Evolution of posture in amniotes–Diving into the trabecular architecture of the femoral head

Extant amniotes show remarkable postural diversity. Broadly speaking, limbs with erect (strongly adducted, more vertically oriented) posture are found in mammals that are particularly heavy (graviportal) or show good running skills (cursorial), while crouched (highly flexed) limbs are found in taxa with more generalized locomotion. In Reptilia, crocodylians have a “semi‐erect” (somewhat adducted) posture, birds have more crouched limbs and lepidosaurs have sprawling (well‐abducted) limbs. Both synapsids and reptiles underwent a postural transition from sprawling to more erect limbs during the Mesozoic Era. In Reptilia, this postural change is prominent among archosauriforms in the Triassic Period. However, limb posture in many key Triassic taxa remains poorly known. In Synapsida, the chronology of this transition is less clear, and competing hypotheses exist. On land, the limb bones are subject to various stresses related to body support that partly shape their external and internal morphology. Indeed, bone trabeculae (lattice‐like bony struts that form the spongy bone tissue) tend to orient themselves along lines of force. Here, we study the link between femoral posture and the femoral trabecular architecture using phylogenetic generalized least squares. We show that microanatomical parameters measured on bone cubes extracted from the femoral head of a sample of amniote femora depend strongly on body mass, but not on femoral posture or lifestyle. We reconstruct ancestral states of femoral posture and various microanatomical parameters to study the “sprawling‐to‐erect” transition in reptiles and synapsids, and obtain conflicting results. We tentatively infer femoral posture in several hypothetical ancestors using phylogenetic flexible discriminant analysis from maximum likelihood estimates of the microanatomical parameters. In general, the trabecular network of the femoral head is not a good indicator of femoral posture. However, ancestral state reconstruction methods hold great promise for advancing our understanding of the evolution of posture in amniotes.


| INTRODUC TI ON
Limbs first evolved during the Devonian Period in aquatic organisms, such as Acanthostega, and presumably were first used for locomotion in shallow waters and to rest on the bottom (Coates, 1996;Laurin, 2010;Molnar et al., 2021). In later organisms, these primordial limbs experienced new functional constraints inherent to land environments, related in particular to the support of body weight.
These constraints shaped the limbs' external and internal morphology, and thereby, the first land vertebrates developed novel locomotor and postural strategies favouring access to various ecological niches and contributing to the evolutionary success of tetrapods.
The first terrestrial vertebrates were quadrupedal with a sprawling limb posture, that is, the stylopod was held horizontally with the distal end pointing laterally (Bakker, 1971;Charig et al., 1972). A recent study combining palaeoichnology (the study of ancient tracks) and robotics supported this inference with quantitative methods for the first time in an early stem amniote (Nyakatura et al., 2019). Today, extant amniote taxa (reptiles and mammals) present a great diversity of postures and locomotor modes associated with a morphological and microanatomical disparity.
Both reptiles and synapsids underwent a postural transition during the Mesozoic Era. The first parasagittally locomoting erect bipedal amniotes seem to have evolved convergently during the Triassic in the archosaurian clades Avemetatarsalia and Pseudosuchia (Cuff et al., 2022;Hutchinson, 2006;Kubo & Benton, 2009;Sereno, 1991;Sullivan, 2015). Parasagittally locomoting erect bipedalism is often cited as a key element in the success of Avemetatarsalia (e.g. Kubo & Kubo, 2012). However, the steps that led to this bipedal state remain enigmatic and more conclusively determining the locomotion and posture adopted by many Triassic taxa, such as the archosauriform Euparkeria, involve considerable obstacles and ambiguities (e.g. Bishop et al., 2020). Although it is accepted that synapsids experienced a postural transition from approximately transversely oriented to more parasagittally oriented limbs, the timing of this transition has been widely debated without reaching a consensus. Some authors (Jenkins, 1973;Jenkins & Parrington, 1976;Pridmore, 1985;Sereno, 2006) have argued that early mammals had already acquired a more parasagittal limb posture and gait by the Late Triassic/Early Jurassic based on anatomical evidence, while others (Gambaryan & Kielan-Jaworowska, 1997;Kielan-Jaworowska & Hurum, 2006) favoured the hypothesis of a later acquisition in early therians based on both anatomy and ichnology. More erect limbs may have existed as early as the Permian. Indeed, several lineages of Permo-Triassic therapsids, such as Anomodontia and Cynodontia, have been described as having had a "semi-erect" posture based on anatomical and biomechanical evidence (Blob, 2001;Fahn-Lai et al., 2018;Fröbisch, 2006). Today, posture in mammals and in older stem taxa, such as Dimetrodon, still raises many questions, triggering numerous studies that enrich our knowledge of the evolution of locomotion in synapsids (Brocklehurst et al., 2022;Jones et al., 2021;Regnault et al., 2020).
Limb bones support the weight of the body and are therefore subject to various forces that partly shape their external and internal form during ontogeny. Yet bone trabeculae tend to orient themselves along the lines of force: this is known as Wolff's law, or the trajectorial theory (Wolff, 1893). Before this law was formulated, von Meyer (1867) had interpreted the spongy structures of the human femoral head in the light of Culmann's remarks, who had noted a certain similarity with the internal tension and compression lines of a crane. Since these early observations, the functional role of trabecular bone, that is, its ability to distribute mechanical stresses to improve strength (Currey, 2013), has received increasing attention.
Methods of ancestral state reconstruction aim to infer the characteristics of ancestral taxa from the characteristics of their descendants using models of character evolution (Pagel, 1999). They have been extensively used to study vertebrate evolution: from inference of metabolic rate (Benton, 2021;Legendre et al., 2016) and lifestyle (Canoville & Laurin, 2010) to "resurrection" of genetic sequences (Chang et al., 2002;Thornton, 2004), diet reconstruction (Brocklehurst, 2016) and soft tissue studies (Campione et al., 2020;Tsai et al., 2018). The use of these methods for postural issues is rarer (Buchwitz et al., 2021;Grinham et al., 2019), and, to our knowledge, they have never been applied to the femoral trabecular architecture in the context of the postural transitions in amniotes during the Mesozoic.
In this study, we use phylogenetic comparative methods, such as phylogenetic generalized least squares (PGLS), to better characterize the relationship between femoral posture and the femoral head trabecular architecture in amniotes. Given previous studies highlighting that larger taxa tend to have greater bone volume and thicker trabeculae (Doube et al., 2011;Houssaye et al., 2016), we expect to find similar scaling relationships with our sample. Also, larger taxa exhibit more erect (adducted, upright) limbs, which reduces weight-related stresses (Biewener, 1990), and this could reduce anisotropy (Doube et al., 2011). As our sample contains taxa with a variety of femoral postures (from erect to sprawling), we expect to find differences in anisotropy between postural groups.
We use ancestral state reconstruction methods in a novel manner to infer the ancestral condition of various microanatomical parameters measured on bone cubes extracted from the femoral head of a sample of extant amniote taxa, but also to more directly infer ancestral posture at nodes of interest in the context of the "sprawling-to-erect" transitions in reptiles and synapsids. This study not only sheds light on the relationship between posture and microanatomy in amniotes but also aims to demonstrate the relevance of ancestral state reconstruction approaches to postural issues in vertebrates.

| Biological sample
To conduct the statistical analyses in this study, we compiled a set of microanatomical data measured on bone cubes extracted from the femoral head of a large number of amniote taxa. We retrieved the list of taxa from Doube et al. (2011) and enriched it with new taxa, notably squamates and turtles, which were not previously included.
However, we did not retain all mammal taxa, as they were overrepresented in the study by Doube et al. (2011). Indeed, if we consider extant species diversity, there are about 5000 extant species of mammals (Upham et al., 2019), compared to about 15 000 extant species of reptiles: 10 000 species of birds (Jetz et al., 2012), about 5000 species of limbed squamates (Brandley et al., 2008), about 350 species of turtles (Thomson et al., 2021) and about 25 species of crocodylians (Brochu, 2003). Our sample is composed of 93 amniote species for which femoral posture is known (Table 1). These include 57 mammal species and 36 reptile species (24 birds, 6 squamates, 3 crocodylians and 3 turtles). Each species is represented by one individual. We tried to build our sample to be as representative as possible of the taxonomic and postural diversity of amniotes. Our sample contains three extinct taxa: Raphus cucullatus, Pezophaps solitaria and Dinornis sp. The latter became extinct recently (within the last five centuries).

| Postural categories
We defined four postural categories: sprawling, crouched, erect and "semi-erect." In sprawling taxa (lepidosaurs, turtles, but also monotremes, such as Ornithorhynchus), the femur extends laterally, while in crouched taxa (small mammals and small birds), it points more or less anteriorly. In erect taxa (large mammals and large birds), the femur is held more vertically under the body. Finally, the "semierect" posture of crocodylians can be regarded as intermediate between sprawling and erect. We are aware of the limitations of such a classification. For example, that limb posture in amniotes is more of a continuum than well-defined postural categories, or that the term "semi-erect" is evolutionarily and functionally ambiguous, but these categories remain practical in the framework of comparative phylogenetic studies.

| Data acquisition
We strictly followed the protocol by Doube et al. (2011) for extracting new bone cubes in order to obtain comparable data. To validate the protocol, we retrieved some of the bone cubes from  (Doube et al., 2010) following the fit sphere routine (Doube et al., 2011). We extracted the largest cube that could be contained in a sphere fitted by least squares in the femoral head ( Figure 1).
First, the scans of the femur were resliced in ImageJ to position the bone vertically. Secondly, we placed six points to delineate the volume of the femoral head: two points to delineate the upper and lower parts of the femoral head, and four additional points (anterior, posterior, medial and lateral) on the slice halfway between the two slices comprising the first two points. Once extracted, the bone cubes were binarized using IsoData thresholding, purified (with BoneJ), eroded (in ImageJ: Process > Binary), purified again and dilated (in ImageJ: Process > Binary). For a detailed description of the procedure for extracting and processing bone cube data, see Doube et al. (2010). We then measured six parameters with BoneJ ( Figure 1): BV/TV, the bone volume fraction, corresponding to the number of bone voxels divided by the total number of voxels in the cube; BS/TV, the bone surface area per unit volume, defined as the bone surface area, obtained by summing the surface area of all the triangles constituting a 3D mesh of the trabecular network, divided by the total volume of the cube; Tb.Th, the mean trabecular thickness; Tb.Sp, the mean trabecular spacing; Conn.D, the connectivity density, which corresponds to the number of trabeculae divided by the total volume of the cube; DA, the degree of anisotropy, reflecting a more or less pronounced trabecular orientation (0 < DA < 1; 0 indicating no orientation and 1 parallel trabeculae).
The new unprocessed bone cubes are publicly available at https:// doi.org/10.5061/dryad.83bk3 j9x2. Ketcham and Ryan (2004) noted that texture orientations could be over-represented towards the edges and corners of a cubic volume. However, our study is not affected by this "edge and corner bias." Indeed, in BoneJ 1.4.3, anisotropy is calculated using the mean intercept length (MIL) method from sampling spheres randomly distributed inside the image stack (see Doube et al., 2010). These spheres are never closer to the sides of the image than their radius (M. Doube, personal communication

| Principal component analysis
We performed a principal component analysis (PCA) on the microanatomical parameters. PCA creates new uncorrelated variables from the original variables and projects them into a space whose dimensions, called principal components (PCs), successively maximize the variance (Jolliffe, 2022). This analysis was performed using the PCA function in the R package FactorMineR (Lê et al., 2008).

| Building reference time-calibrated phylogenies
In this study, we carried out several phylogenetically informed statistical analyses. Therefore, we needed time-calibrated phylogenetic trees comprising the amniote taxa in our sample. We . The trees were assembled in R using the phytools package (Revell, 2012) and TreePar (Stadler, 2011). We set the divergence between mammals and reptiles at 330 Myr based on Didier and Laurin (2020). For later divergence times, we used the online resource TimeTree (Kumar et al., 2017). We set the divergence between Lepidosauria and other reptiles at 281 Myr. We considered turtles as the sister taxon to Archosauria (birds and crocodylians), as suggested by recent molecular studies (Chiari et al., 2012;Irisarri et al., 2017), and set the age of the turtle+archosaur clade (Archelosauria) at 261 Myr.
We set the divergence between Astrochelys radiata and Chelonoidis carbonaria (Testudinidae) and between Chelydra serpentina and was initially set at 77 Myr (adjusted time), but this was older than the age of the Palaeognathae node for some of the trees in our phylogenetic tree set. We therefore decided to branch Dinornis halfway between the Palaeognathae and Tinamidae nodes for each tree. We then removed Tinamus major from our trees as it was not part of our analysed amniote sample. Finally, we set the divergence between respectively. The trees in Newick tree format are available as supporting information (Appendix S1).

| Phylogenetic signal
We tested the phylogenetic signal in femoral posture. This was done using the delta statistic (Borges et al., 2019), which is based on the uncertainty associated with ancestral state reconstruction. The delta statistic is proportional to the phylogenetic signal and inversely proportional to the uncertainty at the nodes. We tested the phylogenetic signal in femoral posture with our 100 trees and calculated a p-value each time based on 10 random permutations of femoral posture at the tips of the tree branches. We also searched for a phylogenetic signal in the aforementioned microanatomical parameters using the phylosig function of the R package phytools (Revell, 2012), which computes the K-statistic (Blomberg et al., 2003). A strong phylogenetic signal, implying that closely related species are more similar to each other than would be expected under a Brownian model of evolution, is indicated by a K-statistic greater than 1. A weaker phylogenetic signal than that expected under a Brownian model of evolution is indicated by a K-statistic less than 1. The function also performs a randomization test to derive a p-value (1000 randomizations). We calculated K for the 100 trees in our phylogenetic tree set.

| Phylogenetic generalized least squares
All the microanatomical parameters presented above have been see Table 1), but also differ greatly in terms of body mass (from 2.33 g in Suncus etruscus to 3.22 t in Elaphas maximus). To explore these relationships with our sample, we designed several linear models in R using the gls function from the package nlme (Pinheiro et al., 2021).
The function fits a linear model using generalized least squares (GLS). It allows the model errors to be correlated and/or have unequal variances. It is especially appropriate in the case of phylogenetic dependence. Here the expected covariance between two taxa for a given trait is the evolution of that trait under a Brownian model during the time between the root and their last common ancestor. PGLS was conducted with all 100 phylogenetic trees.

| Ancestral state reconstruction
We used the ace and fastAnc functions in the R packages ape  (Figure 2). In reptiles, the Triassic divergence between avemetatarsalians and pseudosuchians (Archosauria) also corresponds to the appearance of the first erect forms within these two clades (Hutchinson, 2006). In synapsids, the divergence between monotremes and therians (Mammalia) in the Early Jurassic, and that between metatherians and eutherians (Theria) in the Late Jurassic, are important because they represent two hypothetical origins of more parasagittal limbs in this clade (Kielan-Jaworowska & Hurum, 2006;Pridmore, 1985). For the microanatomical parameters, we constructed a distance matrix to -1993-52). Bone cubes were extracted following the fit sphere routine (Doube et al., 2011). We extracted the largest cube that could be contained in a sphere fitted by least squares in the femoral head. The microanatomical parameters were measured in ImageJ with BoneJ 1.4.3 (Doube et al., 2010).

F I G U R E 1 Proximal femur of Gypaetus barbatus (MNHN-ZO-AC
compare the inferred values at the nodes of interest to our extant sample. Node states and values were reconstructed for the 100 phylogenetic trees at our disposal.

| Phylogenetic flexible discriminant analysis
We PFDA includes a phylogenetic variance-covariance matrix whose terms reflect the shared evolutionary time between two given taxa.
The matrix is multiplied by lambda (Pagel, 1999), which is optimized to minimize the error of the model. We performed leave-one-out cross-validation with our 100 phylogenetic trees to identify the combination of microanatomical variables that best explains femoral posture. PFDA cannot make inferences at nodes. Instead, we inferred femoral posture in three hypothetical common ancestors to which we assigned the values of the microanatomical parameters derived from the ancestral state reconstruction and which we branched 0.1 Myr before each node of interest (branch length = 0.1 Myr; see Appendix S1). Tables S2-S4).

| Phylogenetic signal
The delta statistic for femoral posture ranges from 3.428 to 26.676 and is always significantly higher than the randomized deltas (p-values < 0.001), indicating that femoral posture conveys a strong phylogenetic signal ( Table 2). The K-statistics for the microanatomical parameters are all significantly different from those with a random distribution ( Table 2). However, K is always less than 1, indicating that closely related species are more distinct from each other than would be expected with a Brownian model of evolution.

| Interaction with microanatomy, posture, body mass and lifestyle
The allometric relationships of the microanatomical parameters, as shown by PGLS with our amniote sample (Table 3) Table S5). However, none of the microanatomical parameters are associated with lifestyle or femoral posture (Table 3).

F I G U R E 2
Simplified cladogram showing the relationships between the main amniote taxa studied. Stars indicate nodes of interest for ancestral reconstruction: 1, Archosauria; 2, Mammalia; 3, Theria.

| Postural inferences at nodes
We do not present here the best PFDA model because the crossvalidation results associated with it are very unbalanced between the postural categories (Appendix S2: Table S8). Instead, we show the model with the most balanced cross-validation results for each femoral posture (Table 4) Note: Values are means obtained from 100 phylogenetic trees. Asterisks indicate mean p-values that are statistically significant: one asterisk (*) indicates a mean p-value that is below or equal to 0.05; two asterisks (**) indicate a mean p-value that is below or equal to 0.01; three asterisks (***) indicate a mean p-value that is below or equal to 0.001. pass 50% of correct classification (57% and 50%, respectively).
"Semi-erect" species are always misclassified. We were still able to make postural inferences for the hypothetical ancestral taxa. All hypothetical ancestors are always inferred to be sprawlers ( Figure 5),  Table 3). This may be due to the fact that PCA does not take phylogeny into account, unlike PGLS. Indeed, femoral posture carries a strong phylogenetic signal (Table 2). Furthermore, all these parameters are significantly associated with body mass (Table 3). Indeed, the trabecular thickness (Tb.Th) and the trabecular spacing (Tb.Sp) increase with body mass, while the bone area per TA B L E 3 Effect of body mass, lifestyle and femoral posture on the microanatomical parameters. Note: Body mass is log10 transformed. Asterisks indicate mean p-values that are statistically significant: one asterisk (*) indicates a mean p-value that is below or equal to 0.05; two asterisks (**) indicate a mean p-value that is below or equal to 0.01; three asterisks (***) indicate a mean p-value that is below or equal to 0.001.  Table S5). Previous studies identified similar scaling patterns within mammals and birds (Doube et al., 2011), but also reptiles (Plasse et al., 2019). Here we show that these allometric relationships appear to hold when considering amniotes as a whole. However, this is not surprising since we partially reused data from Doube et al. (2011).

Independent variable Mean chi-square (min-max) Mean p-value (min-max)
Thus, the postural patterns revealed by PCA could be spurious and reflect both the effect of the phylogeny and body mass. Therefore, the microanatomical parameters measured in 3D at the femoral head may not be appropriate proxies to characterize femoral posture once phylogeny and body mass are taken into account, at least with our sample and methods. This may be related to the location where the bone cubes were extracted, that is, the centre of the femoral head. Indeed, several studies of primates have shown that the core of an epiphysis carries less functional signal than the peripheral (subchondral) areas (Cazenave et al., 2021;Georgiou et al., 2020).
This could also be related to the presence of a secondary ossification centre in the femoral head of mammals and lepidosaurs (Carter et al., 1998;Xie et al., 2020). It would be interesting in the future to test for a functional signal with bone volumes from other locations (e.g. metaphysis). In addition, it should be mentioned that trabecular bone in the proximal femur depends, among other things, on the loading conditions at the hip. These vary according to locomotion or posture, but can also vary between taxa within the same postural group (Christen et al., 2014;Ryan & Ketcham, 2005). How this may affect our results requires further investigation.

| Palaeobiological implications
A sprawling posture is the most probable at the Archosauria node based on ancestral state reconstruction (Figure 4; Appendix S2: Table S6). This is consistent with the reconstructed values of the microanatomical parameters at this node that place the ancestor of archosaurs close to Caiman crocodilus (Appendix S2: Table S7), although there is no significant association between the microanatomical parameters and femoral posture (Table 3) of postural transition for archosaurs (Cuff et al., 2022;Kubo & Benton, 2009;Sereno, 1991;Sullivan, 2015). Archosauria may have exhibited a mosaic of characters, as is the case for earlier Triassic taxa, such as Euparkeria capensis, an archosauriform (Demuth et al., 2020), and as posterior probabilities seem to suggest (a crouched posture is the second most probable posture at this node; see Appendix S2: Figure S4 and Table S6). A key issue is that we reconstructed ancestral states and values from extant and recently extinct species only. Crocodylians and birds in particular are very different from what the ancestral archosaur probably was like. Thus, our results may be partially subject to a "pull of the recent" bias. However, the inclusion of fossils with "known" posture in the sample could help to alleviate this issue. Indeed, the posture of some extinct species can be reliably estimated, or "known" well enough (i.e. general consensus in the field, based on good evidence, even if indirect), to accept them as useful "facts" (data) for further analyses. For example, we now "know" that non-avian theropod dinosaurs had more erect limbs than birds (Gatesy, 1991). Similarly, we "know" that sauropod dinosaurs had columnar limbs to reduce weight constraints (Hutchinson, 2021). Including such taxa in the models would certainly help to refine the reconstructions.
The most probable posture at the Mammalia and Theria nodes is crouched, implying that more parasagittal limbs appeared early in the evolution of synapsids, with the first mammals and potentially before. However, these results are in complete contradiction with the maximum likelihood estimates of the microanatomical parameters at these nodes. The latter place the bone microarchitecture of the ancestor of mammals closer to Tiliqua scincoides and the ancestor of therians closer to Basiliscus basiliscus, two squamates with sprawling limbs (Appendix S2: Table S7). In addition to supporting a late origin of parasagittal gait, this implies a potential convergence in the acquisition of more parasagittal femora. However, insofar as we were unable to demonstrate an association between the bone microarchitecture and femoral posture with our amniote sample,

| Inference model
Phylogenetic flexible discriminant analysis does not perform better than PCA in discriminating between femoral postures. The best combination of microanatomical parameters achieved by cross-validation yields a model rate of correct classification of about 65%, but very contrasting results between the postural categories (Appendix S2: Table S8). The main source of error is that some erect species are modelled as crouched. The model presented in the Results section reduces this problem somewhat, but an imbalance persists (Table 4).
A larger sample size could probably reduce the residual error further, but it also appears that the postural signal is weak for the 3D microanatomical parameters. Postural inferences with hypothetical ancestral taxa are consistent with the reconstructed ancestral microanatomical parameters and support a late postural transition in mammals. However, these results should be viewed with caution with regard to the low robustness of the model, which is most likely due to the lack of association between the microanatomical parameters and femoral posture ( Table 3).

| CON CLUS IONS
None of the microanatomical parameters measured on 3D bone cubes extracted from the femoral head of a sample of amniote taxa, that is, the bone volume fraction (BV/TV), the bone surface area However, these results should be taken with caution given the lack of a statistically-validated relationship between the microanatomical data and femoral posture.
The growing interest in postural issues in extant and extinct animals in recent decades has improved our knowledge of vertebrate evolution and augurs exciting future discoveries. In this paper, we show that, despite the weak association between femoral posture and the trabecular architecture of the femoral head in amniotes, ancestral state reconstruction methods applied to postural problems are promising. They deserve a more prominent place in the study of postural transitions, especially in the case of Mesozoic amniotes.

ACK N OWLED G M ENTS
We thank Joséphine Lesur, Géraldine Veron, Jacques Cuisin, to Mathilde Aladini for her kind review of the manuscript and to our two anonymous referees, whose insightful comments helped to improve the quality of this study.

FU N D I N G I N FO R M ATI O N
This work was supported by the doctoral programme Interfaces pour le vivant (IPV), with the cooperation of Sorbonne Université.

CO N FLI C T O F I NTE R E S T S TATE M E NT
The authors declare that they have no conflicts of interest.

DATA AVA I L A B I L I T Y S TAT E M E N T
The data that support the findings of this study are publicly available on the Dryad Digital Repository: https://doi.org/10.5061/ dryad.83bk3 j9x2.