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1 Florida State University Libraries Electronic Theses, Treatises and Dissertations The Graduate School 2012 The Ontogeny of Cranial Morphology in Extant Crocodilians and Its Phylogenetic Utility: A Geometric Morphometric Approach Akinobu Watanabe Follow this and additional works at the FSU Digital Library. For more information, please contact lib-ir@fsu.edu

2 THE FLORIDA STATE UNIVERSITY COLLEGE OF ARTS AND SCIENCES THE ONTOGENY OF CRANIAL MORPHOLOGY IN EXTANT CROCODILIANS AND ITS PHYLOGENETIC UTILITY: A GEOMETRIC MORPHOMETRIC APPROACH By AKINOBU WATANABE A Thesis submitted to the Department of Biological Science in partial fulfillment of the requirements for the degree of Master of Science Degree Awarded: Summer Semester, 2012

3 Akinobu Watanabe defended this Thesis on June 21, The members of the supervisory committee were: Gregory M. Erickson Professor Directing Thesis Dennis E. Slice Committee Member Scott J. Steppan Committee Member The Graduate School has verified and approved the above-named committee members, and certifies that the Thesis has been approved in accordance with university requirements. ii

4 To my nephew Yusei Shibata (b. September 9, 2011) and my grandmother Katsu Watanabe (April 7, 1924 December 30, 2010). iii

5 The palm [of victory] shall be gained by the lucky man who traces back the developmental powers of animal bodies to the general powers or direction of life of the entire world. Karl Ernst von Baer, Entwickelungsgeschichte (in Gould 1977, p. 61) The study of form may be descriptive merely, or it may become analytical. We begin by describing the shape of an object in the simple words of common speech: we end by defining it in the precise language of mathematics; and the one method tends to follow the other in strict scientific order and historical continuity. Thus, for instance, the form of the earth, of a raindrop or a rainbow, the shape of the hanging chain, or the path of a stone thrown up into the air, may all be described, however inadequately, in common words; but when we have learned to comprehend and to define the sphere, the catenary, or the parabola, we have made a wonderful and perhaps a manifold advance. The mathematical definition of a form has a quality of precision which was quite lacking in our earlier stage of mere description; it is expressed in few words or in still briefer symbols, and these words or symbols are so pregnant with meaning that thought itself is economized; we are brought by means of it in touch with Galileo s aphorism (as old as Plato, as old as Pythagoras, as old perhaps as the wisdom of the Egyptians), that the Book of Nature is written in characters of Geometry. D Arcy Thompson, On Growth and Form (1961, p. 269) iv

6 ACKNOWLEDGEMENTS This work represents the culmination of not only the knowledge and experience I have acquired during my two years at Florida State University (FSU), but to a great degree, the efforts of many, including my family, friends, and the faculty. Their guidance and assistance have been indispensable for the completion of the thesis in diverse ways. Numerous people deserving of recognition have undoubtedly been left out below. I apologize in advance for anyone whom I have failed to acknowledge here. First and foremost, I thank my family for their continued support for all aspects of my life. Their contribution to my scientific knowledge may have been marginal, but they have taught me perhaps the most important knowledge of all how to strive to be a Good human being. My parents, Kazunobu and Yoshiko Watanabe, have rarely forced me to pursue anything (with the exception of playing the violin, for which I am retrospectively grateful). Instead, they have allowed me to explore and cultivate my own ideas and skills, but always with guidance and support. Likewise, my brother Michi and sister Yuri have shown enormous faculty to deal with the peculiarities associated with my lifestyle and profession for all of these years. I also extend my gratitude to my second family the Erickson lab members. My peers, Matthew Kolmann and Bonnie Garcia have been a constant source of generosity and emotional support. Paul Gignac, a former Erickson lab member, provided several documents, including his grant essays and prospectus, which were extremely helpful. Profound gratitude and respect go to my advisor, Gregory Erickson, whose efforts have gone far beyond what is expected of an academic mentor. For instance, his daily visits while I was hospitalized for pneumothorax is a clear testament to his commitment for insuring the well being of his students. Greg s ability and willingness to support his students is commendable, and I can only hope to possess similar proficiency as a mentor when my time comes. Besides my primary advisor, several faculty members at FSU have greatly contributed to the project and my development as a researcher. As committee members, Dennis Slice and Scott Steppan provided solutions and constructive criticisms for improving my work. I am especially indebted to Dr. Slice for taking considerable time from his busy schedule to incorporate additional functions to his Morpheus et al. program to allow processing of my morphometric v

7 data. Dr. Steppan s expertise in phylogenetic methods has also been invaluable to the completion of this project. I also thank Peter Beerli for introducing me to programming through his Computational Evolutionary Biology course, which has been and will continue to be an indispensable skill for my research. Brian Inouye was also available to answer questions about statistical methods and assist with R programming. Many friends, both old and new, provided support in various ways during my two years at FSU. First, I broadly extend my gratitude to the entire graduate student body in the Ecology and Evolutionary Biology department. I specifically thank David McNutt for a year of competitive tennis matches. Travel expenses were drastically reduced because of several friends who provided lodging during my museum trips, including Vincent Cheng, Matthias Dean- Carpentier, Chris Hudler, Caroline Patenode, and Chris Zoia. I am truly thankful for the Big Bend Symphony Orchestra and its co-founder Ginny Densmore for allowing me the privilege to continue playing the violin. Besides access to specimens, numerous curators offered guidance and assistance during my visit to various institutions: Dr. David Kizirian and Robert Pascocello (American Museum of Natural History, New York, NY); Drs. Kenney Krysko and Max Nickerson (Florida Museum of Natural History, Gainesville, FL); Alan Resetar and Kathleen Kelly (Field Museum of Natural History, Chicago, IL); Jose Rosado (Museum of Comparative Zoology, Cambridge, MA); Addison Wynn and Ken Tighe (National Museum of Natural History, Washington, DC); and Greg Schneider (University of Michigan Museum of Zoology, Ann Arbor, MI). Funding for this work was provided by the National Science Foundation Graduate Research Fellowship and Sigma Xi Grants-in-Aid of Research (Grant No. G ). Additional organizations provided funding for other research projects and travels during my tenure at FSU, including Department of Biological Science and Congress of Graduate Students at FSU, Short Scholarship in Zoology through the department, and Jackson School of Geosciences through the Society of Vertebrate Paleontology. vi

8 TABLE OF CONTENTS List of Tables...ix List of Figures...xi List of Scripts and Programs...xiii List of Abbreviations...xiv Abstract...xvi 1. INTRODUCTION 1.1 Historical Background of Ontogeny and Phylogeny Geometric Morphometrics Ontogeny and Phylogeny of Crocodylia Significance of the Study ACQUISITION AND TREATMENT OF DATA 2.1 Sampling Landmarks Digitization Data Processing Generalized Procrustes Superimposition PHYLOGENETIC UTILITY OF ALLOMETRIC TRAJECTORIES CONSTRUCTED FROM GEOMETRIC MORPHOMETRIC DATA 3.1 Introduction Materials and Methods Results Discussion Conclusions PRACTIAL UTILITY OF ONTOGENETIC SHAPE CHANGES AS PHYLOGENETIC CHARACTERS 4.1 Introduction Materials and Methods Results Discussion Conclusions CONCLUDING REMARKS...93 APPENDIX A. LIST OF SPECIMENS...96 APPENDIX B. LIST OF LANDMARKS vii

9 APPENDIX C. SCRIPTS AND PROGRAMS APPENDIX D. MISSING POINT REPORT APPENDIX E. CHARACTER MATRIX APPENDIX F. LIST OF SYNAPOMORPHIES REFERENCES BIOGRAPHICAL SKETCH viii

10 LIST OF TABLES 1.1 List of heterochronic processes that result in a paedomorphic or peramorphic descendant Range of skull length and sample size of crocodilian species digitized for this study Sample size of digitized crocodilian species in Datasets 1, 2, and Angles (radians) of low-dimensional allometric trajectories relative to the vertical axis (principal component axis) for each sampled species Distance matrices of angular distances between the low- and high-dimensional allometric trajectories Result of the likelihood ratio tests and relevant parameter values Regression coefficient and R 2 values from the linear regression analysis of trajectory and phylogenetic distances based on observed data, and p-value from the permutational regression analysis P-values obtained from Mantel tests R 2 values from regression analyses on shape and size used to construct the allometric trajectories Summary of results List of landmarks used in this chapter Number and proportion of ontogenetically variable characters (OVCs) for each species Number of unambiguous synapomorphic state changes in the molecular and morphological trees Consistency index (CI), retention index (RI), and rescaled consistency index (RC) obtained from optimization of the character state changes onto molecular and morphological trees, from parsimony analysis on the OVC dataset, and from other datsets that include extant species of Crocodylia...84 A.1 List of specimens...96 B.1 List of landmarks D.1 Number (#MP) and proportion (PMP) of missing points for each digitized specimen ix

11 D.2 Number (#MP) and proportion (PMP) of missing points for each landmark E.1 Character matrix coding the ontogenetically variable landmarks in each species F.1 List of synapomorphies for clades in the tree based on a published molecular tree (Oaks 2011) F.2 List of synapormophies for clades in the tree based on a published morphological tree (Brochu 1999, 2000) x

12 LIST OF FIGURES 1.1 Pure heterochronic processes that result in a paedomorphic descendent as illustrated by larval and metamorphic forms of a generic salamander Cladograms showing current hypotheses on the evolutionary relationships between extant members of Crocodylia based on A, sequence data (Oaks 2011); B, morphological data (Brochu 1999; 2000) Crania of hatchling and adult Alligator mississippiensis in dorsal view Crania of adult Alligator mississippiensis, Crocodylus acutus, and Gavialis gangeticus in dorsal view Distributions of centroid sizes of specimens in the sampled species Positions of landmarks used in Dataset 3 on the cranium of crocodilians Bivariate plots of the first and second principal components (PC1, 2) of Procrustes coordinates Bivariate plots of the first four principal components (PC1 4) of Procrustes coordinates Bivariate plot of the second principal component (PC2) of Procrustes coordinates and log centroid size Shapes changes from mean shape of all sampled specimens in dorsal view associated with A, the first principal component (PC1); B, the second principal component (PC2) Bivariate plot of the first principal component (PC1) of Procrustes coordinates and log centroid size Bivariate plot of the first principal component (PC1) of residuals from the common allometric component and log centroid size Time-calibrated molecular tree based on an ultrametric tree by Oaks (2011) The effect of Pagel s lambda on the structure of a phylogenetic tree Histograms of regression coefficients (RC) recorded from 9,999 iterations of permutational regression analysis on A, low-dimensional trajectories based on PC1 of Procrustes coordinate data; B, low-dimensional trajectories based on PC2 of Procrustes coordinate data; C, low-dimensional trajectories based on PC1 of residuals from the common allometric component...58 xi

13 3.9 Phenograms constructed via unweighted pairwise grouping method based on arithmetic means (UPGMA) based on the angular distances between low-dimensional and highdimensional allometric trajectories Majority-consensus cladogram of Crocodylia based on a modified version of a published morphological dataset (Brochu 1999; 2000; modified by Brochu) Bivariate plots of trajectory and phylogenetic distances Bivariate plot of the first principal component (PC1) of Procrustes coordinates and log centroid size in male and female Caiman crocodilus Optimization of unambiguous autapomorphic and synapomorphic state changes in the A, molecular; B, morphological, trees Maximally parsimonious trees (MPTs) and the strict consensus tree constructed from equally weighted parsimony analysis on the OVC dataset...88 xii

14 LIST OF SCRIPTS AND PROGRAMS C.1 Script for merging the dorsal and ventral coordinate data of one specimen in Morpheus et al. (Slice 2009) C.2 R script for estimating missing coordinate values based on multiple linear regression on coordinate data and skull length for each species C.3 Python program for estimating the coordinate values for a missing point based on bilateral symmetry C.4 R script for constructing the low-dimensional allometric trajectories via principal components analysis on Procrustes shape coordinates C.5 R script for constructing low-dimensional allometric trajectories via principal components analysis on residuals from the common allometric component (CAC), cf. Mitteroecker et al C.6 R script that produces high-dimensional vectors for each species via multiple regression analysis, which describe the orientation of the allometric trajectories C.7 R script for constructing a distance matrix of the angular distances between highdimensional allometric trajectories C.8 Python program for conducting permutational regression analysis C.9 R script that conducts multiple regression analysis on bootstrap samples of Procrustes coordinates and log centroid size to code landmarks that are ontogenetically variable for each species xiii

15 LIST OF ABBREVIATIONS Institutional Abbreviations AMNH FLMNH FMNH MCZ UMMZ USNM American Museum of Natural History, New York City, NY, USA Florida Museum of Natural History, Gainesville, FL, USA Field Museum of Natural History, Chicago, IL, USA Museum of Comparative Zoology, Cambridge, MA, USA University of Michigan Museum of Zoology, Ann Arbor, MI, USA National Museum of Natural History, Washington, DC, USA Taxonomic Abbreviations A. mis. Alligator mississippiensis C. cro. Caiman crocodilus C. acu. Crocodylus acutus C. nil. Crocodylus niloticus C. por. Crocodylus porosus G. gan. Gavialis gangeticus M. nig. Melanosuchus niger O. tet. Osteolaemus tetraspis P. pal. Paleosuchus palpebrosus P. tri. Paleosuchus trigonatus T. sch. Tomistoma schlegelii xiv

16 Anatomical Abbreviations bo bs CN ect en exo fr itf jg lac ls mx ns pa pmx po plf pl prf pt qd qj so sq stf basioccipital basisphenoid cranial nerve ectopterygoid external naris exoccipital frontal infra-temporal fenestra jugal lacrimal laterosphenoid maxilla nasal parietal premaxilla postorbital palatine fenestra palatine prefrontal pterygoid quadrate quadratojugal supraoccipital squamosal supra-temporal fenestra xv

17 ABSTRACT The degree to which ontogenetic data could facilitate the understanding of phylogenetic relationships has long been a subject of contention in evolutionary biology. Known occurrences of paedomorphosis have invalidated strict adherences to the recapitulationist theory and the biogenetic law. Nevertheless, the extent to which patterns of ontogenetic morphological changes are phylogenetically informative remains to be tested. Here I use the extant members of Crocodylia to investigate the phylogenetic information contained in (1) the allometric trajectories describing the ontogenetic changes in cranial morphology; and (2) ontogenetically variable characters (OVCs), or shape variables that undergo significant changes in relative position through ontogeny. Using three-dimensional landmark-based geometric morphometric methods, I digitized the crania of ten crocodilian species and quantified the morphological changes associated with growth. For the first study, the shape data were used to construct allometric trajectories for each sampled species to test whether the similarities in the orientation of these trajectories correlate with phylogenetic relatedness. Crucial to this study was the availability of a time-calibrated molecular phylogeny that provided phylogenetic reconstructions independent from morphological data, with which the phylogenetic signal of these trajectories could be tested. A suite of methods was employed to test the phylogenetic signal, including (1) the K-statistic; (2) a likelihood ratio test based on Pagel s lambda; (3) permutational regression analysis on trajectory and phylogenetic distances; (4) topological comparison between the phenogram constructed from a clustering method and the molecular phylogeny; and (5) a Mantel test. All tests produced nonsignificant results and showed an overall lack of phylogenetic signal, indicating that these allometric trajectories have little phylogenetic information. Interestingly, the topology of the phenogram constructed from the clustering algorithm also differs markedly from the topology of published morphological tree, which suggests that the underlying signal in these trajectories is largely uncorrelated with similarities in adult cranial morphologies. The results of this study counter the assumption that patterns of morphological changes that occur throughout ontogeny contain significant phylogenetic signal and give caution to the use of ontogenetic data for phylogenetic inference. xvi

18 The second study introduces a new class of ontogenetic data for describing ontogenetic changes that could be used in a phylogenetic framework. Ontogenetically variable characters (OVCs) were constructed based on the significance of the correlation between shape and size variables. A character matrix was constructed according to the presence and absence of OVCs. Optimization of implied character state changes on molecular and morphological trees suggests that OVCs, on average, are equally informative for either phylogenetic reconstruction. In contrast, parsimony analysis on the OVC character matrix produces trees that broadly support published molecular trees. These observations indicate substantial potential utility of OVCs as phylogenetic characters, but improvements to the construction of OVCs and further examinations are needed to justify the direct incorporation of OVCs in phylogenetic analyses. xvii

19 CHAPTER ONE INTRODUCTION Historical Background on Ontogeny and Phylogeny From Aristotle to German Evolutionary Zealots For modern evolutionary biologists, a discussion on the relationship between ontogeny and phylogeny may invoke the influential, but outdated concept of ontogeny recapitulates phylogeny championed by nineteenth century German naturalist Ernst Haeckel. However, like many fundamental Western ideas, the notion that the developmental sequence of organisms reflects the hierarchical organization of Animalia has a Greek origin. In his De generatione animalium, Aristotle classified animals into five groups: (1) insects; (2) fish, cephalopods, crustaceans; (3) birds and reptiles; (4) ovoviviparous sharks; and (5) mammals (Gould 1977). He proposed that this order represents increasing levels of perfection and complexity, placing Man at the zenith of creation. In accordance with the asceticism in Greek philosophy, Aristotle rationalized that this increase was perpetuated by the addition of higher souls entering the embryo during development, in which plants merely had the nutritive, animals possessed both the nutritive and the sensitive, and humans acquired the rational soul, in addition to the other two types (Gould 1977). Variations on this theme of the soul as fuel for driving ontogeny along a common trajectory continued into the nineteenth century, and became influential in shaping the discussion on evolutionary theory. An intellectual powerhouse that was the nineteenth century German naturalists was a strong proponent in the scholarly debate on the relationship between ontogeny and phylogeny. One of the most influential figures involved was Ernst Haeckel, who is the best-known advocate for the recapitulation theory, or the concept that the developmental sequence of an organism follows the evolutionary history of adult forms of its ancestors. Although Haeckel recognized that exceptions exist, he believed that the evolutionary changes in anatomical form were largely due addition of developmental stages to a pre-existing developmental series (Nelson 1973; Gould 1

20 1977). In response to the recapitulation theory, another German naturalist, Karl Ernst von Baer, put forward the idea based on the degree of differentiation of anatomical parts throughout ontogeny. This biogenetic law proposed that ontogenetically variable features that are observed more generally among groups of organisms are more primitive than less general features (Gould 1977; Nelson 1978). Despite the differences in their mechanistic explanation, the recapitulation theory and the biogenetic law would produce perfectly congruent phylogenetic reconstructions (Gould 1977), and both ideas were pivotal for demonstrating the potential utility of ontogenetic data to elucidate the evolutionary history of organisms. The Fall of the Recapitulation Theory and the Biogenetic Law A greater understanding of embryology and the eventual acceptance of the genetic theory of inheritance, however, undermined the recapitulationist theory and the biogenetic law. With this new paradigm, both the acceleration and retardation of development were mechanistically plausible, and the evolution of ontogeny was no longer restricted to merely terminal additions of developmental stages (Gould 1977). This bidirectional shift in the rate, as well as the relative timing, of development is referred as heterochrony, a term introduced by none other than Haeckel. Because both acceleration and retardation of developmental processes are possible, heterochrony has two possible outcomes: (1) peramorphosis, or the augmentation to a preexisting developmental trajectory that leads to unforeseen trait in the descendant; and (2) paedomorphosis, or the retention of juvenile characteristics of the ancestor in the adult form of its descendant. Multiple processes could result in these two outcomes (Table 1.1; Fig. 1.1), which has been explained in detail elsewhere (e.g., Gould 1977, Klingenberg 1998). Paedomorphosis, in particular, provided indisputable evidence against the strict adherence to Haeckel s recapitulation theory and von Baer s biogenetic law. To elaborate, the occurrence of juvenile features in the adult form of a descendant would give conflicting phylogenetic signal because these two phyletic approaches would consider the descendent to be more primitive than its true ancestor. The German naturalists were well aware of this phenomenon, but they perceived paedomorphosis as an exception to the general rule of evolutionary changes to ontogenetic trajectories (Gould 1977; Nelson 1978). However, not only does paedomorphosis occur in nature, but it could also occurs locally in certain regions of the body of an organism. Due to its potential to yield drastic phenotypic change, heterochrony 2

21 received much attention among the evolutionary biologists in the latter half of the twentieth century as the driving mechanism for morphological disparity (e.g., Gould 1977; Alberch et al. 1979; McKinney and McNamara 1991). However, the degree to which ontogenetic data could be phylogenetically informative has yet been unclear. Table 1.1. List of heterochronic processes that result in a peramorphic or paedomorphic descendant. and denote increase and decrease, respectively. Modified from Smith 2001: Table 1. Outcome Phylogenetic signal Heterochronic process Description Paedomorphosis Reverse Recapitulation Progenesis Early offset of growth Neoteny shape growth rate Postdisplacement Later onset of growth Proportional dwarfism size growth rate Peramorphosis Recapitulation Hypermorphosis Later offset of growth Acceleration shape growth rate Predisplacement Early onset of growth Proportionate gigantism size growth rate 3

22 Figure 1.1. Pure heterochronic processes that result in a paedomorphic descendent illustrated by larval and metamorphic forms of a generic salamander. A, developmental trajectory of a hypothetical ancestral species; B, progenesis; C, neoteny; D, postdisplacement. Figure modified from Ryan and Semlitsch 1998: Fig. 1. 4

23 Ontogeny and the Cladistic Method As the nineteenth century discussion on ontogeny and phylogeny was intertwined with discourses on evolutionary theory, the reinvigorated interest in heterochrony and ontogeny and phylogeny in the latter half of the twentieth century was strongly linked with the advent of the phylogenetic methods. The cladistic method provided an analytical procedure for phylogenetic reconstruction based on the principle of parsimony, and one that is distinct from phenetic approaches (Hennig 1966). Hennig (1966) argued the superiority of cladistics over systematic approaches based on morphological resemblance in that monophyletic groups could be established based on apomorphic, or derived, characters that occur in any ontogenetic stage It does not matter therefore which stage of development is used to establish relationship on the ground of synapomorphy [shared derived trait]. A monophyletic group remains such even if it can be established only with the characters of a single stage of development (p. 108). However, Hennig (1966) himself recognized the potential problem that heterochrony could impose on parsimony-based phylogenetic reconstructions, stating that [...] paedomorphosis, which leads to pseudoplesiomorph conditions [i.e., traits falsely implied to be primitive], make the establishment of true synapomorphy difficult (p. 108). As expected, the inclusion of paedomorphic taxa in parsimony-based analyses has resulted in the clustering of distantly related paedmorphic taxa, as well as a more basal phylogenetic placement of these taxa (Wiens et al. 2005). In light of these problems, evolutionary biologists began to discuss the role of ontogenetic data into phylogenetic analyses. Although occurrences of paedomorphosis may lead to erroneous reconstructions of phylogenetic trees, are ontogenetic data informative for determining the polarity of character states or could they be phylogenetically informative using different coding schemes to describe developmental trajectories? Nelson (1973) argued that ontogenetic character transformations are the only direct approach for determining the polarity of character states and have been influential for establishing the long-standing higher-level phylogeny of vertebrates (but see Gould 1973). Tucker (1993) relied on the principles of the biogenetic law to polarize some of the ontogenetically variable morphological characters. However, multiple studies (Wake 1989; Mabee 2000) have criticized the use of ontogenetic data for character state polarization because ontogeny evolves bidirectionally and whether the presence or absence of a character state is primitive or derived cannot be determined. This is 5

24 problematic for cladistic analysis because only derived characteristics are informative for constructing phylogenetic trees. Likewise, the direct incorporation of ontogenetic data in phylogenetic analyses has been attempted by using particular coding schemes distinct from traditional character coding. Ontogenetic trajectories have generally been coded by presence and absence of specific character state transformations (e.g., a b coded as 1 ; a a coded as 0 ) or by states representing each distinct trajectory (e.g., a b coded as 0 ; a b c coded as 1 ; b c coded as 2 ) (Mabee 2000). The character state transformations could then be weighted by specifying a cost matrix based on the number of characters separating a pair of trajectories. In spite of these efforts, the use of ontogenetic data in cladistic analyses yet awaits practical and theoretical justifications. Although the use of molecular data for phylogenetic inference has largely circumvented the problem associated with paedomorphosis, morphology-based cladistics still remains the primary method for constructing genealogical hypotheses in paleontological studies. The fossil record contributes additional complications attributed to ontogenetic changes. First, morphological changes during development, as with other sources of intraspecific variation, obscure the taxonomic classification of extinct organisms. Second, there is no guarantee that comparable developmental stages are being sampled. Therefore, phylogenetic analyses in paleontological studies likely include fossil taxa at multiple developmental stages. In fact, histological and census studies suggest that full-grown adults are the rarity, not the norm, in the vertebrate fossil record (Erickson et al. 2004b; Horner et al. 2011). With the availability of fossil specimens at various developmental stages, in conjunction with osteohistological studies, ontogenetic studies on extinct taxa have received considerable interest in recent years (e.g., Erickson 2005; Scanella and Horner 2010). Tykoski (2005) noted that juvenile coelophysoid taxa tend to be placed more basally than adult forms and observed topological changes to the phylogenetic tree when ontogenetically variable characters were taken into account. Ontogenetic data, if they are indeed phylogenetically informative, could be an essential class of characters for inferring the phylogenetic relationship of extinct taxa. Recent Investigations of Ontogeny and Phylogeny More recent advancements in developmental and evolutionary biology have permitted descriptions of developmental processes at greater resolution and phylogenetic inference based 6

25 on increasingly sophisticated models. Current methods for portraying ontogenetic changes have generally followed two contrasting, but not necessarily mutually exclusive, approaches. One involves increasingly detailed account of the morphological changes associated with ontogeny. Major technical breakthroughs in developmental biology have allowed observations of developmental processes in much greater detail across embryonic stages. These additional observations have contributed to the formulation of complex and comprehensive developmental trajectories, which are useful for identifying specific deviations in the developmental sequences. This Ontogenetic Sequence Analysis has shown, for instance, a highly polymorphic developmental trajectory in the Lake Victoria cichlid (de Jong et al. 2009) and plasticity in the developmental timing associated with the presence of predator cues in two gastropod species (Rundle et al. 2010). Although these detailed developmental sequences are useful for detecting specific heterochronic events, their utility is often restricted to intraspecific or intrageneric studies due to highly specialized nature of these sequences. Another approach consists of summarizing the morphological changes that occur throughout ontogeny. These methods have employed multivariate statistical methods, such as the principal components analysis (PCA) and canonical variates analysis (CVA), to visualize and statistically compare developmental trajectories of multiple taxa. The advantage of this approach is that it projects the data points to a space defined by a common set of axes, which allows proper comparisons of developmental trajectories. Dimension-reducing methods (e.g., PCA, CVA) have been used to describe the ontogenetic changes in multiple ways. The most common approach is to construct developmental trajectories by performing a regression analysis on the data points based on a principal component or canonical variates axis against a size variable. Larson (2005), for instance, utilized the correlation coefficient of the regression line based on the first principal components axis (PC1) of linear distance measurements on the crania and snout-vent length (SVL) of Rana tadpoles. Wilson and Sánchez-Villagra (2011) further condensed the data into an allometric space by conducting another set of principal components analysis on a set of first principal components (PC1) scores of the log transformed linear distance measurements of each species. Following the procedure, each data point in the PC plot was used to describe the developmental trajectory of each sampled rodent species. In this multivariate statistical framework, the differences between developmental trajectories could be tested using various parametric and non-parametric significance tests. 7

26 In addition to new descriptive and comparative metrics for ontogeny, the investigation of the link between ontogeny and phylogeny necessary requires the reconstructions of accurate phylogenies. In theory, the true phylogeny cannot be known outside of simulation studies. Nevertheless, the combination of exponential increase in computing power, development of increasingly efficient sequencing protocols, and use of more sophisticated models of evolution have contributed to more rigorous phylogenetic reconstructions. Beyond the basic implementation of maximum likelihood (Swofford et al. 1996) and Bayesian (Huelsenbeck et al. 2001; Alfaro and Holder 2006) approaches to phylogenetic inference, these methods have been applied to study a wide range of related evolutionary issues, including ancestral reconstruction (Ronquist 2004) and divergence time estimates (Drummond and Rambaut 2007). Moreover, standard statistical tests have been adapted to directly incorporate phylogenetic information and many of these tests have been made readily available as programs and software packages. These tests have been used to determine the significance of a number of evolutionary hypotheses, such as the rate change in taxonomic richness (Ricklefs 2007; Glor 2010), topological differences between phylogenetic trees (Kishino and Hasegawa 1989; Shimodaira and Hasegawa 1999), and the phylogenetic signal of a trait (Pagel 1999; Blomberg et al. 2003). These modern approaches to ontogenetic and phylogenetic studies provide powerful tools to revisit the centuries-old discussion on the connection between ontogeny and phylogeny. Combined with statistical tests that incorporate phylogenetic information, new methods for describing ontogenetic changes, offer rigorous approaches to investigating the link between developmental trajectories and phylogenetic relatedness. If developmental trajectories are phylogenetically informative, for example, a general congruence is expected between a phylogenetic tree and a phenogram constructed from a metric describing the developmental trajectories (e.g., correlation coefficient). Larson (2005) noted the compatibility between the topology of the molecular tree to a phenogram based on the Mahalanobis distances of the developmental trajectories based on linear distances and size. Similarly, the correlation between similarities in the developmental trajectories and phylogenetic relatedness could be tested to examine the efficacy of ontogeny for inferring the evolutionary relationships of organisms. This relationship is based on the expectation that closely related taxa have had shorter time since their divergence to accumulate differences than distantly related taxa. However, explicit tests of the 8

27 phylogenetic signal in developmental trajectories have been elusive using the types of methods introduced above. Geometric Morphometrics An increasingly popular method for describing ontogenetic changes in morphology is geometric morphometrics. Corti (1993) introduced the term to denote a field of study concerned with the analysis of shape based on a set of two- or three-dimensional coordinate points. Geometric morphometrics distinguishes itself from traditional morphometrics by its capability of maintaining the full shape information of digitized objects through analysis (Slice 2007a). This is accomplished via Procrustes superimposition, which removes the effect of position, orientation, and scale on coordinates. Conversely, traditional morphometrics involves the use of angles, linear distance measures, and/or ratios of linear distances, which generally cannot fully capture the shape information of an object (Slice 2005). Both traditional and geometric morphometric methods allow the implementation of multivariate statistical methods for shape analysis, although the latter is superior in regards to the visualization of digitized specimens. Due to its strength in capturing shape information, geometric morphometric methods have been employed to record shape changes associated with growth. For instance, coordinate data have been used to construct developmental trajectories, which describe the shape changes associated with growth. Similar to the trajectories based on discrete morphological characters or traditional morphometric data, these trajectories have been represented by single data points via PCA on a collection of PC1 vectors of shape data of each species (Klingenberg and Froese 1991) or by regression lines based on shape and size variables (e.g., Mitteroecker et al. 2004). Mitteroecker and Bookstein (2009) used variance-covariance matrices to examine the variations in the pattern of shape changes throughout post-natal development, in which they found that both rats and humans undergo several major changes in the directionality of shape change. Using geometric morphometric techniques, the shape changes along these trajectories could also be easily visualized. Additonally, the directionality and magnitude of relative positional changes of each landmark could be depicted effectively using thin-plate spline visualizations (Bookstein 1989, 1991). 9

28 Previous studies have discussed the phylogenetic implication of geometric morphometric approaches (Rohlf 1998). Bookstein (1994) opposed the use of shape coordinates as a basis for phylogenetic inference because they are theoretically incompatible with the notion of evolutionary homology. Nevertheless, Zelditch et al. (1995) first proposed the transformation of partial warp scores (Bookstein 1991) into discrete characters for cladistic analysis. According to their procedure, the character states were determined based on identifiable clusters of species in the plot of partial warp scores. Based on a simulation study, however, Naylor (1996) showed that dendrograms constructed from partial warp scores, despite producing an identical tree topology, generated grossly conflicting ancestral shape reconstructions and greater degree of homoplasy. Similarly, Adams et al. (2011) listed practical and theoretical arguments against the use of a modular cladistic approach (González-José et al. 2008), which utilizes the principal components scores of shape in a cladistic framework. A direct incorporation of coordinate data as continuous characters was recently implemented in the TNT phylogenetic program (Goloboff et al. 2008; Catalano et al. 2010; Goloboff and Catalano 2011), although the authors clarify that the method should be primarily for comparisons with established morphological and molecular phylogenetic trees. In practice, studies have examined the degree of congruence between the topologies of a molecular phylogeny and the phenogram constructed from distances between mean shapes among taxonomic units. Carbajal de la Fuente et al. (2011) and Vignon et al. (2011) found largely compatible topologies in the wings of triatome beetles and sclerotized mouthparts of parasitic Cichlidogyrus, respectively. These studies suggest the practical utility of shape data for inferring phylogenies, at least in some taxonomic groups. Several geometric morphometric studies have considered the relationship between ontogeny and phylogeny. Such studies have involved the comparisons of allometric trajectories, and most of these studies have thus far been restricted to research on the occurrences of heterochrony within primates (e.g., Vi arsdóttir et al. 2002; Mitteroecker et al. 2005). However, discussions on heterochrony have largely been qualitative, based on the relative position of the allometric trajectories in a multivariate space or bivariate projection. For example, an occurrence of neoteny (refer to Table 1.1) is implied if a trajectory is nested within the smaller size range of another trajectory. These studies often involve an a priori decision of ancestral and derived condition, which is an issue particularly when sampling is limited to extant taxa. Alternatively, the topological similarity between a phylogenetic tree and the phenogram based on distances 10

29 between allometric trajectories has been used to check for phylogenetic significance of developmental trajectories (e.g., Piras et al. 2010). However, these methods have not incorporated any explicit tests. Vi arsdóttir and Cobb (2004), to my knowledge, have conducted the only geometric morphometric study that has explicitly tested for the tendency of closely related taxonomic units to share similar developmental trajectories. However, the study categorized the specimens into only two discrete ontogenetic stages (i.e., before and after the eruption of the first permanent tooth). Furthermore, only four species were sampled (i.e., Homo sapiens, Gorilla gorilla, Pan troglodytes, P. paniscus), which is highly restrictive in its temporal and phylogenetic scale. Thus, the phylogenetic signal in ontogenetic data needs to be tested using comprehensive sampling and rigorous tests. The work presented here will employ a suite of methods to investigate the degree to which ontogenetic changes in the cranial morphology of crocodilians are phylogenetically informative. Ontogeny and Phylogeny of Crocodylia Crocodylia Gmelin, 1789 is the subject of the study presented in this thesis. The ~85 million year old clade consists of 23 currently recognized extant species that inhabit the pantropics (Grenard 1991). It is also represented by over one hundred extinct species that have been discovered on every continent (Brochu 2003). Phylogenetic analyses using sequence data (e.g., Gatesy et al. 2003; Harshman et al. 2003; Oaks 2011) exhibit compatible topologies, which separate the group into two major subclades: the Alligatoridae and Crocodylinae (Fig. 1.2A). In the molecular tree, the narrow-snouted Indian and Malay gharials Gavialis and Tomistoma, respectively form a monophyletic group within Crocodylinae. In contrast, morphological trees have consistently placed the Indian gharial and other members of Gavialinae as the basal-most divergence in Crocodylia (Fig. 1.2B). This discrepancy has been problematic for character optimization and determining character transformations in the clade. Despite conflicting phylogenetic reconstructions, Crocodylia is a suitable vertebrate lineage for studying morphological changes throughout ontogeny. First, crocodilians undergo 1000 to 5000 fold increases in body mass during development (Grenard 1991) that are associated with major morphological changes in the cranium (Fig 1.3). In addition to ontogenetic variation, 11

30 their cranial morphology exhibits remarkable disparity, particularly in the rostrum (Fig. 1.4). For instance, the American alligator (Alligator mississippiensis) is known for its relatively broad snout, while the narrow-snouted Indian and Malay gharials possess extremely narrow snouts. Critical to the study is the availability of a time-calibrated molecular tree (Oaks 2011), which provides (1) a phylogenetic reconstruction that is essentially independent from morphological data; (2) a tree that could be compared with phenograms constructed from morphometric data; and (3) branch lengths that could be incorporated into statistical tests. Moreover, crocodilians are often considered as modern analogs for extinct archosaurian lineages, including dinosaurs (Dodson 2003). Therefore, the results of this study could have implications for closely related taxonomic groups. Furthermore, the rich evolutionary history and the wide geographical distribution of the group allow for macroevolutionary studies in the temporal and geographic scales that are typical of paleontological studies. Ontogenetic studies on crocodilians, and more generally Archosauria, have been scarce in number considering the extensive literature on the development of vertebrates. Early published descriptions (Brochu 1992 and references therein) were largely qualitative and often restricted to developmental changes that occur in a single taxon. To date, Brochu (1992, 1995) provided arguably the most comprehensive morphological description of ontogenetic changes in crocodilians, but the studies have been limited to postcranial elements, which are generally considered to be morphologically conservative among members of Crocodylia. In addition, previous ontogenetic studies on crocodilians have used traditional morphometric measures (i.e., angles, linear distances, ratios) to record the morphology, which, as mentioned above, commonly fail to adequately capture shape information (Slice 2005). Piras et al. (2010) conducted a landmark-based geometric morphometric study in an attempt to resolve the discrepancy in the phylogenetic placement of the Indian gharial. However, the sampling consisted of only three crocodyline species, and the study did not explicitly test for phylogenetic signal. Here, an extensive three-dimensional coordinate dataset were utilized to record the ontogenetic changes in cranial morphology and conduct a comprehensive analysis on the phylogenetic signal of allometric trajectories. 12

31 Figure 1.2. Cladograms showing current hypotheses on the evolutionary relationships between extant members of Crocodylia based on A, sequence data (Oaks 2011); B, morphological data (Brochu 1999; 2000). These trees are majority consensus trees. Note the difference in the phylogenetic placement of the Indian gharial (Gavialis gangeticus). 13

32 Figure 1.3. Crania of neonate and adult Alligator mississippiensis in dorsal view. A, neonate (AMNH 7128); B, adult (AMNH 9043). Note the differences in the shape of the rostrum and fenestrae. Scaled to similar dimensions to illustrate shape differences. 14

33 Figure 1.4. Crania of adult Alligator mississippiensis, Crocodylus acutus, and Gavialis gangeticus in dorsal view. A, A. mississippiensis (AMNH 9043); B, Crocodylus acutus (USNM ); C, G. gangeticus (AMNH 7138). Note the differences in the shape of the rostrum. Scaled to similar dimensions to illustrate shape differences. 15

34 Significance of the Study The present study contributes to the centuries-old investigation of the link between ontogeny and phylogeny. More specifically, it examines whether developmental trajectories based on shape changes that occur throughout ontogeny are phylogenetically informative. If the results indicate that these trajectories do contain significant phylogenetic signal, then the study would advocate the incorporation of this new class of characters to phylogenetic analyses. Alternatively, a set of non-significant results would demand re-evaluation of studies that have made such assumption and give caution to the use of ontogenetic data in phylogenetic inference. In addition, the three-dimensional coordinate data collected for this study represent the most comprehensive morphometric data of crocodilians. With a total of 134 landmarks, the dataset could be used to establish a standard set of landmarks for morphometric studies on crocodilian crania. Moreover, the dataset could easily be augmented with the inclusion of additional taxa, including specimens of fossil taxa. Furthermore, the study provides a rigorous protocol for testing the phylogenetic signal of allometric trajectories in virtually any taxonomic group. In a broader context, my work here addresses the potential role of ontogenetic data in phylogenetic inference. 16

35 CHAPTER TWO ACQUISITION AND TREATMENT OF DATA Sampling Taxonomic Sampling The morphometric data consist of articulated crania of post-natal crocodilians. I digitized 11 of the 23 extant species of Crocodylia (Table 2.1) currently recognized by the IUCN-SSN (Species Survival Commission of the International Union for Conservation) Crocodile Specialist Group (King and Burke 1989). The taxonomic sampling was based on three factors: (1) the number of available specimens that I could readily access at the following institutions: AMNH, FLMNH, FMNH, MCZ, UMMZ, and USNM; (2) a broad sampling of subclades within Crocodylia; and (3) a good representation of the morphological disparity for the clade. For instance, the narrow-snouted Indian gharial (Gavialis) and the Malay gharial (Tomistoma) were included in the study despite relatively few available specimens. In addition, the dwarf caimans (Paleosuchus) and the African dwarf crocodile (Osteolaemus) were sampled due to their important relevance to comparative ontogenetic studies. Data for Cuvier s dwarf caiman (P. palpebrosus) were not utilized in subsequent analyses because of inadequate specimen and ontogenetic sampling (see below). Although reports of natural hybridization (Ray et al. 2004) and paraphyly (McAliley et al. 2006; Oaks 2011) in crocodilians exist, this study adheres to the taxonomic classification established by King and Burke (1997) because it is a standard adopted by current systematic studies on Crocodylia. Specimen Sampling A total of 256 crocodilian crania were digitized, which represents all intact, non-captive cranial material (see below) that were available for examination during my visits, with the exception of the American alligator (Alligator mississippiensis) and the spectacled caiman (Caiman crocodilus) at the FMNH due to time constraints (Appendix A). 17

36 Digitization was limited to the cranium for several reasons. First, the cranium is generally the most diagnostic region of the vertebrate skeleton and shows the highest degree of morphological disparity among extant crocodilians (Fig. 1.4; Brochu 2001a). For this reason, cranial characters comprise the majority of the morphological data that are used for phylogenetic reconstructions of vertebrate clades, including crocodilians (e.g., Brochu 1999). Conversely, the postcranium is largely conserved among crocodilians, especially in the appendicular elements (Brochu 2001a). With regard to shape analysis, the structural complexity of the cranium provides for a greater number of landmarks. The cranium, as a composite of dozens of skeletal elements, bears many reliable Type I landmarks (sensu Bookstein 1991) defined by triple junction points of bone sutures. In contrast, the mandible and individual postcranial elements would contain a small number of reliable landmarks, a situation that could potentially be rectified with the use of semilandmarks and other outlining methods, but this is beyond the scope of the present analysis. Efforts were made to sufficiently sample the post-natal growth series of each species, but the sampling was restricted according to a set of criteria. First, articulated crania were digitized if all or nearly all of the landmark points were present and identifiable. Hence, the digitized specimens have little to no physical damage and lack extensive scale coverage that obscures the exact location of the suture lines. Similarly, a specimen was not digitized if any of the three common landmark points used for merging the dorsal and ventral sides were missing or unidentifiable. In addition, crania from only non-captive individuals were sampled because wild and captive crocodilians are known to exhibit cranial morphologies altered by phenotypic plasticity (Erickson et al. 2004a). For this reason, morphometric data for specimens without locality data were also not collected. However, all articulated crania of Gavialis and Tomistoma were digitized, regardless of their habitat or lack of locality information because very few specimens of these two species are available at North American institutions. Unfortunately, all but one digitized cranium of Gavialis used in the analysis is labeled as belonging to a noncaptive individual (i.e., MCZ 33950). Meanwhile, captive and potentially captive specimens of Tomistoma (i.e., FLMNH , 54210, 62020, 84888; FMNH ; UMMZ , ) were later found to be distributed among captive specimens in a morphological space based on principal components axes. Still, the degree to which wild and captive specimens exhibit different developmental trajectories is unknown and its investigation is outside the scope 18

37 of the present study. Despite these restrictive measures, the sampling adequately covers the ontogenetic stages from hatchling to adults for each of the eleven species (Table 2.1). Table 2.1. Range of skull length and sample size of crocodilian species digitized for this study. Scientific Name Common Name Sample size Skull length range Alligator mississippiensis American alligator mm Caiman crocodilus Spectacled caiman mm Crocodylus acutus American crocodile mm Crocodylus niloticus Nile crocodile mm Crocodylus porosus Salt-water crocodile mm Gavialis gangeticus Indian gharial mm Melanosuchus niger Black caiman mm Osteolaemus tetraspis African dwarf crocodile mm Paleosuchus palpebrosus Cuvier s dwarf caiman mm Paleosuchus trigonatus Schneider s dwarf caiman mm Tomistoma schlegelii Malay gharial mm Total mm Landmarks Landmark-based geometric morphometric methods were used to conduct the subsequent shape analyses. Landmarks are defined as two- or three-dimensional coordinate data of homologous measurement points (Gunz et al. 2009). Here, homology refers to geometric homology, in which discrete anatomical points are considered to be the same on practical basis and not necessarily homologous evolutionarily, ontogenetically, or functionally. For clarity, a distinction will hereby be made between points and landmarks. A point will refer to a single discrete location on an individual specimen defined by a set of coordinate values two or three values for two- or three-dimensional data, respectively. In contrast, a landmark will denote a class of corresponding points found in multiple specimens. A total of 137 landmarks were identified and digitized, which is comprised of 78 dorsal and 59 ventral landmarks (Appendix B). Landmarks were chosen based on a clearly definable 19

38 class of points that are identifiable consistently in all or a particular group of crocodilian species. The set of landmarks were divided into dorsal and ventral components because the digitization process used in this study requires the dorsal and ventral sides to be digitized separately. Three common landmarks in both datasets were later used to merge the dorsal and ventral sets of points for each specimen: the anterior tip of the rostrum (Landmark 1) and the posterior-most extent of the quadrate-quadratojugal suture on both the left and right sides of the cranium (Landmarks 2, 3). These landmarks were chosen for merging the dorsal and ventral datasets because they are maximally distant identifiable points on the cranium, and minimize the error when stitching the two datasets together. The list of landmarks includes a combination of Type I, II, and III landmarks (Appendix B). In biological systems, Type I landmarks are defined by juxtaposition of multiple structures, such as the triple point of sutures (Bookstein 1991). Type II landmarks are associated with curvature maxima (e.g., apex of a tooth), while Type III landmarks mark the maximum extent of a structure (e.g., anterior-most extent of the skull) (Bookstein 1991). Type I and II landmarks are generally regarded as consistently defined points in coordinate space and are arguably more biologically meaningful than Type III landmarks (Slice 2005). However, the Type III landmarks used in the analyses are few in number compared to Type I landmarks and were consistently identified and digitized. Moreover, many of the Type III landmarks were located at scarcely digitized regions (i.e., Landmarks 85 88, 108, 109) or were used to define the location of relatively small foramina for cranial nerves, thus, any significant changes in the results due to inconsistencies in the digitization of these landmarks are unlikely. Both the left and right components of bilaterally symmetric sets of landmarks were recorded because substantial asymmetry can exist on the crania of crocodilians (pers. obs.). For instance, the right frontal in FLMNH (Caiman crocodilus) does not contact the right nasal, but instead, the right prefrontal-frontal suture intersects anteriorly with the nasal symphysis. Likewise, only the left lacrimal contacts the nasal in AMNH (Gavialis). Whether such variance is a result of disease or injury, or developmental mishap, or simply within the normal range within taxa is indeterminable. Previous geometric morphometric studies on crocodilians have digitized only one side of the skull (Jaszlics and Pardo 2012) or have collapsed the bilateral data into unilateral data by calculating the mean deviation from the median line 20

39 (Piras et al. 2010). Whether the inclusion of both left and right landmarks significantly alters the results of this study remains to be tested. Although 137 landmarks were digitized, some landmarks pertain only to certain crocodilian species. The premaxillary symphysis, for example, does not intersect the anterior margin of the naris in A. mississippiensis. Thus, the landmark associated with this intersection point was not digitized in this taxon, and was treated as missing in the raw data. These speciesor subclade-specific landmarks were subsequently removed from the data for the clade-wide analyses presented here, but were digitized to permit future morphometric studies on a set of particular species. Digitization Three-dimensional coordinates for each landmark were collected to digitize the specimens. A MicroScribe G2 3D digitizer (Immersion Corporation, San Jose, CA, USA) and its companion program Microscribe Utility Software (Immersion Corporation, San Jose, CA, USA), provided by the Florida State University Morphometrics Lab, were used to record the x, y, and z coordinate values in Microsoft Excel 2008 for Mac version (Microsoft Corporation Redmond, WA, USA). The dorsal and ventral landmarks were digitized separately with the intention of merging the two datasets together. If the specimen was small or a landmark point was difficult to identify, a hand lens and additional light sources were utilized to minimize digitization error. Once the digitization of each specimen was completed, the coordinate data on the Excel spreadsheet were copied into TextEdit version 1.5 (Apple, Inc., Cupertino, CA, USA) and converted into the NTSYS format. These NTSYS files were imported into the visualizing software M_vis (Slice 2007b) to visually check for digitization errors. Instead of two-dimensional coordinates, three-dimensional data were collected. Many geometric morphometric studies have employed two-dimensional coordinates on tetrapod skulls, including those of crocodilians (Jaszlics and Pardo 2012) and theropod dinosaurs (Brusatte et al. 2012; Bhullar et al. 2012). Particularly in crocodilians, morphological changes along the dorsoventral axis, e.g., ventral rotation of the occipital region, largely occur later in ontogeny relative to the changes along the frontal plane, e.g., narrowing of the snout (pers. obs.). By ignoring the dorso-ventral axis, the morphometric data may yield different ontogenetic patterns, and the 21

40 plausibility of using two-dimensional landmarks should be tested. By contrast, the use of twodimensional coordinates seems feasible for analyzing the shape of bilaterally compressed structures and organisms, such as fishes (e.g., Klingenberg and Froese 1991) and insect wings (e.g., Rohlf 1993; van der Linde and Houle 2009). However, two-dimensional coordinates are commonly digitized from photographed images of specimens, which may be subject to parallax via lens distortion (Mullen and Taylor 2002). Moreover, the landmark points were occasionally difficult to discern on the crania, which would presumably be less visible and more difficult to digitize with photographs of the specimen. In sum, the three-dimensional coordinates were used to sufficiently capture the ontogenetic changes that occur in highly three-dimensional crania of crocodilians without the possibility of omitting key morphological changes that occur along a coordinate axis. Besides the three-dimensional coordinate data, additional information was recorded for each digitized specimen, including the locality data, approximate ontogenetic stage based on skull length (neonate, juvenile, subadult, adult), skull length (between the anterior tip of the rostrum to the posterior point of the skull roof), snout length (between the rostrum to the median point aligned with the anterior-most point of the orbital margin), snout width (transverse width at the position of the tenth maxillary tooth), inter-quadrate distance (between the medio-lateral extent of the quadrates), premaxilla-quadrate distance (between the anterior tip of the rostrum and the posterior extent of the mandibular condyle), mandibular length (between the anterior point of the mandibular symphysis and the retroarticular process), and tooth count of premaxillary, maxillary and mandibular teeth. The linear distance measurements were recorded with Mitutoyo 6-inch (Mitutoyo Corporation, Aurora, IL, USA) and Neiko 12-inch (CMT Industrial, Inc., Paramount, CA, USA) digital calipers, as well as a tape measure for the larger specimens. All digitized specimens were photographed with Canon PowerShot SD600 (Canon Electronics, Inc., Japan) for post-examination reference. 22

41 Data Processing Merging of Coordinate Data The newly added batch processing function in the Morpheus et al. program (Slice 2009) was utilized to automate the stitching of dorsal and ventral datasets, as well as the merging of all digitized specimens into a single file. Two nested batch files were written to merge the corresponding dorsal and ventral coordinate data for each specimen. The first batch file (Appendix C.1) stitched the two datasets using the following procedure: 1. Open the dorsal and ventral coordinate files. 2. This procedure requires that each landmark point on either dataset has a corresponding point on the other. In other words, the ventral dataset must contain dorsal landmarks that match with the actual dorsal landmarks in the dorsal dataset, and vice versa. Excluding the three common landmark points that exist in both datasets, 56 ventral landmarks with missing values are added to the dorsal dataset and 75 dorsal landmarks with missing values are inserted into the ventral dataset to produce dorsal and ventral datasets with 134 landmark points (i.e., 3 common landmarks with the sum of 75 strictly dorsal and 56 strictly ventral landmark points). 3. Then, the 75 strictly dorsal and 56 ventral landmark points are demoted as secondary points, while maintaining the three common landmarks as primary points that will be used for merging the two datasets. Secondary points are ignored from analyses that are conducted in the program. 4. The program is set to disallow reflections of objects to prevent erroneous merging of dorsal and ventral datasets. Otherwise, the program may produce merged objects with overlapping dorsal and ventral landmark points. 5. Generalized Procrustes superimposition is conducted on the three common primary landmarks in both datasets, which repositions, reorients, and rescales the three landmark points collectively until the sum of squared distance between matching points are minimized. Only the primary landmarks are considered in the Procrustes analysis, but the position of the secondary landmark points changes in correspondence with the three primary landmarks points. 23

42 6. Next, the scale is restored to retain size information, while maintaining the superimposed position and orientation of the two datasets. 7. The secondary landmarks are promoted back as primary landmarks. 8. Finally, the mean shape of the two superimposed datasets is saved as one object. Because the added landmarks with missing values do not contribute to the calculation of the mean shape, this procedure simply records the coordinate values of the repositioned and reoriented dorsal and ventral landmark points. Another batch file was written that calls the first batch file described above for each specified specimen. After stitching the dorsal and ventral coordinate datasets for all digitized specimens, multiple batch files were created to produce coordinate data files with all of the specimens for each species and also a single file that contains the coordinate data of all digitized specimens. Data Cleanup The entire raw coordinate data contain 256 specimens with 134 landmarks (Appendix D.1). However, approximately 20 percent of the points have missing coordinate values due to damaged areas on the specimens or certain landmarks that pertain to only particular taxa. Missing points are problematic because many morphometric programs cannot process missing data. Therefore, the removal of these missing points was necessary. In addition this was required to verify the accuracy of the coordinate data. The procedure went as follows: First, each digitized specimen was checked visually for erroneous data points. M_vis (Slice 2007b) was used to visualize the digitized specimens. Four objects exhibited obvious and unfixable stitching errors and were removed. FMNH (P. palpebrosus) was missing Landmark 2 (left posterior-most extent of the quadrate-quadratojugal suture), which is one of the three common landmark points used for merging the dorsal and ventral datasets. The other three specimens AMNH (G. gangeticus), FMNH (G. gangeticus), and MCZ (A. mississippiensis) showed stitching error due to unknown causes. Differentiating the landmarks on the left and right sides by color helped identify causes for the remaining observable errors. The color differentiation was accomplished in M_vis (Slice 2007b) by demoting all left landmarks as secondary points, which changes the default color of the points from green to 24

43 white. For the following specimens, the errors in the original coordinate data were fixed and the dorsal and ventral datasets were stitched together again to produce correctly digitized objects: FLMNH (A. mississippiensis): the coordinates for Landmarks 2 and 3 were switched. AMNH (A. mississippiensis): Landmarks 37, 39, and 41 were digitized for the wrong side. AMNH 7134 (Crocodylus niloticus): the coordinates for Landmarks 2 and 3 were switched. FMNH (Crocodylus porosus): the dorsal coordinates were copied for ventral landmarks by mistake when creating the NTSYS file for the specimen, thus, the ventral coordinates were correctly copied from the Excel spreadsheet. FMNH (Crocodylus porosus): the coordinates for Landmarks 2 and 3 were switched. AMNH (G. gangeticus): the coordinates for Landmark 49 was very similar to Landmark 48, thus, the coordinates for landmark 49 were removed. In addition, coordinates for Landmarks 62 and 63 were switched. After these errors were fixed, the demoted left landmarks were promoted back as primary landmarks. Next, the landmarks that exist or are appropriate for only certain taxa were removed from the dataset, leaving only those landmarks that were consistently identified in all eleven crocodilian species, i.e., Landmarks 4 14, 17 27, 46, 47, 54 59, 62, 63, 65 70, 72 75, 79 82, 89, 90, 110, 111, 117, 118, 123, and 124. Two A. mississippiensis specimens, AMNH 9043 and AMNH 12572, were later discovered to be missing the locality data, and hence, removed because of the possibility that these specimens were captively raised. This set of procedures resulted in a dataset with 250 specimens and 80 landmarks (Appendix D.2). Still, 662, or approximately 3.31 percent, of the 20,000 points, had missing coordinate values. To further eliminate missing data, I followed three approaches to create three datasets without any missing data. Dataset 1. The first dataset involved removing all specimens with any missing points. This resulted in a dataset with 108 specimens and one that maintains the 80 landmarks 25

44 (Appendix A, B.1). However, the representation of each species and ontogenetic stage suffered from such extensive removal of specimens from the data. Dataset 2. To retain more specimens, both specimens and missing points were systematically removed to produce a dataset that maximizes the sample size. First, landmarks with missing points in three or more specimens in the lesser-sampled taxa (i.e., G. gangeticus, M. niger, O. tetraspis, P. palpebrosus, P. trigonatus, and T. schlegelii) were removed. Then, specimens with missing points were removed only if there were more than two representatives for each approximated ontogenetic stage (i.e., neonate, juvenile, subadult, adult). Next, landmarks with missing points in any of the lesser-sampled taxa were removed. Finally, the specimens of relatively well-sampled species (i.e., A. mississippiensis, C. crocodilus, C. acutus, C. niloticus, and C. porosus) with any missing data were removed. Following this approach, two versions of Dataset 2 were created: one with and another without P. palpebrosus due to its lack of digitized specimens. For creating the latter dataset, all specimens of P. palpebrosus were removed first, and then, the aforementioned steps were taken. The dataset with P. palpebrosus includes 168 specimens and 40 landmarks (Appendix A, B.1), while the dataset without P. palpebrosus is composed of 162 specimens and 44 landmarks (Appendix A, B.1). Dataset 3. The third dataset employed a procedure to estimate the coordinate values for the missing points. First, the coordinate data file was converted from a Morpheus data file to an R data file that could be read in the R program (R Developmental Core Team 2008). From further examination of the coordinate data, additional erroneous points were identified: USNM (A. mississippiensis): coordinates for Landmark 37 (i.e., right prefrontalfrontal suture at the orbital margin) were removed because the values were nearly identical to the coordinate values for Landmark 32 (i.e., right frontal-postorbital suture at the orbital margin), indicating that the same point was digitized twice. FMNH (M. niger): coordinates for Landmark 44 (i.e., intersection of the right palatine-pterygoid suture and the margin of the right palatal fenestra) replaced the original values for Landmark 45 (i.e., intersection of the left palatine-pterygoid suture and the margin of the left palatal fenestra) because the position of the point clearly marks Landmark 45. Consequently, Landmark 44 became a missing point. 26

45 AMNH (O. tetraspis): coordinates for Landmark 2 were removed because the position of the point was not at the expected location of the left mandibular condyle, but was located in the median occipital region. These erroneous points were also removed in Datasets 1 and 2. Then, the specimens with eight or more missing points (greater than 10 percent of the 80 total landmarks in the cleaned dataset with missing data) were pruned from the data, with the exception of a neonate P. palpebrosus (FMNH 69875) and an adult P. trigonatus because they represent data points at the two ends of the growth series in very poorly sampled species. These two specimens had 10 missing points. For estimating the missing values, a multiple regression analysis was conducted on the coordinate data and size. Prior to the regression analysis, however, the digitized specimens needed to be in a common position and orientation. Thus, the coordinate dataset was opened in a previous version of the Morpheus et al. program (Slice 2002) for the Microsoft Windows Operating System, which allows Procrustes analysis to be conducted on shape data with missing points. The scale of the superimposed specimens was subsequently restored, and the specimen orientations were set to a common set of principal components axes for subsequent point estimations. This new orientation essentially realigns the specimen along the common anteroposterior, medio-lateral, and dorso-ventral axes represented by the first, second, and third principal components axes, respectively. An R script was written to automatically replace missing values with estimated coordinate values (Appendix C.2). First, the program conducts a linear regression analysis on each coordinate of individual landmarks and the skull length for each species using a subset of non-missing landmark points on specimens within species. The regression (slope) coefficient and the intercept value of the regression line are recorded and stored as a matrix with 22 rows for the regression coefficients and intercept values of 11 crocodilian species, and 240 columns for x, y, and z coordinates of 80 landmarks. When the script arrives on a missing value ( NA ), the script calls the corresponding regression coefficient and intercept value and calculates an estimated value for that coordinate. The missing value is replaced by the estimated value, and the remaining coordinates are read. With this method, nearly all of the missing values were replaced with estimated values. Furthermore, the majority of the regression analysis yielded high R-square 27

46 values (>0.90) and produced estimated points that were consistent with the general cranial morphologies of crocodilians when checked visually in M_vis (Slice 2007b). However, the program failed to calculate estimated values for several missing points and also produced predicted values that were clearly inaccurate for others. Four specimens AMNH (A. mississippiensis), FMNH (Crocodylus porosus), FLMNH (Caiman crocodilus), and FLMNH (Caiman crocodilus) still had missing points due to missing skull lengths for these specimens or less than two specimens in a species had recorded coordinates for the specific landmark. These specimens were removed from the data. Next, all remaining specimens were visualized in M_vis (Slice 2007b) to identify estimated points that are dubious. Landmark 93 (median point on palatal-pterygoid suture) was removed from all specimens because only a single neonate Crocodylus porosus specimen had recorded coordinates for this landmark and thus, resulted in inaccurate estimations for other Crocodylus porosus specimens with missing values for this landmark. Likewise, Landmark 107 (posterior median point of choanal margin) was removed from the dataset because the predicted points were consistently positioned more ventrally than expected based on the general morphology of other specimens. Next, 15 specimens that contained any dubious estimated points were removed, with the exception of FMNH (T. schlegelii) and MCZ (Caiman crocodilus) because the former is the only neonate Tomistoma and the latter is one of two neonate specimens for the Caiman. Finally, P. palpebrosus was removed entirely from the dataset because points were being estimated based on very few specimens. The two missing landmarks in FMNH and MCZ were instead estimated based on bilateral symmetry. A small program was written in the Python programming language (van Rossum 1995) that outputs predicted coordinate values based on the position of the landmark that is symmetric to the missing point and two points that are located along the median axis (Appendix C.3). The coordinates for Landmark 16 (right triple junction of maxilla, lacrimal, and jugal) in FMNH were predicted based on the x and y coordinate values (in frontal plane) for Landmark 15 (left triple junction of maxilla, lacrimal, and jugal) and Landmarks 91 (median intersection of premaxilla and maxilla on the ventral side) and 92 (median intersection of maxilla and palatine on the ventral side). Because the z coordinate represents the position of a point along the dorso-ventral axis from the alignment based on principal components axes, the z coordinate value for Landmark 16 was used for Landmark 15. Similarly, coordinates for 28

47 Landmark 91 (position of the left tenth maxillary tooth along the alveolar margin) in MCZ were estimated based on the coordinates for Landmark 87 (position of the right tenth maxillary tooth along the alveolar margin) and the two median landmarks Landmarks 91 and 92. These estimated points were visually checked on M_vis (Slice 2007b) and they appeared to be compatible with the general morphology of the cranium. Despite inaccurate predictions for some of the missing points in the data, which were removed from the dataset, the procedure was largely successful in maintaining robust taxonomic and ontogenetic post-natal sampling (Fig. 2.1), as well as the number of landmarks (Fig. 2.2). With 208 specimens and 78 landmarks, Dataset 3 includes more shape information on individuals and species compared to the two other datasets. The first dataset was not analyzed because it contains insufficient taxonomic and ontogenetic sampling, particularly for G. gavialis, M. niger, and O. tetraspis. The use of estimated values needs to also be justified because the assumptions inherent in the calculation of estimated points may alter the results of the study. Therefore, principal components analysis was conducted on all three datasets to verify whether the inclusion of estimated values alter the distribution of the points in the morphospace constructed from principal component scores (Fig. 2.3). The PC plots show a great degree of congruence in the distribution of data points and species clusters between the second and third datasets, which implies that the inclusion of estimated points will not produce contrasting results. Hence, subsequent analyses primarily used the third dataset due to the greater taxonomic and ontogenetic sampling, as well as number of landmarks. 29

48 Table 2.2. Sample size of crocodilian species in Datasets 1, 2, and 3. Taxon Dataset 1 Dataset 2a Dataset 2b Dataset 3 Alligator mississippiensis Caiman crocodilus Crocodylus acutus Crocodylus niloticus Crocodylus porosus Gavialis gangeticus Melanosuchus niger Osteolaemus tetraspis Paleosuchus palpebrosus Paleosuchus trigonatus Tomistoma schlegelii Total

49 31

50 Figure 2.1. Distributions of centroid sizes of specimens in each sampled species. A, Alligator mississippiensis; B, Caiman crocodilus; C, Crocodylus acutus; D, Crocodylus niloticus; E, Crocodylus porosus; F, Gavialis gangeticus; G, Melanosuchus niger; H, Osteolaemus tetraspis; I, Paleosuchus trigonatus; J, Tomistoma schlegelii. Centroid size is in mm. 32

51 Figure 2.2. Positions of landmarks used in Dataset 3 on the cranium of crocodilians. A, dorsal view of AMNH 8058 (Alligator mississippiensis); B, ventral view of AMNH 8058; C, postero-dorsal view of AMNH (A. mississippiensis); D, postero-ventral view of AMNH 12572; E, ventro-lateral view of USNM (Crocodylus niloticus). Dorsal landmarks are shown in A and C; ventral landmarks are shown in B, D, and E. 33

52 Figure 2.3. Bivariate plots of the first and second principal components (PC1, 2) of Procrustes coordinates. A, Dataset 1; B, Dataset 2b; D, Dataset 3. Note the general congruence between the plots of Datasets 3 with 2b and 3, which justifies the use of estimated points in the latter dataset. Paleosuchus palpebrosus was removed from Dataset 1 for constructing these plots to ensure proper comparisons of morphospace (Datasets 2b and 3 do not contain P. palpebrosus). 34

53 Generalized Procrustes Superimposition A standard protocol for conducting shape analysis is the generalized Procrustes superimposition method, which removes the effect of position, orientation, and scale of objects on coordinates (Gower 1975). It involves an iterative minimization of distances between the corresponding points of each specimen and a consensus or reference shape. In mathematical form, the process attempts to minimize E in the general equation, (X 1 1 )H = X 0 + E, in which X 0 is the consensus shape matrix; X 1 is the shape of a specimen; is the scaling coefficient often scaled to unit centroid size; is the translation matrix; and H is the rotation matrix (Rohlf and Slice 1990). Here, the sum of squared elements of E, or the distance between the consensus and the object after translation, rotation, and scaling, is known as Procrustes distance, which is a metric used for differences in the shapes of two objects. After the generalized Procrustes superimposition, what is retained in the data is the information on shape of objects, defined as the geometric properties of an object that are invariant to position, orientation, and isometric scaling (Slice 2007a). The least-squares approach employed here may be problematic because it has a tendency to spread the differences across landmarks even when the shape difference is localized. In other words, a significant change in one part of the object may cause the remaining parts to move during the superimposition process even if no actual change occurred in these parts, referred to as the Pinocchio effect (Chapman 1990). An alternative approach is to use the theta-rho resistant fit method, which is based on medians of angular and distances (Slice 1996). Regarding the crania of crocodilians, a major morphological differences in the snout, defined here as the region on the skull anterior to the orbit, among species and ontogenetic stages may severely alter the position of points in the neurocranium. However, there are considerably more landmarks in the neurocranium than in the viscerocranium, which would help to anchor the positions of the points in the neurocranium during the superimposition process. Hence, a least-squares approach was still used to conduct the superimposition of objects. 35

54 CHAPTER THREE PHYLOGENETIC UTILITY OF ALLOMETRIC TRAJECTORIES CONSTRUCTED FROM GEOMETRIC MORPHOMETRIC DATA Introduction Virtually all organisms undergo remarkable changes in form throughout ontogeny. In addition to growth, or increases in body size, organisms exhibit notable changes in morphology, perhaps best exemplified by the metamorphic arthropods and amphibians. Allometry, or deviations from simple scalar, or isometric, growth describes the shape changes that occur during the development of an organism. Because all organisms begin as a unicellular entity, the differences in adult morphologies must necessarily be due to changes in developmental trajectories (Gould 1977; Alberch et al. 1979; McKinney and McNamara 1991). Consequently, taxa that are morphologically similar in their somatically mature forms are expected to follow similar patterns of developmental morphological change. Following this phenetic reasoning, one may suspect that the similarities in allometric morphological changes imply phylogenetic relatedness. Besides convergent evolution, however, this presumption may not hold true, especially in light of known occurrences of heterochrony, in which distantly related paedomorphic or peramorphic taxa that follow similar developmental trajectories cluster together in phylogenetic reconstructions (e.g., Wiens et al. 2010). To investigate whether patterns in allometric growth are phylogenetically informative, allometric trajectories can be constructed that record the morphological changes that occur during development. Multiple approaches exist for characterizing the morphological changes throughout ontogeny. Ontogenetic sequences of morphological character state changes are easy to interpret, but multivariate statistical methods are difficult to implement for comparing patterns in developmental trajectories. In addition, the discrete nature and non-equivalency of morphological characters (i.e., state changes among morphological characters are not defined under a universal framework) make consideration of variation within taxonomic units difficult. 36

55 Alternatively, sets of discrete morphological characters or linear distances have been used to describe the morphology at various developmental stages or size classes within the context of morphological space. A dimension reducing method (e.g., principal components analysis, canonical variates analysis) could be conducted on the dataset to place the data points in a common morphological space, à la morphological disparity studies (Foote 1997), which could then be used to construct and compare the trajectories. Although multivariate statistical analyses could easily be applied to such data, morphological changes that occur along allometric trajectories are difficult to visualize and interpret. Here, landmark-based geometric morphometric methods were used to construct allometric trajectories to overcome the shortcomings of these other methods. Geometric morphometrics permits statistical comparisons of shape, or geometric properties of an object invariant to position, orientation, and scale (Slice 2007a). It also provides a more direct method of recording shape changes throughout ontogeny by employing landmarks in a common coordinate space. Allometric trajectories could be constructed based on coordinate data of landmark points and a size variable, which record the continuous shape change that occur as organisms grow (Klingenberg 1998). Furthermore, morphological changes that occur on specimens could be modeled and visualized continuously, and changes associated with PC axes could be visualized via thin-plate spline visualization (Bookstein 1989, 1991). Previous studies have used these trajectories to infer the phylogenetic relationships of various taxonomic groups. Campione and Evans (2011), for example, used allometric trajectories to re-evaluate the taxonomic designation of the North American hadrosaurids. Piras et al. (2010) attempted to resolve the discrepancies in the phylogenetic placement of Gavialis between the morphological and molecular trees (Fig. 1.2) based on the similarities in the orientation of the allometric trajectories among Gavialis, Tomistoma, and two other crocodylid species Crocodylus acutus and Mecistops cataphractus. However, these studies presume that similarities in the orientation of these allometric trajectories reflect the phylogenetic affinity between taxa without testing for phylogenetic signal. Among vertebrate groups, explicit tests of the association between the allometric trajectories and phylogenetic relatedness have been limited in number. Using geometric morphometric methods, Vi arsdóttir and Cobb (2004) have shown that the orientation of the allometric trajectories are more similar than expected among closely related hominoids. Based on linear distances, Larson (2005) showed that clusters based on the cranial 37

56 development in Rana tadpoles are largely congruent with their molecular phylogeny, but an explicit statistical test was not conducted. Furthermore, whether this case holds true for other sauropsid taxa, developmental duration, taxonomic scale (e.g., interspecific vs. intergeneric), and with geometric morphometric data remains to be tested. For this study, the extant members of Crocodylia (sensu Clark 1994) were used to explicitly test whether the allometric trajectories constructed from three-dimensional coordinate data of cranial landmarks contain significant phylogenetic signal. Among vertebrates, crocodilians provide an excellent system for studying ontogenetic changes. First, crocodilians undergo remarkable 1000 to 5000 fold increases in body mass (Grenard 1991; Erickson et al. 2004b) and significant morphological changes during development, but not as to prevent continuous record of shape change as in metamorphic amphibian taxa. Crucial to this study are the published molecular phylogenies (e.g., Gatesy et al. 2003; Harshman et al. 2003; Oaks 2011), with which morphological attributes can be optimized and morphology-based dendrograms could be compared. Moreover, crocodilians are often used as modern analogs for extinct archosaurian groups, and thus, understanding the utility of ontogenetic data in phylogenetic inference of Crocodylia may provide insight into other archosaurian clades (e.g., non-avian dinosaurs, Avialae). Furthermore, its rich evolutionary history that dates back to the Late Cretaceous (~85 Ma) and the wide geographical distribution of the group (Brochu 2001a; Oaks 2011) allow for macroevolutionary studies in temporal and geographic scales that are typical of paleontological studies. A suite of methods were employed to test the significance of the phylogenetic signal contained in the allometric trajectories, including (1) the K-statistic, which measures the degree of similarity in trait values between taxa relative to Brownian motion trait evolution (Blomberg et al. 2003); (2) a likelihood ratio test based on Pagel s lambda to test the significance of the likelihood of trait evolution along a phylogeny (Pagel 1999); (3) permutational regression analysis, a non-parametric method for testing the correlation between phenotypic and phylogenetic distances; (4) topological comparisons between the dendrogram constructed from a clustering method and a published molecular phylogeny; and (5) a Mantel test, which is a nonparametric test for the correlation between two distance matrices (Mantel 1967; Sokal and Rohlf 1995) in this case, the angular distances between the allometric trajectories and phylogenetic distances. The results of this study will determine whether previous assumptions about the 38

57 correlation between similarities in allometric trajectories and phylogenetic relatedness are justified. If the study produces non-significant results, then there would be a need to re-evaluate previous studies that have made such assumptions and also give caution to the use of ontogenetic data in phylogenetic inference. Materials and Methods Morphometric Data The morphometric dataset used for the analyses consists of three-dimensional coordinate data for 78 cranial landmarks (Appendix B: Dataset 3) and 208 digitized specimens (Appendix A: Dataset 3) representing 10 extant crocodilian species (Table 2.2). The taxonomic sampling was based on the availability of osteological specimens at six North American institutions (AMNH, FLMNH, FMNH, MCZ, UMMZ, USNM) and an attempt to sample broadly across the Crocodylia clade, both phylogenetically and morphologically. Landmarks, defined as geometrically homologous, but not necessarily evolutionarily homologous, anatomical points (Gunz et al. 2009), were determined based on the consistent and reliable identification of the points on all sampled species across the post-natal developmental series. The dataset included visually confirmed estimated points based on regression analysis of raw coordinates and skull length, as well as symmetry in order to replace missing data (see Chapter 2 for details). However, the analyses were also conducted on another dataset (i.e., Dataset 2b), from which specimens and landmarks were pruned, which ultimately produced similar results that are not shown here. A MicroScribe G2 digitizer (Immersion Corporation) and its companion program Microscribe Utility Software (Immersion Corporation, San Jose, CA, USA), provided by the Florida State University Morphometrics Lab (Tallahassee, FL, USA), were used to record the three-dimensional coordinates. The dorsal and ventral landmarks points were digitized separately and subsequently merged together using the Morpheus et al. program (Slice 2011) by superimposing three landmarks recorded in both the dorsal and ventral datasets. Besides the coordinate data, additional morphometric data were recorded for each digitized specimen, including skull length, rostral length, rostral width, inter-quadrate distance, premaxilla-quadrate distance, and mandibular length (refer to Chapter 2 for definitions of these linear distances). The 39

58 linear distances were measured with Mitutoyo 6-inch (Mitutoyo Corporation, Aurora, IL, USA) and Neiko 12-inch (CMT Industrial, Inc., Paramount, CA, USA) digital calipers, as well as with a tape measure for the larger specimens. Generalized Procrustes superimposition was conducted on the entire coordinate dataset to remove the effects of position, orientation, and scale on the coordinates of the digitized specimens (Fig. 2.4). This procedure converts the three-dimensional coordinate data into Procrustes coordinates, which are then used to compare the shapes of specimens. Allometric Trajectories The combination of Procrustes coordinates and centroid size data of the specimens was used to construct allometric trajectories, which describe the shape changes that occur through ontogeny. To account for the high dimensionality of the shape data, multiple approaches were taken to quantify the orientation of the trajectories: Low-dimensional trajectories (LDT) Dimension-reducing methods, such as principal components analysis (PCA) and canonical variates analysis (CVA), allow the underlying pattern of covariance in high-dimensional data to be condensed into fewer dimensions. As such, a set of allometric trajectories was constructed from conducting PCA on shape data and plotting the PC scores against a size variable (e.g., centroid size). Two types of low-dimensional trajectories were constructed by utilizing PCA. The first type of low-dimension allometric trajectories was constructed by performing the following steps (Appendix C.4): 1. PCA was conducted on pooled Procrustes coordinates. 2. Pairs of PC axes were plotted that individually explain at least five percent of the total variance (Fig. 3.1). Among the first four PCs, the PC2 axis was most closely associated with ontogenetic shape variation because the size series of most species are distributed along this axis (Fig. 3.1). Thus, PC2 was used to construct the trajectories for the primary analysis. 3. PC2 was plotted against log centroid size of each specimen and trajectories were constructed from regression lines obtained from linear regression analysis for each species (Fig. 3.2). 4. The angle between the regression line and the horizontal axis was calculated by solving the arctangent of the regression (slope) coefficient and adding /2 to avoid negative 40

59 angles. This angle, in radians, was used as a univariate trait value for the analyses (Table 3.1). This approach of using PCA allows the allometric trajectories to be easily visualized and has been employed in other studies on allometry (e.g., Piras et al. 2010). However, this approach dramatically reduces the dimensionality of the original shape data and may fail to sufficiently capture the total variance in the data. In fact, PC2, which is associated with the relative compression of the neurocranium (Fig. 3.3B), explains less than 20 percent of the total variation. To incorporate more of the shape variation in the data, trajectories constructed from the plot of PC1, which explains approximately 40 percent of the total variance, over log centroid size were also analyzed (Fig. 3.4) despite the fact that variance along PC1 is mostly associated with differences among species, not size series within species. The first principal component is primarily associated with changes in the shape of the rostrum (Fig. 3.3A). 41

60 Figure 3.1. Bivariate plots of the first four principal components scores (PC1 4) of Procrustes coordinates. 42

61 Figure 3.2. Bivariate plot of the second principal component (PC2) of Procrustes coordinates and log centroid size. Lines indicate regression lines for each species. Centroid size in mm. 43

62 Fig 3.3. Shape changes from the mean shape of all sampled specimens in dorsal view associated with A, the first principal components axis (PC1); B, the second principal components axis (PC 2). Visualized using MorphoJ (Klingenberg 2011). The dots denote the position of pooled mean shape and lines represent the extent of positional shift corresponding to an increase of 0.1 units of Procrustes distance in the negative direction of corresponding PC axis. 44

63 Figure 3.4. Bivariate plot of the first principal component (PC1) of Procrustes coordinates and log centroid size. Lines indicate regression lines for each species. Centroid size in mm. 45

64 Low-dimensional trajectories using the common allometric component (LDT CAC) Mitteroecker et al. (2004) suggests an approach that involves a PCA on the residuals from a common allometric component (CAC). It still employs a dimension-reducing method, and the orientation of the trajectories was again described by univariate angles. The following procedure details the steps taken to construct these allometric trajectories (Appendix C.5): 1. Procrustes coordinate data were centered by species means. 2. The CAC was determined by conducting a set of linear regression analysis on centered Procrustes coordinates and log centroid size of the entire dataset. 3. Residuals of each shape variable from the CAC for each specimen were subjected to a PCA. 4. PC1 of residuals was plotted against log centroid size (Fig. 3.5). 5. A linear regression analysis was conducted for each species to construct the allometric trajectories. The regression (shape) coefficient of the regression lines was used to calculate the angle of the trajectories relative to the horizontal axis and /2 was added to each angle to prevent negative values (Table 3.1). Similar to the first approach, these low-dimensional trajectories could easily be visualized, but with the cost of considerable reduction in dimensionality. The first principal component only explains approximately 20 percent of the total variance of the deviation from CAC. Hence, much of the variation is not accounted for with this method and may give a signal that differs from that of the entire dataset. This method was used in this study because this approach presents a different way for constructing allometric trajectories and may potentially yield different results than the first method. 46

65 Figure 3.5. Bivariate plot of the first principal component (PC1) of residuals from the common allometric component and log centroid size. Lines indicate regression lines for each species. Centroid size in mm. 47

66 Table 3.1. Angles (radians) of low-dimensional allometric trajectories relative to the vertical axis (principal component axis) for each sampled species. Abbreviations: LDT PC1, lowdimensional trajectories based on PC1 of Procrustes shape data; LDT PC2, low-dimensional trajectories based on PC2 of Procrustes shape data; LDT CAC, low-dimensional trajectories based on PC1 of residuals from the common allometric component. Taxon LDT PC1 LDT PC2 LDT CAC Alligator mississippiensis Caiman crocodilus Crocodylus acutus Crocodylus niloticus Crocodylus porosus Gavialis gangeticus Melanosuchus niger Osteolaemus tetraspis Paleosuchus trigonatus Tomistoma schlegelii High-dimensional trajectories with (HDT + I) and without intercept data (HDT) Multiple regression analysis was used to construct high-dimensional vectors that describe the ontogenetic shape changes while maintaining the dimensionality of the Procrustes shape data. The procedure consists of the following steps (Appendix C.6): 1. For each species, a multiple regression analysis was performed on each shape variable and log centroid size, and the regression (slope) coefficients and the intercept values were recorded. 2. These recorded values were incorporated into a vector for each species to construct highdimensional trajectories that describe the positional changes at each landmark. Two types of vectors were created. One set of vectors contained only the regression (slope) coefficients, as was done in a previous geometric morphometric study on crocodilians (Piras et al. 2010). However, differences in the intercept values were also considered because taxa with identical rate of morphological change could still have distant trajectories due to different intercept values, which resulted in vectors with a combination of 234 correlation coefficients and 234 intercept values. 48

67 Although these high-dimensional allometric trajectories cannot easily be plotted, these trajectories maintain the dimensionality of the shape data. Therefore, these vectors have a far greater capability of describing the shape changes that occur across the cranium. Distances between trajectories Angular distances were used as a metric for quantifying the differences between the orientations of both the low- and high-dimensional allometric trajectories. For the low-dimensional trajectories, the angular distances are simply the difference in the angles between the allometric trajectories and the vertical axis. The angular distance between the high-dimensional allometric trajectories (Table 3.2) were calculated based on the formula = arccos a b a b, in which a and b represent the two vectors, is the dot product, and is the vector length. An R program was written to produce a distance matrix from a set of high-dimensional vectors (Appendix C.7). Other distance measures have been used to quantify the differences between high-dimensional allometric trajectories, including Euclidean (e.g., Piras et al. 2010) and Mahalanobis distances (e.g., Larson 2005). Additional set of analysis was done with Euclidean distances to investigate whether difference distance measures could yield contrasting results. 49

68 Table 3.2. Distance matrices of angular distances between the low- and high-dimensional allometric trajectories. The distances are in radians. Abbreviations: HDT, high-dimensional trajectories constructed from only regression (slope) coefficients; HDT+I, highdimensional trajectories constructed from both regression coefficients and intercept values. HDT A. mis. C. cro. C. acu. C. nil. C. por. G. gan. M. nig. O. tet. P. tri. C. cro C. acu C. nil C. por G. gan M. nig O. tet P. tri T. sch HDT+I A. mis. C. cro. C. acu. C. nil. C. por. G. gan. M. nig. O. tet. P. tri. C. cro C. acu C. nil C. por G. gan M. nig O. tet P. tri T. sch

69 Time-Calibrated Phylogeny Phylogenetic reconstructions based on molecular data provide hypotheses of evolutionary relationships that are essentially independent from morphological data. The phylogenetic tree used to test for phylogenetic signal (Fig. 3.6) was based on a time-calibrated tree by Oaks (2011) because it (1) utilized an extensive set of sequence data for crocodilian phylogenetic reconstructions, i.e., 10 nuclear loci; (2) sampled all 23 extant crocodilian species; (3) is largely congruent with other molecular trees; and (4) provides temporally scaled branch lengths that could be used for the tests that incorporate phylogenetic information. Figure 3.6. Time-calibrated molecular tree based on an ultrametric tree in Oaks Taxa were pruned from the original published tree accordingly. Numbers indicate Ma. 51

70 Phylogenetic Signal Using both the low- and high-dimensional metrics for quantifying the orientation of the allometric trajectories, several methods were employed to examine the degree to which the trajectories are phylogenetically informative. K-statistic. One way of checking for phylogenetic signal is to determine whether closely related taxa are associated with similar trait values. The K-statistic (Blomberg et al. 2003) describes the degree of interspecific similarity in trait values relative to the similarity expected from the Brownian motion model of trait evolution along a given phylogeny. A K-statistic value between zero and one implies that the trait values have no association with phylogeny. Alternatively, a value greater than one signifies that the trait values are more similar between closely related taxa than expected by Brownian motion, which may indicate shared selective pressure acting on the trait. The K-statistic value was calculated using the ape (Paradis et al. 2004) and picante (Kembel et al. 2010) R packages, and the angles of the low-dimensional trajectories were used as trait values because the input is limited to a univariate variable. The K- statistic is a descriptive parameter, and thus, is not a statistical test for phylogenetic signal (i.e., null distribution is unknown). However, it provides useful information on the general distribution of trait values in a phylogenetic context. Likelihood ratio tests using Pagel s lambda. The significance of the phylogenetic signal of a trait could be determined via Pagel s lambda (Pagel 1999), which transforms the structure of phylogenetic trees. A lambda value has a range between zero and one, in which a value of zero produces a completely polytomous tree and a value of one perfectly maintains the topological structure and branch lengths of a given phylogeny (Fig. 3.7). In the geiger R package (Harmon et al. 2008), the fitcontinuous function determines the lambda value that maximizes the likelihood of the implied trait evolution based on given trait values. A Pagel s lambda near zero would indicate that the trait values contain little phylogenetic signal. By implementing Pagel s lambda, the likelihood ratio test could be used to compare the likelihoods of the character traits evolving on this altered phylogenetic tree and on an entirely polytomous tree (i.e., null). Here, the test is used to determine the significance of shared evolutionary histories for explaining similarities in trait values compared to a random distribution of trait values among sampled taxa. The traits are modeled to evolve linearly across branch lengths. 52

71 Because the function only allows univariate data, the angles of low-dimensional trajectories were used for the analysis. Permutational regression analysis. Perhaps a more direct approach to test for phylogenetic signal is to examine the correlation between the phenotypic and phylogenetic distances. Because parametric statistical methods make assumptions that are often violated in biological systems, a non-parametric permutational regression analysis was conducted. For conducting the analysis, a program was written (Appendix C.8) using Python (van Rossum 1995). First, the program randomizes the species at the tips of a phylogeny while keeping the topology and branch lengths constant. In each iteration, the pairwise differences between univariate trait values and the phylogenetic distance, which is the total branch length separating two taxa (equivalent to twice the estimated divergence time at the shared node), are calculated and recorded. Then, these phenotypic and phylogenetic distances are subjected to linear regression analysis and the regression (slope) coefficient is recorded for each randomized dataset. After a specified number of iterations (10,000 for this study), a histogram is constructed based on the frequency distribution of regression coefficient values. The significance of the regression coefficient given by the observed data could then be determined based on the p-value of obtaining a regression coefficient that is as or more distant from zero than the coefficient values recorded from randomized data. Presently, the program only accepts univariate trait values, but implementation to support n-variable data is planned for future updates to the program. UPGMA phenogram. Unweighted pairwise grouping method based on arithmetic means (UPGMA) is a clustering algorithm used to construct a dendrogram based on a distance matrix. Here, it was used to produce a phenogram based on the angular distances between the low- and high-dimensional trajectories, as well as the Euclidean distances between the latter. If allometric trajectories are phylogenetically informative, then congruence between the topologies of the phenogram and molecular phylogeny is expected. The proportion of shared nodes was used to measure the topological difference between the molecular tree and the phenogram. Clustering was done in R using the upgma() function in the phangorn R package (Maechler et al. 2002). Mantel test. Similar to the permutational regression analysis, the Mantel test is a nonparametric method for testing the significance of covariance between two distance matrices (Sokal and Rohlf 1995). The trajectory and phylogenetic distances of both the low- and high- 53

72 dimensinoal trajectories were used in the analysis, in addition to the Euclidean distances between the high-dimensional allometric trajectories. The test was conducted with the mantel.rtest() function in the ade4 R package (Dray and Dufour 2007) with 9,999 randomizations. Bivariate plots of trajectory and phylogenetic distances Both the permutational regression analysis and the Mantel test assume linear correlation between the trajectory and phylogenetic distances. However, these two distances may be associated non-linearly or could be correlated within particular temporal scale. For example, the allometric trajectories may be phylogenetically informative for relatively recent divergences, but the phylogenetic signal is lost at greater divergence times. Therefore, bivariate plots of trajectory and phylogenetic distances were plotted to check for any observable patterns. 54

73 Figure 3.7. The effect of Pagel s lambda on the structure of a phylogenetic tree. A, Pagel s lambda = 1; B, Pagel s lambda = 0.5; C, Pagel s lambda = 0.1; D, Pagel s lambda = 0. 55

74 Results K-Statistic The K-statistic for all three types of low-dimensional trajectories was calculated to be below 1. This result implies that the trajectory angles are more dissimilar among closely related species than are expected from a Brownian motion of character evolution along the timecalibrated tree. The low-dimensional trajectory based on the common allometric component yielded the lowest K value (= 0.247), while the trajectory constructed from the PC2 from Procrustes coordinates produced the greatest value (= 0.711), but still below 1. Likelihood Ratio Test Using Pagel s Lambda For all three types of low-dimensional trajectories, the p-value obtained from the likelihood ratio test was not significant, i.e., p-value > 0.05 (Table 3.3). The maximally likely lambda values given the observed distribution of trait values were all calculated to be well above zero, which could be an indication of some degree of phylogenetic signal. In particular, the calculated lambda value for LDT PC2 was 1, which may initially be considered as a strong indication of phylogenetic signal. Despite the magnitude of these lambda values, the maximum likelihoods were not significantly different from the likelihoods of Brownian trait evolution along an entirely polytomous tree (i.e., lambda = 0). These results suggest that the orientations of the low-dimensional allometric trajectories are randomly distributed among members of Crocodylia. However, they may be due to low power from low sample size (i.e., n = 10). Table 3.3. Result of the likelihood ratio tests and relevant parameters values. Abbreviations: LDT PC1, low-dimensional trajectories based on PC1 of Procrustes shape data; LDT PC2, lowdimensional trajectories based on PC2 of Procrustes shape data; LDT CAC, low-dimensional trajectories based on PC1 of residuals from the common allometric component; LRT, likelihood ratio test. Parameter LDT PC1 LDT PC2 LDT CAC ML lnml lnl ( = 0) LRT p-value

75 Permutational Regression Analysis The permutational regression analysis produced a non-significant p-value for all three types of low-dimensional trajectories (Table 3.4). Thus, the angular distances between the trajectories showed no significant correlation with phylogenetic distances based on estimated divergence times. A poor correlation is also apparent from the low R 2 values obtained from regression analysis of the observed data (Table 3.4). The frequency distributions of recorded regression coefficients from randomized samples exhibit a normal distribution (Fig. 3.8). Relative to the p-values from the likelihood ratio test, corresponding p-values obtained from the permutational regression analysis are consistently greater. Yet, the results are congruent with the p-values from the likelihood ratio tests, in which LTD PC2 shows the most significance among the three trajectory types. Table 3.4. Regression coefficient and R 2 values from the linear regression analysis of trajectory and phylogenetic distances based on observed data, and p-value from the permutational regression analysis. Abbreviations: LDT PC1, low-dimensional trajectories based on PC1 of Procrustes shape data; LDT PC2, low-dimensional trajectories based on PC2 of Procrustes shape data; LDT CAC, low-dimensional trajectories based on PC1 of residuals from the common allometric component. Parameter LDT PC1 LDT PC2 LDT CAC Regression coefficient R 2 value p-value

76 58

77 Figure 3.8. Histograms of regression coefficients (RC) recorded from 9,999 iterations of permutational regression analysis on A, low-dimensional trajectories based on PC1 of Procrustes shape data; B, low-dimensional trajectories based on PC2 of Procrustes shape data; C, lowdimensional trajectories based on PC1 of residuals from the common allometric component. UPGMA Phenograms The phenograms constructed by UPGMA differ markedly from the time-calibrated phylogeny of Crocodylia (Fig. 3.9). Alligatorid and crocodylid species, which comprise two major lineages in Crocodylia (Fig. 3.6), were intermixed in all phenograms, and none of the nodes occured in the time-calibrated molecular tree. Similarly, no shared nodes existed between the phenogram and a tree (Fig. 3.10) that was constructed from the morphological dataset by Brochu (1999, 2000), with the exception of the basal-most node in the phenogram constructed from the angular distances of LDT PC2 and HDT+I (Fig. 3.9B, E). In fact, these phenograms are not similar among themselves, suggesting that the underlying similarities among allometric trajectories are highly dependent on the metric used. 59

78 60

79 Figure 3.9. Phenograms constructed via unweighted pairwise grouping method based on arithmetic means (UPGMA) based on the angular distances between low-dimensional and highdimensional allometric trajectories. Phenogram constructed from A, low-dimensional trajectories based on PC1 of Procrustes coordinates (LDT PC1); B, low-dimensional trajectories based on PC2 of Procrustes coordinates (LDT PC2); C, low-dimensional trajectories based on PC1 of residuals from the common allometric component (LDT CAC); D, high-dimensional trajectories without intercept values (HDT); E, high-dimensional trajectories with intercept values (HDT+I). Figure Majority-consensus cladogram of Crocodylia based on a modified version of a published morphological dataset that (Brochu 1999; 2000; modified by Brochu). All unsampled extant and extinct taxa were pruned from the tree, and thus, only the sampled species are shown. 61

80 Mantel Test The Mantel test did not produce any significant results for any of the low- and highdimensional trajectory types (i.e., p-value > 0.05), which implies that there is no correlation between the angular and phylogenetic distances (Table 3.5). Among the low-dimensional trajectory types, the LDT CAC yielded the lowest p-value, instead of LDT PC2, which had a slightly greater value. Angular distances based on HDT+I produced the lowest p-value (= ), and both types of high-dimensional trajectories generated lower p-values than the lower-dimensional trajectories. A Mantel test was also conducted using Euclidean distances for the high-dimensional trajectories, which resulted in p-values that were greater than those obtained from angular distances. Table 3.5. P-values obtained from Mantel tests. Abbreviations: HDT, high-dimensional trajectories without intercept values; HDT, high-dimensional trajectories with intercept values; HDT+I, high-dimensional trajectories with intercept values; LDT PC1, low-dimensional trajectories based on PC1 of Procrustes shape data; LDT PC2, low-dimensional trajectories based on PC2 of Procrustes shape data; LDT CAC, low-dimensional trajectories based on PC1 of residuals from the common allometric component. Distance metric LDT PC1 LDT PC2 LDT CAC HDT HDT+I Angular distance Euclidean distance Bivariate Plots of Trajectory and Phylogenetic Distances The bivariate plots do not show any unambiguous patterns (Fig. 3.11). However, two possible patterns are discernable. First, the upper bound of trajectory distances seems to increase in conjunction with phylogenetic distance at least within ~100 Myr, with the exception of figures 3.11A and 3.11D). As such, variance increases with divergence time. However, data points at ~130 Myr exhibit considerably smaller trajectory distances, which counter this general trend. Nevertheless, this phylogenetic distance is limited to A. mississippiensis and all other alligatorids, thus, represents merely a single contrast. Second, the bivariate plots based on the angular distances in HDT and Euclidean distances in HDT and HDT+I show a sign of positive correlation within 25 Myr of phylogenetic distance (Fig. 3.10:E G). 62

81 63

82 Figure Bivariate plots of trajectory and phylogenetic distances. The former is measured using both angular and Euclidean distances, and the latter is calculated as the total branch length separating a pair of species, which is equivalent to twice the estimated divergence times for the extant species sampled for this study. The plot for A, low-dimensional trajectories based on PC1 of Procrustes coordinates (LDT PC1); B, low-dimensional trajectories based on PC2 of Procrustes coordinates (LDT PC2); C, low-dimensional trajectories based on PC1 of residuals from the common allometric component (LDT CAC); D, high-dimensional trajectories without intercept values (HDT) using angular distances; E, high-dimensional trajectories with intercept values (HDT+I) using angular distances; F, HDT using Euclidean distances; G, HDT+I using Euclidean distances. 64

83 Discussion Allometric Trajectories The bivariate plots of shape and size contain notable information regarding the developmental trajectories of crocodilians. Both the PC1 and PC2 of Procrustes coordinates show that the allometric trajectories of Gavialis and Tomistoma are quite distinct from the other crocodilian species, which is expected given that hatchling individuals of the two gharial species already bear narrow snouts akin to their adult forms. The bivariate plot of PC1, in particular, exhibits clusters of alligatorids and crocodylids, with the exception of P. trigonatus (fig. 3.4). This separation between these two major crocodilian subclades is likely driven by snout shape because PC1 is primarily associated with the shape of the rostrum (Fig. 3.3). The allometric trajectories based on PC1 of Procrustes coordinates, however, indicate general convergence among species as individuals grow to counter the general observation of divergent morphology among adult forms in vertebrates. In contrast, the allometric trajectories constructed from PC2 of Procrustes coordinates diverge as size increases (Fig. 3.2), which indicate contrasting depictions of the developmental trajectories in crocodilians than the PC1 and the CAC low-dimensional trajectories. In fact, the orientation of the trajectories based on the CAC show little discernable pattern, in which Crocodylus porosus and Tomistoma schlegelii follow nearly identical trajectories (Fig. 3.5). The allometric trajectories of dwarf taxa present both expected and unexpected patterns. As anticipated, the trajectory of the Schneider s dwarf caiman (Paleosuchus) occupies the lower size of the trajectories of other alligatorid taxa in the bivariate plots of both PC1 and PC2 of Procrustes coordinates (Fig. 3.2, 3.3). This placement supports the idea that Paleosuchus is a dwarf taxon and suggest an early offset of development as the cause, although more robust sample size is needed to make such conclusion. Interestingly, the allometric trajectory of the African dwarf crocodile (Osteolaemus) is more proximate to those of alligatorids than crocodylids. This outcome could be due to the relatively broad rostrum of Osteolaemus, which resembles that of alligatorines (Grenard 1991). Multiple approaches were taken to quantify the orientation of the allometric trajectories. The use of regression lines inherently assumes a correlation between shape and log centroid size. On average, the regression analyses conducted on the PC1 of residuals from the CAC and size, 65

84 as well as PC1 of Procrustes coordinates and size, give much lower R 2 values than those on PC2 of Procrustes coordinates (Table 3.6), which indicates weak associations between growth and PC1 of both the Procrustes coordinates and the deviations from the CAC. In comparison, the R 2 values from the regression analysis on PC2 of Procrustes coordinates are consistently high and the bivariate plot (Fig. 3.2) illustrates its strong correlation with size. Therefore, this set of trajectories seems to best capture the shape changes that are associated with growth among the three types of low-dimensional trajectories used in this study. The relatively lower p-values for LDT PC2 overall may suggest that these trajectories contain more phylogenetic signal than the other two types of low-dimensional trajectories, and that allometric trajectories are more phylogenetically informative than the other two types. Nevertheless, the p-values are still insignificant (Table 3.7). Differences in how high-dimensional trajectories were quantified and their distances produced slightly variable results (Table 3.7). However, the superiority of one metric over another is difficult to determine and cannot be argued based on the relative significance implied by the p-values. The addition of intercept values to the trajectory vectors contributed to lower p- values, which suggest that the extrapolated embryonic form of crocodilians is phylogenetically informative to some extent. Whether this is the case in reality is yet to be tested and would require the digitization of pre-natal specimens. As mentioned above, three of the bivariate plots for the high-dimensional trajectories imply a possible indication of positive correlation between trajectory and phylogenetic distances within ~15 20 Myr divergence time, i.e., phylogenetic distance of ~35 Mya (Fig. 3.10E G). Unfortunately, the data points are too few in number to infer a positive correlation during this time interval. Sampling of additional species and fossil taxa are necessary to determine whether these high-dimensional trajectories contain phylogenetic signal under certain temporal scales. 66

85 Table 3.6. R 2 values from regression analyses on shape and size used to construct the allometric trajectories. Abbreviations: LDT PC1, low-dimensional trajectories based on PC1 of Procrustes shape data; LDT PC2, low-dimensional trajectories based on PC2 of Procrustes shape data; LDT CAC, low-dimensional trajectories based on PC1 of residuals from the common allometric component. Taxon LDT PC1 LDT PC2 LDT CAC Alligator mississippiensis Caiman crocodilus Crocodylus acutus Crocodylus niloticus Crocodylus porosus Gavialis gangeticus Melanosuchus niger Osteolaemus tetraspis Paleosuchus trigonatus Tomistoma schlegelii Phylogenetic Signal All statistical tests for phylogenetic signal produced non-significant results, and both descriptive and observational methods corroborate this finding (Table 3.7). This study shows that the allometric trajectories are not phylogenetically informative and thereby invalidates the assumption that similarity in the orientation of these trajectories implies phylogenetic affinity. Among the significance tests, permutational regression analysis appears to be the most conservative based on the magnitude of p-values, but the generality of this case is unknown. In particular, the strength of the permutational regression analysis and the likelihood ratio test based on Pagel s lambda is difficult to compare because these methods incorporate phylogenetic information differently. Relative to the permutational regression analysis, the p-values obtained from the Mantel test are lower due to inflated degrees of freedom. The strength of the Mantel test for testing evolutionary hypotheses has been criticized (Harmon and Glor 2010). Nevertheless, the suite of analyses employed in this study, including the Mantel test, point to the lack of phylogenetic signal in allometric trajectories in Crocodylia. At present, the factors contributing to the underlying signal of the allometric trajectories is unclear. Some degree of topological differences was expected between the phenogram constructed by UPGMA and the time-calibrated molecular tree given the discrepancies between 67

86 the current morphological and molecular phylogenetic reconstructions, most notably the phylogenetic placement of Gavialis as the most basal member of Crocodylia in the former. However, nodes that occur in both molecular and morphological trees were not present in the phenogram. In fact, not a single node is shared between the phenogram and the morphological tree. This result is interesting because taxa that exhibit similar adult morphology, at least in some cases, exhibit similar developmental trajectories. Instead, the post-hatchling allometric trajectories are phylogenetically uninformative across the entirety of Crocodylia, possibly because these trajectories (1) evolve randomly with high variation; (2) contain phylogenetic signal that becomes saturated in the temporal range examined in this study; or (3) have an entirely different signal from molecular or morphological data. Similar to snout morphology, the allometric trajectories of crocodilians show rampant convergent evolution. Identifying key factors associated with allometric trajectories (e.g., environmental, genetic) will be important for elucidating the reason for why these allometric trajectories are not phylogenetically informative. Table 3.7. Summary of results. Abbreviations: HDT, high-dimensional trajectories without intercept values; HDT, high-dimensional trajectories with intercept values; LDT PC1, lowdimensional trajectories based on PC1 of Procrustes shape data; LDT PC2, low-dimensional trajectories based on PC2 of Procrustes shape data; LDT CAC, low-dimensional trajectories based on PC1 of residuals from the common allometric component. Method LTD PC1 LTD PC2 LTD CAC HTD HTD+I K-statistic Likelihood ratio test (p-value) Permutational regression analysis (p-value) UPGMA phenogram (p. shared nodes) Molecular tree 0/9 0/9 0/9 0/9 3/9 UPGMA phenogram (p. shared nodes) Morphological tree 0/8 1/8 0/8 0/8 3/8 Mantel test (p-value): Angular distance Mantel test (p-value): Euclidean distance

87 Sampling The taxonomic sampling was partly based on the availability of osteological specimens at North American institutions. Yet, robust sampling was not possible for certain species and ontogenetic stages due to the lack of intact cranial material. A. mississippiensis, Caiman crocodilus, and Crocodylus porosus, for example, were heavily sampled, while the sample sizes for G. gangeticus, M. niger, and O. tetraspis were each less than ten (Table 2.2). Although confidence intervals were not considered in this study, poor sampling jeopardizes statistical power and also prevents adequate sampling of ontogenetic stages. Sampling of hatchling and adult individuals is especially critical for establishing the orientation of the developmental trajectories. Despite the large sample size of Caiman crocodilus, only a single hatchling specimen was sampled. Nevertheless, the LDTs based on PC1 and PC2 of Procrustes coordinates largely follow a linear trajectory, thus, poor sampling, if any, likely would not affect the orientations of these trajectories. Because preserved neotentic specimens generally outnumber osteological specimens, the sampling of neotenic specimens, if needed, could be augmented with the use of CT scans in future studies. Intraspecific variation This study did not directly consider non-ontogenetic sources of intraspecific variation due to the difficulty of implementing measures to control for these factors. Crocodilians exhibit sexual dimorphism, in which adult males attain larger asymptotic sizes than the females (Grenard 1991). Thus, it has the potential to inflate the shape variation later in ontogeny. Unfortunately, sexual dimorphism is difficult to consider for this study because the sex of an individual is seldom recorded in non-captive osteological specimens. Moreover, osteological correlates for identifying sex is currently lacking in crocodilians (Prieto-Márquez et al. 2007). Nevertheless, sex identification was available for 20 digitized crania of C. crocodilus. A bivariate plot of PC1 of Procrustes coordinates of only Caiman crocodilus specimens and log centroid size suggests that there is no observable distinction between the orientation of the male and female allometric trajectories in Caiman, although one may argue that males may have marginally greater loading on the PC1 than females at any given size (Fig. 3.12). Consistent sexual dimorphism has been reported in both hatchling (Piña et al. 2007) and captive (Verdade 2003) specimens of the broadsnouted caiman (Caiman latirostris) based on linear distance measurements. However, the 69

88 magnitude of the variation due to sexual dimorphism may be minimal compared to ontogenetic variation. Furthermore, if the sexual dimorphism is limited to size differences, sexual dimorphism is not expected to alter the result of this study to any great extent because allometric trajectories constructed for this study are based on size, and not age. Clearly, greater representation of known sex individuals is needed to allow for a more comprehensive understanding of the effects of sexual dimorphism on allometric trajectories in crocodilians. Besides sexual dimorphism, this study did not control for population-level variations due to limitations in available samples. Previous studies have reported on intra-specific differences in developmental rates (Brochu 1992). Hatchlings of A. mississippiensis, for example, were found to exhibit morphological differences depending on locality (Milnes et al. 2001). Such variation would undoubtedly increase the variance of the shape data, but to what degree this effect would obscure the inter-specific distinction of allometric trajectories is yet unclear. Although locality data were collected for each digitized specimen in this study, a systematic sampling of specimens from multiple localities is necessary to determine the population-level variation in the shape and allometric trajectories of crocodilian species. 70

89 Figure Bivariate plot of the first principal component (PC1) of Procrustes coordinates and log centroid size in male and female Caiman crocodilus. Centroid size in mm. 71