LETTER. Evolution of the snake body form reveals homoplasy in amniote Hox gene function

doi:10.108/nature102 Evolution of the snake body form reveals homoplasy in amniote Hox gene function Jason J. Head 1 & P. David Polly 2 Hox genes regulate regionalization of the axial skeleton in vertebrates 1 7, and changes in their expression have been proposed to be a fundamental mechanism driving the evolution of new body forms 8 1. The origin of the snake-like body form, with its deregionalized pre-cloacal axial skeleton, has been explained as either homogenization of Hox gene expression domains 9, or retention of standard vertebrate Hox domains with alteration of downstream expression that suppresses development of distinct regions 10 1. Both models assume a highly regionalized ancestor, but the extent of deregionalization of the primaxial domain (vertebrae, dorsal ribs) of the skeleton in snake-like body forms has never been analysed. Here we combine geometric morphometrics and maximum-likelihood analysis to show that the pre-cloacal primaxial domain of elongate, limb-reduced lizards and snakes is not deregionalized compared with limbed taxa, and that the phylogenetic structure of primaxial morphology in reptiles does not support a loss of regionalization in the evolution of snakes. We demonstrate that morphometric regional boundaries correspond to mapped gene expression domains in snakes, suggesting that their primaxial domain is patterned by a normally functional Hox code. Comparison of primaxial osteology in fossil and modern amniotes with Hox gene distributions within Amniota indicates that a functional, sequentially expressed Hox code patterned a subtle morphological gradient along the anterior posterior axis in stem members of amniote clades and extant lizards, including snakes. The highly regionalized skeletons of extant archosaurs and mammals result from independent evolution in the Hox code and do not represent ancestral conditions for clades with snake-like body forms. The developmental origin of snakes is best explained by decoupling of the primaxial and abaxial domains and by increases in somite number 15, not by changes in the function of primaxial Hox genes 9,10. In Amniota (Mammalia 1 Reptilia), Hox genes are expressed sequentially in the somitic mesoderm, resulting in a series of distinct anatomical regions along the anterior posterior axis of the vertebral column. Anatomical boundaries coincide with anterior borders of Hox gene expression or areas where expression of two genes overlaps,5. In Squamata (lizards, including snakes), the pre-cloacal vertebral column is less differentiated than in highly regionalized mammals and extant archosaurs. Vertebrae possessing synapophyses that articulate with dorsal ribs extend from the first post-atlanto-axial vertebra to the sacrum in many squamates 16 (Fig. 1 and Extended Data Fig. 1a). In limbed lizards, two regional boundaries, cervical thoracic and thoracic lumbar, are known to correspond to Hox gene expression patterns 10,12. These boundaries are not recognized in snakes and snake-like squamates, which are considered to possess deregionalized 11 axial skeletons with increased numbers of vertebrae and ribs and reduction or loss of limbs and sternum 16. Two conflicting hypotheses have been proposed for the role of Hox genes in the evolution of the snake-like axial skeleton on the basis of domain mapping and transgenic expression 9 1. In the first hypothesis, loss of regionalization is caused by upstream modification of Hox expression and (or resulting in) a shift of HoxC6 and HoxC8 domains, which are associated with the thoracic region in mammals and archosaurs, forward to the first post-atlanto-axial vertebral position 9. In the second, loss of regionalization in snakes is caused not by shifts in the boundaries of Hox expression, but by downstream changes in cis-regulation 10 1.Both hypotheses invoke modifications to Hox activity in the paraxial mesoderm, which forms the primaxial skeleton (vertebrae, dorsal ribs 17 ), but axial regionalization is at least partially dependent upon spatial relationships with the abaxial skeleton (limbs, sternum 17,18 ), which is derived from lateral plate mesoderm and has independent Hox regulation,5. The extent to which the primaxial domain has become homogenized in clades with snake-like body forms has, to our knowledge, never been examined in a comparative phylogenetic context. To test the hypothesis that the primaxial skeleton of snakes and snakelike squamates is deregionalized relative to limbed amniotes, we performed geometric morphometric analysis on vertebral morphology to measure quantitatively intracolumnar shape variance and combined it with a maximum-likelihood estimation of the number of regions and positions of regional boundaries in the pre-cloacal skeleton of representative taxa based on segmented linear regression (Methods, Extended Data Fig. 2 and Extended Data Table 1). To capture the axial gradient in shape, we placed 12 homologous landmarks on vertebrae along the pre-cloacal skeleton 19 (Fig. 1, Methods and Extended Data Table 2). We included comparisons with Alligator mississippiensis and Mus musculus because Hox expression boundaries in their regionalized axial skeletons are well documented 2 6,20 (Methods and Extended Data Fig. ). We found that total intracolumnar shape variance in the primaxial domain was substantially less in all squamates than in Alligator (Fig. 2a). Mean variance was significantly lower in snake-like squamates than in a b 6 5 7 2 1 Figure 1 Morphological variation in the pre-cloacal vertebral column of limbed lizards and snakes. a, b, Pogona vitticeps (a) and Pantherophis guttatus (b) pre-cloacal vertebrae in anterior view, from left: first post-atlanto-axial, mid-trunk and posterior-most pre-cloacal vertebrae. Numbered landmarks shown on mid-trunk vertebra of Pogona were used to characterize vertebral shape (Extended Data Table 2). 12 9 10 11 8 1 Department of Earth and Atmospheric Sciences and Nebraska State Museum of Natural History, University of Nebraska Lincoln, Lincoln, Nebraska 68588-00, USA. 2 Departments of Geological Sciences, Biology and Anthropology, Indiana University, Bloomington, Indiana 705-105, USA. 8 6 N AT U R E V O L 5 2 0 2 A P R I L 2 0 1 5

RESEARCH b Variance a 0.02 Intracolumnar shape variance 0.018 0.01 0.01 0.006 0.002 Snake-like Limbed c Alligator mississippiensis Cordylus giganteus Eumeces schneideri Corucia zebrata Amphisbaeana alba Tupinambis teguixin Neusticurus rudis Iguana iguana Physignathus cocincinus Pogona vitticeps Pseudopus apodus Heloderma suspectum Varanus bengalensis Typhlops punctatus Rena dulcis Anilius scytale Tropidophis canus Xenopeltis unicolor Loxocemus bicolor Leiopython albertisii Morelia spilota Python regius Charina bottae Lichanura trivirgata Candoia carinata Eryx johnii Boa constrictor Corallus caninus Eunectes notaeus Calabaria reinhardtii Acrantophis dumerili Sanzinia madagascarensis Cylindrophis ruffus Uropeltis woodmasoni Acrochordus granulatus Oxyrhabdium leporinum Crotalus ruber Agkistrodon contortix Daboia russelli Cerberus rynchops Erpeton tentaculatum AIC c 260.02 16.99 1.7 19.98 16.99 1.78 150.69 150.52 18.05 16.09 Madagascarophis colubrina Actractaspis irregularis Hydrophis semperi Micrurus fulvius Naja nigricollis Heterodon platyrhinos 1. 1.62 Waglerophis merremii Thamnophis sirtalis Boiga irregularis Ptyas mucosus Coluber constrictor Pantherophis guttatus 1.7 1 10 20 0 0 50 60 70 80 90 100 Per cent body length RS 1.0 d Evolutionary models of regionalization 2 2 2 0.6 0.6 0.0 0.0 2 2 2 Figure 2 Regional boundaries, evolutionary models of regional changes, and intracolumnar variance. a, Consensus phylogeny of selected taxa. Terminal branch lengths are scaled to intracolumnar shape variance. b, Box plot of intracolumnar variances in limbed (n 5 10 specimens) and snake-like (n 5 2 specimens) squamates. c, Regional boundaries in primaxial domains for each taxon subsampled at 5% intervals. Coloured cells represent vertebrae in limbed taxa (see Methods). Nevertheless, there was no consistent difference in shape variance between limbed and snake-like squamates, and the range of variances in snake-like squamates exceeds the range in limbed taxa (Fig. 2b). Several snake taxa have greater intracolumnar shape variance than any of the sampled limbed squamates, even after standardizing for differences in the number of vertebrae. The number of primaxial regions in snakes and snake-like lizards does not systematically differ from limbed squamates and Alligator (Fig. 2c, d). Three or four regions were found in all taxa, irrespective of the presence or absence of limbs or the total number of vertebrae. The origin of snakelike body forms was not associated with a reduction in the number of regions when we tested four competing evolutionary models of deregionalization (Fig. 2d, Methods and Extended Data Table ). The model in which limbed squamates and Alligator have four regions and this is reduced to three in snake-like taxa was no better supported than the hypothesis that all squamates share three regions and Alligator has four (relative support 5 0.6 for both hypotheses). Models in which snake-like taxa have two regions and limbed taxa have either three or four regions different regions of the best-fit model, for which corrected Akaike information criterion (AIC c ) scores are given. Taxa in bold are snakes and snake-like squamates. d, Best-fit distribution of regions (left) compared with four models for evolutionary changes in regionalization. Each is depicted by the number of regions (2 to ) expected in limbed and snake-like taxa. RS, relative support (Methods). had virtually no support (relative support 5 0). These results indicate that, although average shape variance within and between individual primaxial regions of snake-like taxa is less than in their limbed relatives, there was no reduction in the number of regions or changes in the relative location of regional boundaries associated with the origin of snakes or snake-like taxa. To determine if morphometric regional boundaries are associated with Hox expression, we fit regional models to entire pre-cloacal primaxial skeletons of representative taxa and compared best-fit results to mapped Hox expression boundaries,,20. Four regions were found in most taxa (Extended Data Fig. and Extended Data Table ). In Mus and Alligator, four-region models recovered morphometric boundaries that either exactly matched Hox expression boundaries for regional transitions or were within one vertebral position of boundaries (Fig. and Supplementary Information). In the snake Pantherophis guttatus, the best-fit regional boundaries correspond to Hox expression domains that govern the cervical thoracic transition and the thoracic region in limbed amniotes (Fig. ). The 2 A P R I L 2 0 1 5 V O L 5 2 0 N AT U R E 8 7

RESEARCH LETTER HoxB5 HoxA5 HoxD HoxC HoxB Mus musculus Alligator mississippiensis Pantherophis guttatus HoxC8 HoxA7 HoxC6 HoxB5 HoxA5 HoxD HoxC HoxB C C C5 C6 C7 C8 C9 T1 T2 T T T5 T6 T7 T8 T9 T10 L1 L2 L L L5 HoxC8 HoxA7 HoxC6 Hox9 HoxC8 HoxA7 HoxC6 Hox10 C C C5 C6 C7 T1 T2 T T T5 T6 T7 T8 T9 T10 T11 V V10 V9 T12 T1 L1 L2 L L L5 L6 HoxA10 Figure Correspondence between Hox expression domains and morphometric boundaries for four-region models of primaxial regionalization. Coloured bars represent expression domains for Mus,20 and Alligator 20, and the range of anterior expression boundaries for Pantherophis 10 12. Hox expression domains for the thoracic lumbar transition in Alligator have not yet been mapped 20. Cells represent individual vertebrae in each region for the entire pre-cloacal/pre-sacral vertebral column in each taxon. Cell colours represent morphometric regions. Grey bars indicate regions of overlap between genes and morphometric regions. C, cervical; L, lumbar; T, thoracic; V, vertebra. V181 V22 boundary between the first and second regions occurs between postatlanto-axial vertebrae 10 11, which corresponds to the diffuse anterior expression boundary of HoxC6 (ref. 10). This correspondence was also recovered in limbed squamates (Supplementary Information). The boundary between the second and third morphological regions occurs between post-axial vertebrae 9 50, which falls within the diffuse anterior expression boundary of HoxC8 (ref. 10) and is only five vertebrae posterior to the anterior expression region for HoxA7 (ref. 10). The boundary between the third and fourth morphological regions in Pantherophis occurs between post-axial vertebrae 180 181, which is anterior to expression of HoxA10 and C10 near somites 195 to 210 (refs 10, 12). This apparent discrepancy may arise from individual, possibly sex-linked 21, differences in vertebral number between our sample and Hox-mapped specimens (Supplementary Information). Regardless, the fit of the fourth morphometric regional boundary to Hox10 expression boundaries was statistically indistinguishable from the best-fit model (Methods and Extended Data Fig. 5). Regional transitions in Pantherophis and the other squamates in our study are gradational, unlike the more abrupt boundaries of Mus or Alligator, in which differences in the presence, articulation or fusion of vertebral processes and ribs add to regional differentiation (Extended Data Fig. 1 and Fig. ). Both boundary types emerge from Hox gene expression. HoxC8 expression is associated with relative sizes of the neural arch and apophyses 20, and the expression of this gene is graded over a series of segments in snakes rather than having a sharply defined boundary as in limbed taxa 10. Topographic correlation between Hox expression boundaries and morphometric regions in Pantherophis (Fig. ) is evidence that Hox domains in the snake primaxial skeleton are functional, even though regional boundaries lack discrete structural changes in processes and ribs. Paleozoic amniotes, including stem members of Reptilia and Mammalia, possessed a comparatively homogeneous vertebral column and dorsal rib cage that lacked the distinct regional boundaries found in mammals and extant archosaurs, even though mapped domains for extant reptiles, mammals and anamniotes,10,20,22,2 indicate that a fully regionalized and functional set of Hox genes along the anterior posterior axis was ancestral for Amniota (Fig. ). Our evidence indicates that the specific functions of Hox genes in patterning the regionalized primaxial domain of mammals and extant archosaurs are probably homoplastic Age (Myr ago) 0 80 160 20 20 Cen. Mesozoic Pal. Seymouria Captorhinus Alligator Uromastyx Lichanura 2 1 Anterior Hox 6 5 7 8 9 10 Posterior Figure Time-calibrated phylogeny of selected extant and fossil amniotes, illustrating pre-cloacal and pre-sacral primaxial skeletal regionalization and the generalized ancestral amniote pattern of Hox expression. Node numbers label the total clades for Amniota (1), Reptilia (2) and Mammalia (), and the crown clades for Reptilia () and Squamata (5). Archosauria is 5 Thrinaxodon represented by Alligator, crown Mammalia is represented by Mus. Coloured bars represent relative positions of anterior expression domain boundaries for Hox 10 paralogues along the anterior posterior axis in Amniota. See Supplementary Information for data sources. Cen., Cenozoic; Pal., Palaeozoic. Daggers indicate fossil taxa. Mus 8 8 N AT U R E V O L 5 2 0 2 A P R I L 2 0 1 5

RESEARCH exaptations of an ancestral Hox code whose original function in amniotes was regulation of subtle gradations in primaxial morphology. This pattern is conserved in snakes and most other squamates (Fig. ). We conclude that the origin of snakes was not associated with deregionalization of the primaxial domain, but rather with loss of the abaxial skeleton and increases in vertebral numbers independent of primaxial Hox domain boundaries. We recommend that future studies of the origin of the snake-like body form concentrate on elucidating the developmental mechanisms by which the primaxial and abaxial skeletons become dissociated 18,2. The lateral somitic frontier is recognized as the boundary between the two developmental systems 25, and we hypothesize that future mapping of that frontier will demonstrate that major innovations in squamate body form are the result of abaxial modification whereas primaxial regionalization is conserved across amniotes, and potentially across vertebrates. Online Content Methods, along with any additional Extended Data display items andsource Data, are available in the online version of the paper; references unique to these sections appear only in the online paper. Received 0 July; accepted November 201. Published online 5 January 2015. 1. Favier, B. & Dollé, P. Developmental functions of mammalian Hox genes. Mol. Hum. Reprod., 115 11 (1997). 2. Burke, A. C., Nelson, C. E., Morgan, B. A. & Tabin, C. Hox genes and the evolution of vertebrate axial morphology. Development 121, 6 (1995).. Wellik, D. M. & Capecchi, M. R. Hox10 and Hox11 genes are required to globally pattern the mammalian skeleton. Science 01, 6 67 (200).. Wellik, D. M. Hox patterning of the vertebrate skeleton. Dev. Dyn. 26, 25 26 (2007). 5. McIntyre, D. C. et al. Hox patterning of the vertebrate rib cage. Development 1, 2981 2989 (2007). 6. Carapuço, M., Novoa, A., Bobola, N. & Mallo, M. Hox genes specify vertebral types in the presomitic mesoderm. Genes Dev. 19, 2116 2121 (2005). 7. Vinagre, T. et al. Evidence for a myotomal Hox/Myf cascade governing nonautonomous control of rib specification with global vertebral domains. Dev. Cell 18, 655 661 (2010). 8. Gaunt, S. J. Conservation in the Hox code during morphological evolution. Int. J. Dev. Biol. 8, 59 552 (199). 9. Cohn, M. J. & Tickle, C. Developmental basis of limblessness and axial patterning in snakes. Nature 99, 7 79 (1999). 10. Woltering, J. M. et al. Axial patterning in snakes and caecilians: evidence for an alternative interpretation of the Hox code. Dev. Biol. 2, 82 89 (2009). 11. Woltering, J. M. From lizard to snake; behind the evolution of an extreme body plan. Curr. Genomics 1, 289 299 (2012). 12. Di-Poï, N. et al. Changes in Hox genes structure and function during the evolution of the squamate body plan. Nature 6, 99 10 (2010). 1. Guerreiro, I. et al. Role of a polymorphism in a Hox/Pax-responsive enhancer in the evolution of the vertebrate spine. Proc. Natl Acad. Sci. USA 110, 10682 10686 (201). 1. Müller, J. et al. Homeotic effects, somitogenesis and the evolution of vertebral numbers in recent and fossil amniotes. Proc. Natl Acad. Sci. USA 107, 2118 212 (2010). 15. Gomez, C. et al. Control of segment number in vertebrate embryos. Nature 5, 5 9 (2008). 16. Hoffstetter, R. & Gasc, J. P. in Biology of the Reptilia (eds Gans, C., Bellair, A. d A. & Parsons, T. S.) Vol. 1, 201 10 (Academic, 1969). 17. Burke, A. C. & Nowicki, J. L. A new view of patterning domains in the vertebrate mesoderm. Dev. Cell, 159 165 (200). 18. Buchholtz, E. A. & Stepien, C. C. Anatomical transformation in mammals: developmental origin of aberrant cervical anatomy in tree sloths. Evol. Dev. 11, 69 79 (2009). 19. Polly, P. D. & Head, J. J. in Morphometrics Applications in Biology and Paleontology (ed. Elewa, A. M. T.) 197 222 (Springer, 200). 20. Mansfield, J. H. & Abzhanov, A. Hox expression in the American Alligator and evolution of archosaurian axial patterning. J. Exper. Zool. B Mol. Dev. Evol. 1, 629 6 (2010). 21. Shine, R. Vertebral numbers in male and female snakes: the roles of natural, sexual, and fecundity selection. J. Evol. Biol. 1, 55 65 (2000). 22. Prince, V. E., Joly, L., Ekker, M. & Ho, R. K. Zebrafish hox genes: genomic organization and modified colinear expression patterns in the trunk. Development 125, 07 20 (1998). 2. Mallo, M., Wellik, D. M. & Deschamps, J. Hox genes and regional patterning of the vertebrate body plan. Dev. Biol., 7 15 (2010). 2. Shearman, R. M. & Burke, A. C. The lateral somatic frontier in ontogeny and phylogeny. J. Exp. Zool. B Mol. Dev. Evol. 12, 60 612 (2009). 25. Nowicki, J. L., Takimoto, R. & Burke, A. C. The lateral somitic frontier: dorso-ventral aspects of anterio-posterior reigonalization in avian embryos. Mech. Dev. 120, 227 20 (200). Supplementary Information is available in the online version of the paper. Acknowledgements We thank K. DeQueiroz, G. Zug, R. McDiarmid, K. Seymour, D. Gower, C. McCarthy, C. Bell, H. Voris, C. J. Cole, P. Holroyd and T. Labedz for specimen access, A. K. Behrensmeyer for access to microscopy facilities, and A. Goswami, K. Johnson, P. Mitteroecker, R. Raff, R. Reisz and M. Rowe for useful comments and discussion. This work was supported in part by a US National Science Foundation Postdoctoral Fellowship in Biological Informatics (DBI-020082) to J.J.H., a Natural Sciences and Engineering Research Council of Canada Discovery Grant to J.J.H., and a US National Science Foundation Grant (EAR-0895) to P.D.P. Author Contributions J.J.H. and P.D.P. designed the study. J.J.H. and P.D.P. collected morphometric data. J.J.H. and P.D.P. conducted morphometric analysis. P.D.P. designed and conducted segmented linear regression and maximum-likelihood analyses. J.J.H. and P.D.P. prepared figures and wrote the manuscript. Author Information Morphometric data have been deposited in Dryad (http:// dx.doi.org/10.5061/dryad.jq285). Reprints and permissions information is available at www.nature.com/reprints. The authors declare no competing financial interests. Readers are welcome to comment on the online version of the paper. Correspondence and requests for materials should be addressed to J.J.H. (jhead2@unl.edu) or P.D.P. (pdpolly@indiana.edu). 2 APRIL 2015 VOL 520 NATURE 89

RESEARCH LETTER METHODS Morphometric analysis. We quantified morphological regionalization using principal component shape variables derived from Procrustes superimposition 26 of two-dimensional landmarks on vertebrae in anterior view 19. We chose a taxonomic sample that covers all major squamate body forms and major clades (n 5 5 specimens; Extended Data Table 1). We selected anterior view because the centrum, neural arch and apophyses could all be identified by homologous landmarks. The landmarkswe selected (Fig. 1 and ExtendedDataTable 2) define theaforementioned structures, and are homologous among sampled squamates. For anatomical regions where distinct dorsal ribs are fused with vertebral apophyses (the ultimate pre-sacral vertebra in Pogona, Physignathus and Cordylus; Fig. 1), landmarks for the diapophysis and parapophysis were placed at the dorsal and ventral edges of points of fusion. In Alligator and Mus, we modified the landmarks for their taxon-specific vertebral morphologies (Extended Data Fig. and Extended Data Table 2; see Supplementary Information for discussion and references). Because vertebrae are approximately bilaterally symmetrical, we digitized only the left side and midline of each specimen 19. We omitted the atlas axis complex from all analyses because it is a distinct anatomical system common to all amniotes. We used two-dimensional landmarks to make our data set more applicable for future analyses of fossil specimens whose breakage and flattening frequently prohibits accurate three-dimensional analysis. Scores from the first five components, which represent more than 90% of shape differences along the anterior posterior axis for all taxa, were used as shape variables for maximum-likelihood analyses of regionalization. To minimize the effects of ontogenetic variation, we only sampled somatically mature specimens for each taxon. Sampling along the anterior posterior axis. For most analyses we used a standardized sampling strategy in which we collected shape data at 5% intervals along the anterior posterior axis beginning with the first post-atlanto-axial vertebra. If a vertebra at a sampling point was pathologically or teratologically malformed, we sampled the next normally shaped element. This strategy facilitates comparisons of regional models between taxa with radically different numbers of vertebrae, but does not allow the correspondence between morphological regions and Hox expression boundaries to be assessed at the level of individual segments. To make direct comparisons between morphometric regions and Hox expression boundaries, we sampled the complete pre-cloacal column for key taxa. Intracolumnar shape variance. We measured intracolumnar shape variation for each individual specimen as the total variance of Procrustes coordinates among the pre-cloacal vertebrae. Total variance is expected to be higher in taxa with more regional differentiation. We used a permutation test to determine whether intracolumnar variance in squamate vertebral shape was significantly different in limbed versus snake-like taxa and in taxa identified as having four versus three regions. To adjust for biases related to imbalance in the number of taxa in each category and non-normal distribution of variances, we used a non-parametric permutation test inwhich the observeddifferenceintheaverage varianceineachgroup was compared to a distribution of the same statistic calculated from 10,000 random permutations of taxa between groups. Limbed taxa had significantly greater intervertebral variance (limbed 5 0.01, snake-like 5 0.0095, P 5 0.007), but taxa with four regions were not significantly more variable than taxa with three regions (four region 5 0.010, three region 5 0.0100, P 5 0.825). Likelihood models of regionalization. Our analysis treats vertebral column regions as a series of morphological gradients. Vertebrae within a region are not expected to be identical: adjoining vertebrae spanning the boundary of two regions may be more similar than each is to its opposite regional end member. Standard cluster analysis is therefore inappropriate because it recovers hierarchical patterns of variation, not gradients of similarity. Our approach uses segmented linear regression (SLR) 27,28 on the first five PC scores to recover gradients of morphology and the breaks between them (Extended Data Fig. 2). In SLR, a series of contiguous regression lines are fit to the data such that each segment has its own slopes and intercepts. Boundaries are estimated by finding the break points that minimize the residual sum of squares, adding an additional parameter to the model for each pair of segments. In our models, each segment of the regression therefore corresponds to a morphological region, its slope(s) describe its shape gradient, and the break points correspond to the regional boundaries. To estimate the number of regions and the positions of regional boundaries, we iteratively fit four classes of model with one, two, three and four segments, respectively, to each vertebral column. The classes correspond to a morphological spectrum from complete deregionalization (one segment) to hyper-regionalized (four segments: cervical, anterior thoracic, posterior thoracic, lumbar). Each class of model has many specific instances that differ in the slope of the regression segments and the position of the boundaries between them (Extended Data Fig. 2). The likelihood of each instance of each model was assessed using a likelihood ratio, which in its general form is: l(x)~ L(h 0jx) ð1þ L(h 1 jx) where l(x) is the likelihood of hypothesis H 0 relative to hypothesis H 1 (the hypotheses in our case are different models of regionalization), L(h 0 jx) is the likelihood of h 0, which are the parameters of the H 0 model given the data (which in our case are the vertebral shape scores), and L(h 1 jx) is the likelihood of the H 1 model parameters. Specifically, we calculated the log- likelihood ratio test statistic, D, for our segmented regressions using the residual sum of squares (RSS) as follows: D~{2ln(l)~nln(S 0 =S 1 ) where l is the likelihood ratio, n is the number of data points (five times the number of vertebrae since we used scores from the first five dimensions of our vertebral shape spaces), and S 0 and S 1 are the RSS for H 0 and H 1, respectively 29. The regression slopes and intercepts were found by exact calculation (the parameters that maximize the likelihood function are the same as those found by least-squares fitting). We used a grid search to calculate the likelihood of every possible set of regional breaks, thus providing us with a complete statistical distribution for testing alternative regional models 29. Model selection using AIC c. The likelihoods of models with different numbers of regions are not directly comparable because the number of parameters differ. Our models have 10k 1 k 2 1 parameters for each of their k regions: one slope and intercept for each of the five dimensions in each region plus one boundary between each region (Extended Data Fig. 2). Our one-region model class has 10 parameters, the two-region class has 21 parameters, the three-region class has 62, and the four-region class has 8. The more parameters a model has, the better it fits the data (when the number of regions increases to equal the number of vertebrae it will always fit the data perfectly). Model comparisons thus require an adjustment for the number of parameters, especially when comparing taxa with different numbers of vertebrae (a 20-region model will fit a 20-vertebrae lizard column perfectly, but it will not fit a 200-vertebrae snake column as well). We used the corrected AIC c to adjust the likelihood ratios by the number of model parameters and data points so that they could be compared between model classes to objectively select the best model of regionalization: n AIC c ~D{2(pz1) ðþ n{p{2 where D is the log-likelihood ratio from equation (2), p is the number of parameters (10k 1 k 2 1 for our study, where k is the number of regions), and n is the number of data points (five times the number of vertebrae in our study). This correction penalizes the log likelihood for each additional parameter and makes the penalty proportionally heavier for smaller data sets. This value is scaled so that the best model is the one with the highest AIC c value. Testing hypotheses of evolutionary changes in regionalization. We assessed the relative support for four competing hypotheses of evolutionary changes in regionalization in squamates and the ancestral state of regionalization in snake-like forms. For each hypothesis, the expected number of regions was mapped onto phylogeny (Fig. 2d). Total support for each hypothesis was estimated as the sum of the AIC c support values for the best corresponding regional model for each taxon (Extended Data Table ). For example, support for the hypothesis that all reptiles have two vertebral regions can be calculated by summing the AIC c values for the best tworegion model of all of species in the analysis. The highest possible support for any such hypothesis occurs when each taxon is assigned the number of regions that is best supported by its own data (Fig. 2d, left bar). The sum of the AIC c values is not meaningful when taxa vary in the number of vertebrae, so we used the data sampled at 5% intervals, which have a maximum summed AIC c support of 28,10.6. Note that, although this measure of total support varies with the number of taxa included in an analysis, the number of taxa is constant across the four hypotheses; relative support for the competing evolutionary hypotheses can therefore be measured as the fractional difference of the summed AIC c values of each model relative to the total AIC c of the best- and worst-supported hypothesis (1.0 5 best, 0.0 5 worst) 0. Comparison of morphometric boundaries to boundaries of Hox expression. Because one of our aims is to determine whether morphological regionalization corresponds to Hox gene expression domains, it is necessary to test statistically whether the morphometric regional boundaries differ from expression boundaries. Our likelihood framework allows the relative support of the best morphometric regional model to be compared to other models. The probability that an alternative set of boundaries differs from the best morphometric model was assessed by counting values in which the fit was better than or equal to the alternative model and normalizing by the number of possible regional models. The resulting P value is the ð2þ

RESEARCH probability that expression boundaries differ from the best regional model (Extended Data Fig. 5). All calculations were performed using Mathematica v.9.0. 26. Rohlf, F. J. & Slice, D. Extensions of the Procrustes method for the optimal superimposition of landmarks. Syst. Biol. 9, 0 59 (1990). 27. Hudson, D. Fitting segmented curves whose join points have to be estimated. J. Am. Stat. Assoc. 61, 1097 1129 (1966). 28. Feder, P. The log likelihood ratio in segmented regression. Ann. Stat., 8 97 (1975). 29. Lerman, P. Fitting segmented regression models by grid search. Appl. Stat. 29, 77 8 (1980). 0. Claeskens, G. & Hjort, N. Model Selection and Model Averaging (Cambridge Univ, Press, 2008).

RESEARCH LETTER Extended Data Figure 1 Skeletal morphology and intracolumnar shape variation in the pre-cloacal vertebral column of limbed lizards and snakes. a, Skeleton of limbed lizard (Pogona minor) in dorsal view. b, Skeleton of snake (Hypsiglena torquata) in dorsal view. c, Principal component analysis (PCA) ordination of pre-cloacal vertebral shape variables derived from geometric morphometric analysis in a limbed lizard (Pogona vitticeps) based on first two principal components (PC 1 and PC 2). d, PCA ordination of pre-cloacal vertebral shape variables in a snakes (Pantherophis guttatus). Ordination using the first two components describes intracolumnar shape change along the anterior posterior axis of the pre-cloacal vertebral column and explains.90% of overall shape variation.

RESEARCH Extended Data Figure 2 Model fitting with segmented linear regression. a f, A series of regional models were fit to each taxon using a series of segmented linear regressions. In each case vertebral shape variables (orange dots) were regressed onto position in the vertebral column (brown lines). Models differ in both the number of regions and the position of regional boundaries. a f, Two examples are shown for each of two, three and four regions, where the right column shows the best fitting example for each. Red arrows mark the regional boundaries in each example. The slope of each segment (heavy dark line) represents the shape gradient each region and the residual sum of squares (RSS) represents the lack of fit of the model to the data. f, The model with the highest likelihood. The log likelihood of each model is proportional to this model. However, the number of parameters increases with the number of regions, as does the likelihood of the model; therefore corrected Akaike adjustment (AIC c ) is required to select the best model. b,the best model using AIC c. It is the two-region model with the breakpoint 25% along the pre-cloacal vertebral column. This example is based on the first principal component of Eunectes notaeus.

RESEARCH LETTER Extended Data Figure Morphometric landmarks used to quantify primaxial shape variance and regionalization in pre-cloacal vertebrae of Mus and Alligator. a, b, Elements for both Mus (a) and Alligator (b) are, from top to bottom: first post-atlanto-axial vertebrae, third thoracic (Mus) and sixth dorsal vertebrae (Alligator), last lumbar vertebrae. See Extended Data Table 2 and Supplementary Information for description of landmarks and discussion of landmark selection.

RESEARCH Extended Data Figure Best-fit regionalization models for complete pre-cloacal skeletons of Mus, Alligator and select squamates. AIC c scores are reported for the best regional model from each taxon. Taxa in bold are snakes or have snake-like body forms. Cells represent individual vertebrae in each region for the complete pre-cloacal/pre-sacral vertebral column in each taxon. Cell colours represent morphometric regions. C, cervical; L, lumbar; T, thoracic.

RESEARCH LETTER Extended Data Figure 5 Comparison of best-fit four-region model with models fitting morphometric regional boundaries to expression boundaries for Hox10 genes. a, Best-fit model. b, Fit to anterior expression boundaries of HoxA10 and HoxC10 from ref. 12. c, Fit to anterior expression boundary for HoxC10 from ref. 10. d, Fit to posterior expression boundaries of HoxA10 and HoxC10 from ref. 12. Abbreviations are the same as for Fig.. Only the posterior boundaries of Hox10 expression are significantly worse fits than the best-fit model. RSS, residual sum of squares for segmented linear regression. P values are probability that the Hox boundaries differ from the best regional model.

RESEARCH Extended Data Table 1 Examined specimens AMNH, American Museum of Natural History, New York; BMNH-R, The Natural History Museum, London; FMNH, Field Museum of Natural History; IU, Indiana University; ROMV-R, Royal Ontario Museum Recent Vertebrate Collection; TMM, Texas Memorial Museum, University of Texas at Austin; UCMP, University of California Museum of Paleontology; UNL ZM, University of Nebraska Lincoln, Museum of Zoology; USNM, United States National Museum, Smithsonian Institution. * Specimens not used in morphometric analysis.

RESEARCH LETTER Extended Data Table 2 Landmarks and corresponding morphology used in morphometric analysis Landmarks document intracolumnar variation in vertebral shape for squamates, Alligator and Mus. For discussion and references, see Supplementary Information.

RESEARCH Extended Data Table AIC c values for regionalization models Autologous virus isolates HIV-1 envelopes cloned from plasma Dose ID Day post infusion BNC117 IC 50 ( g/ml) BNC117 IC 50 Clone Cloning procedure Vector backbone BNC117 (IC 50; g/ml) Average (geo. mean) 1 mg/kg 2A1 2A 2A Day 0 Day 28 0.90 Day 0 0.11 Day 28.78 Day 0 0.07 Day 28 0.9 5. 1.5 mg/kg 2B1 2B2 2B Day 0 0.78 Day 28 >20 Day 0 >20 Day 28 Day 0 0.20 Day 28 0.0 25.9 1.5 2C2 Day 0 0.9 Day 56 0.0 0.1 2C Day 0 >20 Day 28 >20 No change 10 mg/kg 2C5 Day 0 Day 28 0.09 15.6 167.0 2C5_D0_12 gp120 psviii 0.015 2C5_D0_21 gp120 psviii 0.017 2C5_D0_27 gp120 psviii 0.017 2C5_W_59 gp120 psviii 11.5 2C5_W_22 gp120 psviii 6.77 2C5_W_27 gp120 psviii 7.51 2C5_W_28 gp120 psviii.95 2C5_W_ gp120 psviii 8.758 0.02 7.09 2C1 Day -7 Day 28 0.5 1.78 1.8 2C1_D0_12 gp120 psviii 0.209 2C1_D0_22 gp120 psviii 0.158 2C1_D0_2 gp120 psviii 0.006 2C1_W_12 gp120 psviii 0.0 2C1_W_18 gp120 psviii 0.225 2C1_W_1 gp120 psviii 0.262 0.06 0.1 2D1 Day 0 Day 28 0.68 0.90 1. 2D1_D0_D5 gp160 pcdna.1 0.165 2D1_D0_B.1 gp160 pcdna.1 0.128 2D1_D0_B10 gp160 pcdna.1 0.172 2D1_W_7 gp120 psviii 0.578 2D1_W_0 gp120 psviii 0.501 2D1_W_69 gp120 psviii 0.65 2D1_W_71 gp120 psviii 0.52 0.15 0.52 2D Day 0 0.1 Day 28 0.5 2.7 0 mg/kg 2E1 Day 0 Day 28 0.0 2E1_D0_12 gp160 pcdna.1 0.10 2E1_D0_20 gp160 pcdna.1 0.115 2E1_D0_ gp160 pcdna.1 0.068 2E1_W_2 gp160 pcdna.1 0.01 2E1_W_E1 gp160 pcdna.1 0.590 2E1_W_F6 gp160 pcdna.1 0.96 0.09 0.2 2E2 Day 0 Day 28 0.18 2.2 12. 2E2_D0_A10 gp160 pcdna.1 0.017 2E2_D0_C gp160 pcdna.1 0.010 2E2_D0_E9 gp160 pcdna.1 0.018 2E2_W_B9 gp160 pcdna.1 0.017 2E2_W_C11 gp160 pcdna.1 0.020 2E2_W_D5 gp160 pcdna.1 0.057 0.01 0.0 2E Day 0 0.18 Day 28 1.10 6.1 2E Day 0 0.2 Day 28 2E5 Day 0 0.0 Day 28 Values are for models from one to four morphological regions through the pre-sacral/pre-cloacal vertebral columns of select amniotes sampled at 5% intervals along the anterior posterior axis.

RESEARCH LETTER Extended Data Table AIC c values for regionalization models Values are for models from one to four morphological regions through the complete pre-sacral/pre-cloacal vertebral columns of select amniotes.