootstrap supports and fit to stratigraphy. Few pairs of characters significantly covary showing the relevance of including ontogenetic variations in coding schemes. Classic parameters of ammonite shell shape, usually considered to be very homoplastic are less subject to homoplasy when taking ontogeny into account. The method proposed here provides tools for coding a variety of morphological traits, whether discrete or continuous and to extract a high level of information from ontogeny. This method can be used with all taxa. It will be particularly useful when ontogenetic feature variations seem determinant in a group's evolution (e.g. arthropods) and for groups in which coding ontogeny with above-mentioned methods is challenging (e.g. molluscs, brachiopods). Homology has more to do with the path followed than the destination reached.

We used classic models discussed in [START_REF] Alberch | Size and shape in ontogeny and phylogeny[END_REF] on classic ammonite features to produce new characters. Linear ontogenetic trajectories were obviously best described by linear regressions. Saturating growth law was well-suited for several shape parameters because amaltheids show a very variable phase before reaching stable values in late ontogeny as evoked by several authors (e.g. [START_REF] Meister | Ontogenèse et évolution des Amaltheidae (Ammonoidea)[END_REF]). However, as noted by [START_REF] Klingenberg | Heterochrony and allometry: the analysis of evolutionary change in ontogeny[END_REF], none of [START_REF] Alberch | Size and shape in ontogeny and phylogeny[END_REF] parameters match to parameters from other classic growth functions like logistic or Gompertz functions. The selection of the growth functions is thus a key step of the method which will determine the information extracted from the raw ontogenetic data and used for the phylogenetic inference. These growth models have mainly been established because of good fit to data. Subsequently, a large literature has attempted to describe new growth models with more biological meaning. In mollusks for example, new models try to explain the mechanical bases of shell formations (e.g. [START_REF] Moulton | Mechanical growth and morphogenesis of seashells[END_REF]). More generally, [START_REF] West | A general model for ontogenetic growth[END_REF] developed a model based on energy needs between existing and new tissues. Next steps will be to find most meaningful models to use in phylogenetic inference. It seems obvious that using models with a biological base may provide coded parameters closer to what we consider to be a good homology hypothesis. This opens very exciting insights to associate ontogeny, phylogeny and biological/physical constraints in studies of shapes.

Young G., Bird J. 1828. A geological survey of the Yorkshire Coast: describing the strata and fossils occurring between the Humber and the Tees, from the German Ocean to the Plain of York. 2nd edition. Kirby, Whitby. One should note that the two morphological traits show different variation through ontogeny. Even one character, here the tuberculation, can show different variation in its own trajectory. This justifies the coding of ontogenetic trajectories for each morphological trait and that heterochronic trends can be different even in one ontogenetic trajectory. The module experiences fragmentation or integration in the evolution of the ingroup. We use a stepmatrix to code the whole module (online appendix 5: http://morphobank.org/permalink/?P1271).

number of chevrons number of ribs

We treat the number of chevrons divided by the number of ribs which corresponds to a number of divisions Note: Correlated morphological traits that have been combined to provide independent characters. Character numbers correspond to the analysis a (online appendix 2: http://dx.doi.org/10.5061/dryad.0c1p0); remarks give a short explanation of the correlation. Note: Counts of ghost and taxa lineages for phylogenetic interpretations a' and b' (Fig. 6) rounded to the nearest 0.5. Note: Consistency Index (CI) and Retention Index (RI) for characters coding the umbilical width (Uw), the whorl section shape (WbWh) and ribbing frequency (Ribbing) both for analyses a (with ontogeny) and b (without ontogeny). Note: Summary of variant parameters for classic heterochronies with the two models used in this study (i.e. linear growth and saturating growth law). α: onset, β: offset, σ0: shape at onset, σ1: shape at offset, k: growth rate.

-

  The second matrix (i.e. matrix b) excludes the ontogenetic information (online appendix 4: http://purl.org/phylo/treebase/phylows/study/TB2:S16472?x-access-code=2c3cb8ceba8b4a3fe755da29ff1e1713&format=html). The characters that express ontogeny in the first matrix have been replaced by a coding of the adult stage morphology based on the same data. The total number of characters is thus reduced to 22. To make the reading easier, this second matrix is called matrix b, is involved in analysis b and leads to tree b. Both matrices and illustrations of characters are available on MorphoBank website (O'Leary and Kaufman 2012; online appendix 5: http://morphobank.org/permalink/?P1271).Coding of Ontogenetic Trajectories of Continuous Characters -Ontogenetic trajectories of the continuous characters are described from measurements of specimens selected to cover the maximum range of size and ontogenetic shape variation. Regressions have been performed on continuous character data using two different growth laws: linear growth law (Eq. 1) and saturating growth law (Eq. 2).The best fitting model is retained in further analysis. Every ontogenetic stage is treated separately. ܻ = ݇ ܽ + ߪ0 Equation 1 Equation 1. Linear growth law. σ0: values of Y (shape) at the beginning of the stage, k: growth rate. ܻ = ߪ1(1 -ܾ݁ ି(ି∝ሻ ሻ Equation 2 Equation 2. Saturating growth law. σ1: values of Y (shape) when a (age) tends to the infinity which corresponds to the final value of the character, α: size at the beginning of the stage, b: equal to 1 or -1, its sign determine if the function is increasing (+) or decreasing (-), k: growth rate.

Figures captionsFigure 1 .

 1 Figures captions

Figure 2 .

 2 Figure 2. Three ontogenetic trajectories and the corresponding coding scheme of the

Figure 3 .

 3 Figure 3. Ontogenetic trajectories of three types of characters: a. binary, b. multistate

Figure 4 .

 4 Figure 4. Logic chart of the method of coding ontogeny. Parameters from examples

Figure 5 .

 5 Figure 5. Most parsimonious trees for analysis with (a) and without (b) considering

Figure 6 .

 6 Figure 6. Phylogenetic interpretations a' and b' of trees a and b (Fig. 4). Ghost and

Figure 7 .

 7 Figure 7. Subset of tree a showing transformations of tuberculation at nodes and the

Table 1 .

 1 Title: Details on the ingroup. Note: Names of the 24 taxa which comprise the ingroup and the number of specimens used in the study. In the column "Id", "incl." means that specimens have been included within the OTU above.

	Id	Taxa	Authors and years	Number of specimens
	1	Amaltheus bifurcus	Howarth 1958	23
	incl.	Amaltheus rectiradius	Mattéi 1985
	2	Amaltheus stokesi	(Sowerby 1818)	52
	3	Amaltheus talrosei	(Repin 1968 in Efimova et al. 1968)	29
	4	Amaltheus subbifurcus	(Repin 1968 in Efimova et al. 1968)	6
	incl.	Amaltheus sensibilis	Dagis 1976
	5 6 7 8 incl. 9 incl. 10 11 12 13 14	Amaltheus repressus Amaltheus conspectus Amaltheus viligaensis Amaltheus wertheri Amaltheus tenuis Amauroceras ferruginum other species of Amauroceras Amaltheus subnodosus Amaltheus striatus Amaltheus gloriosus Amaltheus gloriosus morph. W Amaltheus gibbosus	Dagis 1976 Dagis 1976 (Tuchkov 1954) (Lange 1932) (Simpson 1855) (Young and Bird 1828) Howarth 1955 Hyatt 1867 (Schlotheim 1820) Mattéi 1985	5 17 25 37 47 157 45 61 54 68	http://sysbio.oxfordjournals.org/ Downloaded from
	incl. 15 16 17 18 incl. incl.	Amaltheus postremus Amaltheus salebrosus Pleuroceras bechteri Pleuroceras transiens Pleuroceras solare Pleuroceras solare solitarium Pleuroceras solare trapezoidiforme	Mattéi 1985 Hyatt 1867 (Frentzen 1937) (Frentzen 1937) (Phillips 1829) (Simpson 1855) (Maubeuge 1951)	14 18 12 34	at UPMC on June 20, 2016
	19	Pleuroceras quadratum	Howarth 1958	2
	20	Pleuroceras apyrenum	(S. Buckman 1911)	7
	21	Pleuroceras spinatum	(Bruguière 1789)	43
	22	Pleuroceras hawskerense	(Young and Bird 1828)	13
	23	Pleuroceras paucicostatum	Howarth 1958	3
	24	Pleuroceras yeovilense	Howarth 1958	16

Table 2 .

 2 Title: Features correlations.

	Character	Feature 1	Feature 2	Remarks
		Uw growth rate	Uw values at the
	5	for linear growth	begining of the	The parameters are perfectly covarying
		model (k)	ontogeny (σ0)
				Buckman's law: strength of ornamentation
	6-8	whorl breadth	ornamentation strength	correlates negatively with the degree of shell compression (Buckman 1892; Westermann 1966; Guex et al. 2003;
				Hammer and Bucher 2005)
		onset of Gibbosum	offset of Gibbosum
	20	stage (i.e. complex	stage (i.e. complex
		tuberculation)	tuberculation)

Table 3 .

 3 Title: Homoplasy in trees. Consistency Index (CI), Retention Index (RI) and Rescaled Consistency Index (RC) for trees resulting from analyses a and b, respectively with and without including ontogeny.

		CI	RI	RC
	Tree a	0.7020	0.8808	0.6183
	Tree b	0.6484	0.8703	0.5643
	Note:

Table 4 .

 4 Title: Counts of ghost and taxa lineages.

		Ghost taxa Ghost lineage Total gap
	Tree a'	5.5	1	6.5
	Tree b'	11	5	16

Table 5 .

 5 Title: Comparison of homoplasy between analyses with and without ontogeny.

		Uw	CI	RI	WbWh	CI	RI	Ribbing	CI	RI
		Uw σ1	0,512 0,776 WbWh σ1	0,62	0,719 Ribs σ1	0,317 0,389
		Uw k SGL	0,742 0,281 WbWh k SGL 0,317	0,317 Ribs k SGL 0,502 0,518
	With ontogeny	Uw k linear	0,844	0	WbWh k linear	0,967	0,485
	(analysis a)	Type of growth	0,5	0,8	Type of growth	0,5	0,8
		Slope of Uw	1	1
		Mean	0,6495	0,5 Mean	0,601 0,58025 Mean	0,4095 0,4535
	Only
	adult (analysis	Uw	0,403 0,672 WbWh	0,276	0,211 Ribs	0,324 0,401
	b)

Table 6 .

 6 Title: Models and heterochrony.

		Linear growth	Saturating growth
	Pre displacement	α ↓ + σ1 ↑	α ↓
	Post displacement	α ↑ + σ1 ↓	α ↑ + σ1 ↓
	Progenesis	β ↓ + σ1 ↓	β ↓ + σ1 ↓
	Hypermorphosis	β ↑ + σ1 ↑	β ↑
	Acceleration	k ↑ + σ1 ↑	k ↑ + σ1 ↑
	Neoteny	k ↓ + σ1 ↓	k ↓ + σ1 ↓
	Pre formation	σ0 ↑	σ0 ↑
	Post formation	σ0 ↓	σ0 ↓

Proportional gigantism every (α & β + k) ↑ + σ1 ↑ every (α & β + k) ↑ + σ1 ↑ Proportional dwarfism every (α & β + k) ↓ + σ1 ↓ every (α & β + k) ↓ + σ1 ↓

at UPMC on June 20, 2016 http://sysbio.oxfordjournals.org/ Downloaded from

Downloaded from

ACKNOWLEDGMENTS

We would like to thank Pr. Martin Pickford and Pr. David Horne who kindly reviewed and improved the English of the manuscript. We are grateful to Dieter at UPMC on June 20, 2016 http://sysbio.oxfordjournals.org/ Downloaded from Korn, Peter Wagner, Norman MacLeod (AE), Frank Anderson (EIC) and Thomas Near (EIC) for the very useful comments they provided on an earlier draft of the manuscript.

FUNDING

This work was supported by the MNHN, the UPMC and the French ministry of research through the funding of my PhD of which this study is a part.

Three ontogenetic trajectories of the umbilical width (Uw) and the tuberculation for the species: A. gibbosus, A. salebrosum salebrosus and A. bechteri. U: umbilical length, D: diameter, P: Perlatum stage (black bars), C: Gibbosum stage (grey bars). One should note that the two morphological traits show different variation through ontogeny. Even one character, here the tuberculation, can show different variation in its own trajectory. This justifies the coding of ontogenetic trajectories for each morphological trait and that heterochronic trends can be different even in one ontogenetic trajectory. 297x420mm (300 x 300 DPI) at UPMC on June 20, 2016 http://sysbio.oxfordjournals.org/ Downloaded from Three ontogenetic trajectories and the corresponding coding scheme of the umbilical width (Uw) for the species: A. gibbosus, A. talrosei and P. solare. U: umbilical length, D: diameter, k: growth rate, σ1: final value of Uw. Growth laws are used to modelled ontogenetic trajectories; this allows the extraction of more information about the morphological traits. 297x420mm (300 x 300 DPI) at UPMC on June 20, 2016 http://sysbio.oxfordjournals.org/ Downloaded from Ontogenetic trajectories of three types of characters: a. binary, b. multistate and c. continuous. 0, 1, 2: discrete states, σ0: initial value of the trait, σ1: final value of the trait, α: age of onset, β: age of offset. 276x363mm (300 x 300 DPI) at UPMC on June 20, 2016 http://sysbio.oxfordjournals.org/ Downloaded from Logic chart of the method of coding ontogeny. Parameters from examples are those of models herein used to represent ontogenetic trajectories. 276x363mm (300 x 300 DPI) at UPMC on June 20, 2016 http://sysbio.oxfordjournals.org/ Downloaded from Most parsimonious trees for analysis with (a) and without (b) considering ontogeny. Bootstrap supports are indicated in italics. Trees are presented in a biostratigraphic schemes. 276x363mm (300 x 300 DPI) at UPMC on June 20, 2016 http://sysbio.oxfordjournals.org/ Downloaded from Phylogenetic interpretations a' and b' of trees a and b (Fig. 4). Ghost and taxa lineages are represented with dashed lines. 276x363mm (300 x 300 DPI) at UPMC on June 20, 2016 http://sysbio.oxfordjournals.org/ Downloaded from Subset of tree a showing transformations of tuberculation at nodes and the corresponding heterochronies using Alberch et al. (1979) nomenclature. 297x420mm (300 x 300 DPI) at UPMC on June 20, 2016 http://sysbio.oxfordjournals.org/

Consequently, comparisons are difficult. Most of the nodes are identical. All works agree with the placement of A. bifurcus at the base of amaltheids. A. stokesi is usually invoked as the ancestor of NW European species (i.e. node 7 in tree A, Fig. 5a).

However, these previous works did not take into account Boreal species (i.e. node 3 in tree A, Fig. 5a). The only work which includes the latter [START_REF] Dagis | Late Pliensbachian ammonites (Amaltheidae) of the North Siberia[END_REF]) proposes a superspecies regrouping A. bifurcus and A. stokesi giving rise to a part of the Boreal species, the clade regrouping A. wertheri and representatives of the genus Amauroceras as well as NW European amaltheids. Our tree proposes a clade (node 7) placing A. wertheri and representatives of the genus Amauroceras (node 8) with classic NW European amaltheids (node 9). A. stokesi is placed at the base of a clade (node 2) with all Boreal species (node 3). However, the weakness of support of node 2 implies that A. stokesi should be placed in a trifurcation with nodes 3 and 7. Moreover, optimisation of characters at node 1 is very similar to A. stokesi coding. This widespread and common species may be the ancestor of both the Boreal and NW European species.

A novelty in this phylogeny is the monophyly of the Boreal clade (node 3) that refutes the hypothesis of two or three origination events from A. margaritatus proposed by [START_REF] Dagis | Late Pliensbachian ammonites (Amaltheidae) of the North Siberia[END_REF]. This clade results from the coding of ontogeny as it is only supported by synapomorphies from the characters herein proposed (i.e. characters 1, 3, 4, 14 and 15). The major difference between the Boreal (node 3) and NW European clades (node 7) consists in their growth patterns of UW and WbWh which are respectively linear versus saturated. The monophyly of the Boreal clade is in SUPPLEMENTARY MATERIAL Supplementary material, including data files and/or online-only appendices, can be found:

-in the Dryad data repository at http://datadryad.org, doi: 10.5061/dryad.0c1p0 for appendices 1, 2 and 6 -from the treebase website at http://purl.org/phylo/treebase/phylows/study/TB2:S16472?x-access-code=2c3cb8ceba8b4a3fe755da29ff1e1713&format=html for appendices 3 and 4 -from the Morphobank website, project 1271: http://morphobank.org/permalink/?P1271 for appendix 5.