The Evolution of Growth Patterns in Mammalian Versus Nonmammalian Cynodonts

Home , Morganucodon, Oligokyphus, Probainognathia, Probainognathus, Sinoconodon, Tritylodon

Paleobiology, 42(3), 2016, pp. 439–464 DOI: 10.1017/pab.2015.51

The evolution of growth patterns in mammalian versus nonmammalian cynodonts

Rachel N. O’Meara and Robert J. Asher

Abstract.—One of the major evolutionary transitions of the mammaliaform lineage was the origin of a typically mammalian pattern of growth. This is characterized by rapid juvenile growth followed by abrupt cessation of growth at adult size and may be linked with other important mammaliaform apomorphies of dental replacement and morphology. Investigation of growth patterns in the tritylodontid cynodont Oligokyphus and the basal mammaliaform Morganucodon provides insight into this crucial transition. We collected mandibular depth measurements from large samples of Morganucodon and Oligokyphus and constructed distributions of mandibular depth versus frequency for each species. These were compared with distributions from species from three different growth classes of extant amniote: testudines + crocodilians, mammals + birds, and lepidosaurs. Discriminant function analysis was used to differentiate between known growth classes by using different combinations of three measures of mandibular depth distribution shape (skew, kurtosis, and coefﬁcient of variation) as proxies for different juvenile and adult growth patterns. Classiﬁcation of the fossil species showed that Morganucodon closely resembled extant placental mammals in having rapid juvenile growth followed by truncated, determinate adult growth. Oligokyphus showed intermediate growth patterns, with more extended adult growth patterns than Morganucodon and slightly slower juvenile growth. This suggests a gradual evolution of mammalian growth patterns across the cynodont to mammaliaform transition, possibly with the origin of rapid juvenile growth preceding that of truncated, determinate adult growth. In turn, acquisition of both these aspects of mammalian growth was likely necessary for the evolution of diphyodont tooth replacement in the mammaliaform lineage.

Rachel N. O’Meara and Robert J. Asher. University Museum of Zoology, Downing Street, Cambridge, CB2 3EJ, United Kingdom. E-mail: [email protected]

Accepted: 12 November 2015 Published online: 28 April 2016 Supplemental material deposited at Dryad: doi: 10.5061/dryad.8rv01

Introduction determinate (or “truncated” in contrast to Once erupted, teeth cannot increase in size “extended”) skull growth in mammals may (although some species, including rodents, limit the requirement for continuous tooth have open-rooted dentitions and show contin- replacement (Crompton and Jenkins 1973; uous eruption). Therefore, continuous growth Zhang et al. 1998; Luo et al. 2004). This is of the jaw requires that teeth are succeeded by supported by observations in mammals that larger replacement teeth or that additional most postnatal cranial growth (up to 80%) teeth are added to the tooth row to maintain a occurs before deciduous eruption is complete functional dentition (Edmund 1960; Osborn (Crompton and Parker 1978) and that after the 1974). Hence, in many amniotes with “indeter- deciduous dentition has erupted relatively minate” growth patterns in which growth little further growth of the jaw is required to continues for most of the animal’s life span accommodate the replacement permanent den- (here referred to as “extended” adult growth) tition and new permanent molars (Pond 1977; such as crocodilians, some dinosaurs, and Crompton and Parker 1978). Rapid juvenile some nonmammalian cynodonts, polyphyo- growth, particularly of the skull, in mammals dont replacement of larger teeth has been limits the time during which teeth of inter- linked with continuous jaw growth (Edmund mediate size are required and hence also 1960; Hopson 1971; Osborn 1971; Osborn and permits the reduction of tooth replacement Crompton 1973; Westergaard and Ferguson (Pond 1977; Zhang et al. 1998). Therefore, both 1986, 1987; Butler 1995). In contrast, determinate, truncated adult growth and rapid

© 2016 The Paleontological Society. All rights reserved. 0094-8373/16 Downloaded from https://www.cambridge.org/core. Pendlebury Library of Music, on 14 Sep 2017 at 12:50:04, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/pab.2015.51 440 RACHEL N. O’MEARA AND ROBERT J. ASHER

juvenile growth are correlated with, and may et al. 2002; Kielan-Jaworowska et al. 2004). have permitted the evolution of, diphyodonty. Antemolars in Morganucodon were replaced Maternal provisioning by lactation may also only once, and molars were probably unre- be linked with the evolution of diphyodonty placed in both M. watsoni and M. oehleri (Mills (Ewer 1963; Hopson 1971, 1973; Zhang et al. 1971; Parrington 1971, 1973, 1978; Kermack and 1998; Kielan-Jaworowska et al. 2004) since Kermack 1984; Luo 1994; Crompton and Luo (1) maternal provisioning results in rapid 1993), although further evidence is required to juvenile growth, particularly of the skull show that the ultimate molar was unreplaced relative to the postcranium (Pond 1977), and (Luo et al. 2004). Similarly, molar replacement (2) functional teeth are not required until a has not been observed in the morganucodontan neonate mammal is weaned, so eruption of the Dinnetherium (Crompton and Luo 1993; Luo first generation of teeth is delayed in mammals 1994), leading Luo et al. (2004) to suggest that relative to diapsids (Ewer 1963; Hopson 1971; mammal-like diphyodont tooth replacement Pond 1977). Thus, the jaw usually reaches a may be common to all morganucodontans. greater proportion of adult size at the time of The docodont Haldanodon is also diphyodont eruption of the first generation of teeth in and lacks molar replacement (Martin and mammals compared with diapsids, further Nowotny 2000; Nowotny et al. 2001). The limiting the requirement for polyphyodonty diphyodont condition is widely considered an in the former (Ewer 1963; Pond 1977). Varia- apomorphy of the clade comprising the last bility may of course occur, but usually entails common ancestor of morganucodontans and growth preceding eruption (Asher and crown Mammalia and its descendants (Luo Lehmann 2008; Asher and Olbricht 2009; 1994; Kielan-Jaworowska et al. 2004; Luo et al. Ciancio et al. 2012), rather than eruption 2004), although some gobiconodontids do show preceding growth, for obvious mechanical replacement of at least anterior molariforms requirements of having space in the jaw into (Jenkins and Schaff 1988; Kielan-Jaworowska which teeth may erupt (although in some and Dashzeveg 1998), which may complicate species the relationship between size and this interpretation. eruption is not straightforward; cf. Godfrey Given the theoretical links between diphyo- et al. 2005). Lactation, diphyodonty, rapid donty and mammalian growth patterns, Luo juvenile growth, and determinate growth et al. (2004) hypothesized that Morganucodon may in turn be linked with several other experienced determinate (truncated) growth important mammalian morphological and and rapid juvenile growth and, by implication, behavioral apomorphies. These include may have provisioned its young by lactation. increased precision of molar occlusion Evidence for determinate growth is based on (Crompton and Jenkins 1973; Pond 1977; the narrow range of skull lengths in M. oehleri Crompton 1995); the increased complexity of (Luo et al. 2001, 2004; Kielan-Jaworowska et al. enamel microstructure and evolution of 2004). This range is much more restricted than enamel prisms, which may prevent propaga- that of the basal mammaliaform Sinoconodon, tion of cracks and hence reduce wear (Grine which did not have diphyodont tooth replace- and Vrba 1980; Crompton et al. 1994); ment (Zhang et al. 1998). Hence, M. oehleri was mammalian jaw-closing mechanisms (Cromp- inferred to have had a more mammal-like ton and Jenkins 1973; Pond 1977; Crompton growth pattern than Sinoconodon, and perhaps and Parker 1978; Crompton 1995); and mutua- also nonmammalian cynodonts, although listic social behavior (Pond 1977). comparable studies have not been carried out Dating from the Late Triassic–Early Jurassic, in more basal cynodont species. Morganucodon is the geologically oldest mam- Rapid juvenile growth in Morganucodon has maliaform (defined following Rowe [1998] as also been inferred from the high proportion of the clade comprising the last common ancestor adult to juvenile specimens in M. watsoni of Sinoconodon and crown Mammalia, and its (Parrington 1971, 1978; Kermack et al. 1973, descendants) and the most cladistically basal to 1981; Gow 1985; Luo 1994), suggesting that the have had diphyodont tooth replacement (Luo juvenile stage was of short duration relative

Downloaded from https://www.cambridge.org/core. Pendlebury Library of Music, on 14 Sep 2017 at 12:50:04, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/pab.2015.51 EVOLUTION OF MAMMALIAN GROWTH PATTERNS 441

to overall life span in this genus (Gow 1985; abruptly terminating growth of mammals and Luo et al. 2004). In addition, bone histology lepidosaurs as “determinate” or “truncated” supports the hypothesis of mammal-like adult growth and the less strongly plateaued growth patterns in Morganucodon; the high growth of testudines and crocodilians (Fig. 1) bone-deposition rates in early ontogeny, as “extended adult growth.” followed by a reduction in the rate of bone Evidence from tooth replacement studies formation in M. watsoni, are similar to those suggests that many nonmammalian cynodonts observed in extant mammals (Chinsamy and had “indeterminate” (extended) growth Hurum 2006). patterns (Kielan-Jaworowska et al. 2004; Luo Here, we present evidence of determinate et al. 2004). For example, in the epicynodont (truncated) growth and rapid juvenile growth Thrinaxodon, small predecessor teeth are in Morganucodon. Luo et al. (2001) suggested replaced by larger successors at posterior tooth M. oehleri underwent determinate growth loci even in large individuals, indicating that based on a necessarily limited sample of eight jaws continued to lengthen throughout life skulls (Luo et al. 2001, 2004). To further test (Osborn and Crompton 1973). Bone micro- this inference, we sample 531 dentaries of structure studies show that there was consider- M. watsoni, a species (of the four currently able variation in growth strategies throughout recognized in Morganucodon) that has not the nonmammalian cynodont lineage (Botha previously been evaluated in this respect. By and Chinsamy 2000, 2005; Ray et al. 2009; investigating a large sample of M. watsoni and Botha-Brink et al. 2012), although with a comparing them with extant mammals and general trend toward more rapid bone- diapsids with known growth trajectories, we deposition rate in more crownward groups aim to establish the nature of growth in extinct (Ray et al. 2009; Botha-Brink et al. 2012). taxa such as Morganucodon. Discriminant Several studies suggest that the growth function analysis permits us to investigate both strategy of nonmammalian cynodonts was juvenile and determinate, truncated adult more plastic than that of extant mammals, growth simultaneously and has the potential permitting decrease in growth rates in unfa- to illuminate not only whether or not growth vorable conditions (Ray et al. 2004; Chinsamy was determinate or not but also the degree to and Hurum 2006; Chinsamy and Abdala 2008). which growth in Morganucodon resembles that Most cynodonts and therapsids show a of extant mammals. decrease in growth rate in adulthood and Definitions of amniote growth patterns as eventual cessation of growth (Botha-Brink either determinate or indeterminate can differ et al. 2012; Hurum and Chinsamy-Turan depending on the context of study (Lee et al. 2012). This clearly asymptotic growth pattern 2013). Life history studies usually define may be consistent with either mammal-like indeterminate growth as occurring if an animal determinate, truncated growth or with rela- continues to grow past sexual maturity tively more extended growth patterns (Charnov et al. 2001; Congdon et al. 2013), as (although it is unlikely to resemble the more in most nonavian diapsids. However, devel- extreme extended adult growth of turtles and opmental or histological studies commonly crocodilians). adopt a definition of growth based on the The paucity of quantitative comparisons of plasticity of the growth trajectory of an absolute growth rates through ontogeny and individual as it ages (Lee et al. 2013). In this the difficulties of accounting for the effect of context, almost all amniotes exhibit lack of differences in size on bone tissue growth plasticity of growth in later life and thus have (Botha-Brink et al. 2012), together with the asymptotic and therefore determinate skeletal flexible growth strategy of nonmammalian growth, contrasting with the truly indetermi- cynodonts, make it difficult to assess the nate growth of plants (Sebens 1987). Thus, the degree to which growth trajectories differed term “indeterminate” is ambiguous when between nonmammalian cynodonts and extant applied to amniotes. Hereafter we avoid this mammals. It is likely that growth patterns of term, but distinguish between the relatively many cynodonts were intermediate between

those of a basal amniote ancestor with Extant Mammal + Bird Growth Class extended growth and those of extant mam- Mammals have a characteristic growth pat- mals, although rapid growth with truncated tern in which juveniles grow rapidly to reach a adult growth has also been observed in maximum adult size, at which point growth some therapsids and basal cynodont species abruptly ceases (determinate, truncated (Botha and Chinsamy 2005; Butler 2010; growth). This typically results in a sigmoid Huttenlocker and Botha-Brink 2014). individual growth curve (Fig. 1) with a definite To probe this question of nonmammalian plateau (e.g., mice and rats [Eisen 1976]; cynodont growth patterns, we also assessed Peromyscus maniculatus [Dice and Bradley size measurements from the tritylodontid 1942]; Sorex unguiculatus [Nesterenko and Oligokyphus in this study and compared them Ohdachi 2001]; domestic dog breeds [Helmink with Morganucodon. Bone histology shows that et al. 2000]; Monodelphis domestica [Cothran tritylodontids exhibited sustained and rapid et al. 1985]; dolphins [Fernandez 1998]). The growth, which slowed later in ontogeny, unique mammalian apomorphy of lactation similar to Morganucodon, suggesting they may permits rapid and sustained postnatal growth also have had a fairly mammalian determinate, throughout juvenile and subadult stages. truncated pattern of adult growth (Chinsamy Growth is much faster in young mammals and Hurum 2006; Hurum and Chinsamy- (Case 1978), which attain a much greater Turan 2012). Oligokyphus conforms to this proportion of adult size and weight by the tritylodontid pattern (de Ricqlès 1969), time of weaning relative to nonavian diapsids although with slower overall growth than in of comparable age and size (Pond 1977; Tritylodon (Botha-Brink et al. 2012). Crompton and Parker 1978). In addition, we assessed growth patterns in In particular, there is an accelerated rate of the extinct lepidosaur Gephyrosaurus bridensis. growth of the skull relative to the postcrania Gephyrosaurus is the most basal known rhynch- and of the facial region relative to the skull ocephalian (Evans and Jones 2010), and it likely (e.g., Rattus norvegicus [Jackson and Lowrey had determinate, truncated adult growth and a 1912; Moss and Baer 1956]; Gorilla gorilla slow period of juvenile growth, in common [Krogman 1931]; reviewed in Pond 1977). with extant lepidosaurs, including the only Among nonavian diapsids, skull and postcra- extant rhynchocephalian genus, Sphenodon. This nial growth rates are roughly similar (e.g., is supported by its bone histology, which is Crocodylus niloticus [Cott 1961]). Lactation in similar to that of extant squamates (Chinsamy mammals permits a delay in the eruption of the and Hurum 2006). Gephyrosaurus is particularly first generation of teeth relative to nonavian useful for our comparisons, because it occurs diapsids and, in many species, the rate of contemporaneously with Morganucodon watsoni growth declines abruptly following weaning (Evans 1980); specimens used in this study were (Pond 1977). Therefore, in comparison with from the same fissure-fill deposits (St. Bride’s, nonavian diapsids, relatively less growth Wales) as M. watsoni. This permits comparison occurs between complete eruption of the first of Morganucodon and Oligokyphus with another generation of teeth and the attainment of extinct taxon fossilized in a similar taphonomic maximum adult size (Pond 1977; Crompton environment and enables us to determine and Parker 1978), permitting diphyodont tooth whether factors such as preservation bias affect replacement, as discussed above. The cessation the assignment of fossil species to a particular of growth is usually followed by the attain- growth class in this study. ment of sexual maturity (Lee and Werning Morganucodon, Oligokyphus, and Gephyro- 2008), at least in mammals of small to medium saurus specimens were compared with repre- size. In larger mammals with relatively pro- sentatives from three different groups of longed periods of growth, such as elephants, amniotes that exhibit clearly distinct modes of sexual maturity is frequently attained before growth (hereafter referred to as its growth maximum adult size is reached, and growth class): (1) mammals + birds, (2) lepidosaurs, curves, especially in male elephants, do not and (3) testudines + crocodilians. evince such distinct plateau regions as those of

smaller mammals (Schrader et al. 2006; Lee and lepidosaurs and extended growth in testudines Werning 2008). and crocodilians. Extant birds have growth patterns similar to those of extant mammals, showing strongly plateaued growth curves and rapid juvenile Lepidosaur Growth Class growth (Case 1978; Lee and Werning Determinate, truncated growth, in which a 2008); they are therefore included within the maximum adult size is reached and growth same growth class, distinct from slow-growing then terminates relatively abruptly, is observed nonavian diapsids. Precocial birds show in most extant lepidosaurs (Shine and Charnov growth rates similar to those of eutherian 1992). Their growth curves show a distinct mammals of comparable size, while altricial plateau when maximum size is reached (e.g., birds grow at approximately twice the rate of van Devender 1978; Kolarov et al. 2010; comparable extant eutherians (Case 1978). Zúñiga-Vega et al. 2005). Bone histology Bone histology provides evidence for the studies in squamates show that there is a evolution of this growth pattern within the decrease in the rate of bone deposition with dinosaurian lineage, suggesting that nonavian increasing age and that bone deposition ceases dinosaurs had elevated rates of growth in many years before death, as in mammals comparison with nondinosaurian diapsids (Castanet and Báez 1991; Chinsamy et al. (Erickson et al. 2001; Padian et al. 2001; 1995). This is true also in the only living species Erickson 2005) but did not attain the extremely of rhynchocephalian, Sphenodon punctatus, rapid growth rates of extant altricial birds which has slower growth than any other living (Erickson et al. 2001). Later, extreme reduction reptile (Castanet et al. 1988). In this species, size of the duration but not the rate of rapid reaches a maximum at between 20 and 35 years juvenile growth may have enabled the minia- of age; an individual may continue living turization of neoavian birds (Padian et al. 2001; without further growth for more than 30 years Lee and Werning 2008). (Dawbin 1982). Complete fusion of long-bone The mammal + bird growth class is there- epiphyses occurs in a taxonomically broad fore defined as having rapid juvenile growth range of squamates (Haines 1969; Maisano and determinate, truncated adult growth. 2002). Maisano (2002) found that this indicates Nonavian diapsids differ from mammals in that an individual is within 20% of the species having growth rates an order of magnitude maximum size (although the individual may lower than mammals of comparable weight have reached its own maximum), consistent (Case 1978). Even in elephants, which have with determinate, truncated skeletal growth in relatively slow growth and a more prolonged this group. period of growth than other mammals, growth We thus define the lepidosaur growth class rates are far in excess of even the fastest- as having slower juvenile growth and determi- growing large extant nonavian diapsids (Case nate, truncated adult growth. 1978). Growth in nonavian diapsids also differs from mammals in that it can be arrested or greatly reduced during unfavorable environ- Testudine + Crocodilian Growth Class mental conditions and increased again when Growth in testudines and crocodilians com- conditions improve (Pond 1977; Adolph and monly continues throughout life, with the Porter 1996). Furthermore, in contrast to most qualification that growth rates slow with age mammals, significant growth continues after (Porter 1972; de Ricqlès 1976; Andrews 1982; sexual maturity in nonavian diapsids Scheyer et al. 2010). Most studies on testudine (Andrews 1982; Shine and Charnov 1992; growth patterns focus on growth after sexual Shine and Iverson 1995; Scheyer et al. 2010), maturity (a definition of “indeterminate” including in some nonavian dinosaurs (Sander growth that we try to avoid in this study), and Klein 2005). Nonavian diapsid growth rather than on lifetime growth, and show that trajectories may be divided into two distinct such continued growth after maturity is com- types: determinate, truncated growth in mon in a range of taxa (Dunham and Gibbons

1990; Lovich et al. 1990; Congdon et al. 2003), mammals, but future studies might profitably although again growth slows with age to examine this overlap by inclusion of additional become almost negligible in later life (Balazs species of large nonavian diapsids. 1980; Frazer and Ladner 1986; Zug et al. 1986; Since most testudines and crocodilians show Seminoff et al. 2002; Bjorndal et al. 2013). The growth throughout the majority of their life attainment of skeletal maturity (Woodward span and lack the relatively more abrupt et al. 2011) and cessation of growth is certainly termination of growth characteristic of deter- possible (Wilkinson and Rhodes 1997) in some minately growing lepidosaurs, their mode of crocodilians and is quite probably more wide- growth can be considered to be distinct. We spread in the group than previously thought. refer to this pattern of continuous, gradually Whether cessation of growth is common declining lifetime growth in testudines and among testudines and crocodilians is difficult crocodilians as “extended growth.” Testudines to establish due to variation of individual and crocodilians also show the slower juvenile growth patterns within a species (Carr and growth typical of extant diapsids, as Goodman 1970; Tucker et al. 2006; Congdon outlined above. et al. 2013) and the paucity of long-term studies Thus, we divide extant amniotes into three focusing on lifetime growth rather than growth growth classes: (1) mammals + birds with following sexual maturity. rapid juvenile growth followed by determinate, However, some studies have also investigated truncated growth; (2) lepidosaurs with slow growth in individual testudines across the life- juvenile growth followed by determinate, trun- time size range of a species and found that some cated growth; and (3) testudines + crocodilians growth, albeit slow, continues even in the largest with slow juvenile growth followed by turtles (Zug et al. 1986; Seminoff et al. 2002). extended adult growth. We used linear size Gradually declining growth of this kind has also measurements (mandibular depth) taken from been observed in crocodilians, with growth rates different species belonging to each of these slowing, and in some individuals ceasing, in growth classes to construct a size-frequency later life (Cott 1961; Andrews 1982; Rootes et al. distribution for each species. We aimed to 1991; Wilkinson and Rhodes 1997; Tucker et al. establish whether a species could be assigned 2006). Thus, the relatively abrupt decline in to its correct growth class on the basis of metrics growth rates typical of determinately growing relating to the shape of these size distributions, lepidosaurs is not apparent in testudines and using discriminant function analysis. The three crocodilians. Andrews (1982) reports that the species of unknown growth class—Morganuco- inflection points of growth curves of iguanids don, Oligokyphus,andGephyrosaurus—were then (lepidosaurs) tend to occur at lengths greater classified on the basis of the resulting statistical than 50% of asymptotic (maximal) length and model. This permitted growth patterns in mass. In large, longer-lived reptiles, such as Morganucodon and Oligokyphus to be compared crocodilians, inflection points are closer to 30% with each other and with those of extant of asymptotic (maximal) mass, indicating a less amniotes of known growth patterns, to better distinct plateau in growth curves of the crocodi- illuminate the evolution of mammalian growth lians. Lack of complete epiphyseal ossification in patterns across the nonmammaliaform cyno- testudine and crocodilian long bones suggests dont to mammaliaform transition. that continued growth throughout life is phy- siologically possible in these animals (Haines 1969). Lack of epiphyseal ossification in very Materials and Methods large individuals is also seen in some large, long- lived lepidosaur species, such as varanids (de Museum Abbreviations Buffrénil et al. 2004). There is therefore some FMNH, Field Museum of Natural History, overlap in growth patterns between testudines Chicago, U.S.A.; NEWHM, Hancock Museum, + crocodilians and lepidosaurs. In this study, we Newcastle, U.K.; NHMUK, Natural History included only smaller lepidosaur species in our Museum, London, U.K.; OUM, Oxford Univer- sample,asourfocusisoncomparablysmall sity Museum of Natural History, Oxford,

FIGURE 1. Individual growth curves (top) and expected differences in size-frequency distributions (middle) of different growth classes with a phylogeny of extant amniotes (bottom). A, Mammals and birds have rapid juvenile growth followed by determinate, truncated adult growth. Thus, both tails of the distribution are expected to be relatively truncated, and the mammal + bird distribution is expected to show more negative kurtosis and lower coefﬁcient of variation (CV) than the other groups. B, Testudines and crocodilians have slow juvenile growth followed by extended adult growth. Thus, both tails of the distribution are expected to be relatively long in comparison with the mammal + bird distribution. The testudine + crocodilian distribution is expected to be less negatively skewed than that of lepidosaurs and with less negative kurtosis and greater CV than either of the other groups. C, Lepidosaurs have slow juvenile growth followed by determinate adult growth. Thus, the right tail is expected to be relatively truncated, but the left tail is expected to be relatively long compared with mammal + bird distributions. The lepidosaur distribution is expected to be more negatively skewed than the other distributions, with an intermediate CV. Individual growth curves after: Peromyscus maniculatus: Dice and Bradley (1942); Crocodylus johnstoni: Tucker et al. (2006); Xenosaurus grandis: Zúñiga-Vega et al. (2005). Phylogeny of extant amniotes follows phylogenomic analyses by Chiari et al. (2012) and Crawford et al. (2015), with fossil cynodont relationships following Luo et al. (2002).

U.K.;UCL,UniversityCollegeLondon,U.K.; Gephyrosaurus specimens and compared these UCLGMZ, University College London, Grant with large sample sizes of similar measure- Museum of Zoology, London, U.K.; UMZC, ments from different extant amniotes belonging University Museum of Zoology, Cambridge, U.K. to the three major growth classes. In species with determinate, truncated growth (mammals + birds and lepidosaurs; Fig. 1A,C) one would Assigning Growth Classes to Morganucodon expect the right tail of a size-frequency histo- and Oligokyphus using Distribution Shape of gram of mandibular depth measurements to be Size Data relatively more truncated than the right tail of We collected mandibular depth measure- such a distribution from a testudine or crocodi- ments from Morganucodon, Oligokyphus,and lian with extended adult growth (Fig. 1B).

This results from the fact that a few very would expect a lepidosaur distribution to be old individuals would reach extreme size in relatively more negatively skewed than dis- testudines and crocodilians. In contrast, in the tributions from testudine + crocodilian or determinately growing species even the oldest mammal + bird growth classes. One would individuals would have ceased growing at a expect a testudine + crocodilian distribution to predetermined maximum size. In species with be less negatively kurtotic than a mammal + rapid juvenile growth (mammals + birds), one bird distribution, less negatively skewed than a would expect the left tail of the distribution to lepidosaur distribution, and probably also less be relatively more truncated (Fig. 1A) than in negatively skewed than a mammal + bird those species with slower juvenile growth distribution, as the right tail would be longer (testudine + crocodilian and lepidosaur growth than in either of the other groups. class; Fig. 1B,C). This is because individuals The CV is a normalized measure of disper- with rapid juvenile growth spend a relatively sion of data and is the standard deviation shorter proportion of their life spans at a small divided by the mean, which may be expressed size. Thus, fewer small individuals are expected as a percentage (Sokal and Rohlf 2012). This to be present in a given population at any one permits comparison of the variation of size time relative to species with slower juvenile data of different species, taking into account growth. Differences in the shapes of the size- differences in means. One would expect lowest frequency distributions would therefore allow CV values of body-size indices in members of more nuanced quantification of the idea that the mammal + bird growth class, as both tails high ratios of adult to juvenile specimens of their size-frequency distributions would be indicate rapid juvenile growth (Parrington relatively short (rapid juvenile growth, deter- 1971, 1978; Kermack et al. 1973, 1981) or that a minate, truncated adult growth). Intermediate narrow range of specimen sizes indicates CV values would be expected in species of the determinate, truncated growth in Morganucodon lepidosaur growth class, as only one tail is (Luo et al. 2001, 2004). expected to be relatively truncated (slow Distribution shape can be quantified and juvenile growth, determinate, truncated adult compared using three different measures: growth). The greatest CV values would be skewness, kurtosis, and the coefficient of expected in the testudine + crocodilian growth variation (CV). Skewness is a measure of the class, in which both tails would be relatively asymmetry of a distribution, while kurtosis is a long (slow juvenile growth, extended adult measure of the relative proportions of data growth). found in the shoulders versus tails of a distribution. A negatively kurtotic distribution has a greater proportion of data in the Specimens shoulders than the tails relative to a normal We measured 531 specimens of Morganuco- distribution, while a positively kurtotic dis- don watsoni held at the UMZC and 49 speci- tribution has more data in the tails or center of mens of Oligokyphus sp. from the NEWHM, the distribution and less data in the shoulders NHMUK, and UMZC. The M. watsoni speci- (Sokal and Rohlf 2012). Figure 1 illustrates mens were from the Pont Alun quarry, expected differences between the size- Glamorgan, South Wales, and were previously frequency distributions of different growth designated as the species Eozostrodon parvus. classes. With relatively truncated left tails The Welsh form of E. parvus is now considered (individuals pass through small size quickly) to be indistinguishable from M. watsoni, and right tails (individuals stop growing although E. parvus is still a valid taxon for abruptly), one would expect a distribution specimens from Holwell quarry, Oxfordshire from a species of the mammal + bird growth (Clemens 1979). The fissure-fill deposits at the class to be relatively more negatively kurtotic Pont Alun quarry are part of the St. Bride’s than the distribution from a testudine + Island locality, Wales, and were formed crocodilian or lepidosaur growth class. With a in Carboniferous limestone (Robinson 1957). truncated right tail but a longer left tail, one The St. Bride’s fissures are between the latest

Triassic (Rhaetian) and the Early Jurassic finches (Fringilla montifringilla), pigeons (Sinemurian) in age (Kermack et al. 1973; (Columba livia), rails (Gallinula chloropus), and Kielan-Jaworowska et al. 2004; Säilä 2005), kingfishers (Alcedo atthis). Minimum sample although they are generally agreed to be Early size for any individual species was 40. Jurassic, most probably Sinemurian (Robinson Mammal and bird specimens are held at the 1957; Kermack et al. 1981; Evans and Kermack NHMUK and UMZC. Numbers of monotreme 1994). Gephyrosaurus bridensis specimens were specimens available in museum collections are from the same locality as M. watsoni and come limited, and hence no monotreme is included from collections at UCL and UMZC. in our mammal sample. Thus, our “mammal” All Oligokyphus specimens were from the growth class is based on Theria, excluding Mendip 14 locality, Windsor Hill, Shepton monotremes and other, nontherian crown Mallet, England. This locality is also a fissure- mammals. fill deposit formed in Carboniferous limestone Museum collections of more than a handful of but is Charmouthian (Pliensbachian) and thus individual testudines or crocodilians of the younger than the St. Bride’s fissures (Kühne same species are rare, but we did find samples 1956). The Mendip adult Oligokyphus speci- >40 for 4 species of extant testudines and mens comprise two size morphs (Kühne 1956), crocodilians (spanning 4 distinct families) at and Oligokyphus mandibular depth distribu- the collections of the FMNH, NHMUK, OUM, tion from this study shows significant depar- and UMZC. These included sea turtles (Chelonia ture from unimodality (Supplementary mydas), tortoises (Testudo graeca), terrapins Material S8). Although Kühne (1956) named (Mauremys caspica), and caimans (Caiman croco- the small and large forms as separate species dilus). Thirteen extant species across 10 lepido- (Oligokyphus minor and Oligokyphus major, saur families were included from the FMNH, respectively), he also considered it likely that NHMUK, OUM, UCL, UCLGMZ, and UMZC: the two morphs may result from sexual lacertids (Lacerta viridis, Podarcis muralis, dimorphism within one species, especially as Acanthodactylus boskianus), skinks (Mabuya there are few morphological differences striata), geckos (Tarentola gigas, Tarentola annu- between the two forms. Since juvenile speci- laris, Bunopus tuberculatus), snakes (Lapemis mens had to be included in this study, and due curtus, Typhlops schlegeli, Natrix maura), agamids to the difficulty of distinguishing O. major from (Agama sinaita, Calotes versicolor), and anguids O. minor based only on dentary fragments, we (Anguis fragilis). The minimum sample size for treated the two morphs as a single species, here any individual lepidosaur species was 63. referred to simply as Oligokyphus sp. Of course, Within each species, we took measurements if the two morphs are in fact distinct species, from all specimens available in the museum conclusions regarding their growth cannot be collections with the relevant anatomy pre- drawn from this analysis, and so results from served. The only specimens excluded for Oligokyphus must be interpreted with this reasons other than damage were those that in mind. had been collected with an explicit age-related We also measured extant amniotes represen- bias. For example, a box containing only tative of the three different modes of growth, juvenile specimens, within an otherwise including 13 species across 8 orders and 13 unsorted collection of specimens, was families of extant mammals, and 5 species excluded. We assume that the proportions of across 5 families of birds. Mammals included differently sized museum specimens reflect bats (Pipistrellus kuhli), marsupials (Didelphis those of animals in the original populations or marsupialis, Dasyurus hallucatus), xenarthrans at least that any bias in collecting from a (Dasypus novemcinctus), rodents (Microtus particular size group applies consistently agrestis, Tatera indica, Mus musculus), lipotyph- across growth classes. Here we follow previous lans (Sorex araneus, Talpa europaea, Suncus studies (e.g., Parrington 1971; Gow 1985; Luo murinus, Erinaceus europaeus), and carnivorans et al. 2001, 2004; Kielan-Jaworowska et al., (Mustela erminea and Canis familiaris). Bird 2004) that have commonly inferred growth species included falcons (Falco tinnunculus), patterns in mammaliaforms using the relative

proportions of small to large individuals or the

size ranges of sampled species; our method is 1mm Coronoid simply an extension of these types of studies. Process Moreover, our access to mammaliaforms (Morganucodon) and lepidosaurs (Gephyrosaurus) from the same basal Jurassic localities in South Wales provides a further means to test whether

differences we observe between them are due to Dentary Condyle M artifacts of taphonomy or actual patterns of Angular growth. Ideally, time-homogenous sampling of Process aspecies,frombirthtodeath,wouldbeusedto test this assumption. Unfortunately museum FIGURE 2. Mandibular depth measurement in the Morganucodon specimen (UMZC D61). Mandibular depth samples generally do not have data on indivi- (M) in extant mammals, Morganucodon, and Oligokyphus dual ages, and no sample can guarantee even was defined as the shortest distance from the base of the representation across age cohorts of populations anterior border of the coronoid process to the ventral that have been extinct for millions of years. edge of the dentary, in lateral view. However, to the extent that such data could be collected for extant species (difficult but not impossible for long-lived species such as sea the mandible in lateral view. Any loose tissue turtles) they would certainly comprise a valu- around the area being measured was pulled as able, future test of our conclusions. taut as possible to standardize measurements. Within a species, the same definition of mandibular depth was used for all individuals. Measurements This enabled assessment of how mandibular We measured dentary depth as a proxy for depth is distributed at varying growth overall size in Morganucodon, Oligokyphus, and stages within a species and did not require all mammal species using fossil or osteological identification of homologous landmarks specimens, as it is among the most consistently between species. preserved metric we could recognize across The majority of species chosen were of small fossil and extant members of our sample. We size, so as to be comparable to Morganucodon. defined dentary depth as the shortest distance For these species, we took measurements to the from the base of the anterior border of the nearest 0.1 mm using a light microscope and coronoid process to the ventral edge of the graticule. For larger species, measurements dentary, in lateral view (Fig. 2). were taken to the nearest 0.1 mm using digital Measurements closely analogous to dentary calipers. When digital calipers were used, we depth at the anterior coronoid process were took an average of three measurements of taken from the lepidosaur, testudine, and mandibular depth for each individual. crocodilian specimens. For most of these diapsid species, osteological specimens were used. In those species in which sutures were Statistics clearly visible, we defined mandibular depth Distributions of mandibular depth for each as the shortest distance from the anterior edge species can be quantified using different of the coronoid bone to the ventral edge of the measures of the shape of the size-frequency mandible, in lateral view. Where this was not distribution. In this study, we used three such possible, we measured mandibular depth from measures for mandibular data of each species: the posterior edge of the tooth row to the Fisher’s skewness, Fisher’skurtosis,andthe ventral edge of the mandible. In diapsid wet CV. Skew, kurtosis, and CV of each species’ specimens or (in the case of bird specimens) data distribution, and also Box-Cox power skins, we defined mandibular depth as the transformation of variables in order to meet shortest distance from the posterior-most assumptions of discriminant function analysis extent of the oral cavity to the ventral edge of (Supplementary Material S2.2), were calculated

in the statistical program R, Version 2.15.1 (R In Dasyurus and Fringilla, sample size barely Core Team 2012). Whenever multiple signifi- reached the recommended minimum sample cance tests were carried out, false discovery rate size for a robust test of skewness or kurtosis (FDR) corrections (Benjamini and Hochberg (n = 40). In Canis, although the majority of 1995; Curran-Everett 2000) were applied to individuals were of the same breed (39 of 57 p-values. individuals were greyhounds), the remaining Discriminant Analysis of Distribution Shape.— specimens were of unknown breed, albeit with Stepwise discriminant analysis was carried out, similar cranial morphology to the greyhounds. including all species listed above, using the However, the high variability in size and statistical program SPSS, Version 21, to assess morphology of dog skulls could lead to whether the three measures of mandibular misleading values of skew, kurtosis, and CV in depth distribution shape (skew, kurtosis, and this species. We also analyzed only those Canis CV) can be used to assign a particular species to specimens unambiguously identifiable as one of the three growth classes: mammal + bird, greyhounds in a further analysis. Domestication testudine + crocodilian, or lepidosaur. of pigeons may have led to a similar problem in Discriminant analysis is a multivariate Columba livia. Canis, Dasyurus, Fringilla,and statistical technique in which predictor Columba were therefore excluded to test variables (i.e., measures of distribution shape) whether their inclusion biased results. The are used to predict group membership (i.e., analysis was also repeated excluding the two growth class) by finding dimensions along marsupials, Didelphis and Dasyurus,totest which known members of groups differ and whether the differing growth patterns of deriving classification functions to predict marsupials relative to placentals (Tyndale- group membership where it is unknown (i.e., Biscoe 2001; Geiger et al. 2014) affect the for the fossil species Morganucodon, Oligokyphus, position of fossil species relative to the and Gephyrosaurus). The predictors most mammals during classification. important in discriminating different groups Since the taxa in this study are not indepen- were identified by the procedure in which dent from one another, but related in a predictor variables were added stepwise to the hierarchical phylogeny (Fig. 1), closely related model, with all variables evaluated at each step species may resemble each other more than spe- to determine which contributed most to cies selected at random, and hence phylogenetic discrimination between groups by minimizing signal is likely to be present in the data (Harvey overall Wilks’s lambda. The stepping-method and Pagel 1991; Münkemüller et al. 2012). criteria for predictor variable inclusion were This can introduce difficulties in interpreting twofold: maximum significance of F to discriminant function analyses, as correlation enter = 0.05 and minimum significance of F to between the predictor variables (skew, kurtosis, remove = 0.1. Interpretation of the structure CV) and growth classes may be caused by both matrix of correlations between predictors and having phylogenetic signal. In an extreme case, discriminant functions permitted more detailed even if a predictor variable had no relationship to evaluation of how predictors discriminate growth class, members of a particular class may groups. Only those correlations greater than share similar predictor values simply because 0.32 (10% of the variance) were considered they are closely related. Thus, although presence eligible for interpretation (Comrey and Lee of an underlying phylogenetic signal does not 1992). Classification functions for predicting exclude the possibility of functional or growth membership of the fossil species were derived, effects (as such effects themselves are likely to and cross-validation was used to assess the have been influenced by phylogeny), phyloge- adequacy of these classification functions. netic and functional signals may be difficult to An additional analysis was carried out, distinguish. In these circumstances, cases of similar to the main analysis described above, convergent evolution can be extremely impor- but excluding two mammal species, Canis tant in distinguishing phylogenetic from func- familiaris and Dasyurus hallucatus, and two bird tional effects (Barr and Scott 2014; Chen and species, Fringilla montifringilla and Columba livia. Wilson 2015). We have therefore included in our

sample birds, which are known to have evolved discrimination of groups. Life history data were their growth patterns independently from those obtained from peer-reviewed literature or from of mammals (Fig. 1; Chiari et al. 2012; Crawford the Animal Ageing and Longevity Database et al. 2015). The position of birds in the canonical (de Magalhaes and Costa 2009; Supplementary discriminant function plot helps to determine the Material S5). relative influences of functional (growth) versus phylogenetic effects. As birds and mammals are Results known to share a pattern of growth but are The distribution of mandibular depths for ’ not each other s closest relatives, we can assume each species shows a general pattern in the that mammal and bird species cluster together in degree of skew and kurtosis observed, corre- this analysis because of common functionality sponding with the growth class to which it and not solely because of their phylogenetic belongs.Table1givesmeanvaluesforskew, history. kurtosis, and CV in each growth class, with Assessing the Effects of Body Size and Life values for individual species in the Supplemen- — History. Following the discriminant analysis of tary Material (S1). Mean skew is close to zero mandibular depth distribution shape and among mammals + birds, which is also the fi classi cation of unknown species, an additional growth class with the lowest mean CV and the stepwise discriminant analysis was performed to only growth class for which mean kurtosis is assess the effects of body size and life history. negative. This is consistent with patterns of This analysis included three additional predictor rapid juvenile growth and determinate adult variables: mean mandibular depth (a proxy for growth in mammals and birds (Fig. 1), in which overall size), maximum longevity, and mean both tails of the mandibular depth distribution number of offspring per year. It is probable that are relatively truncated. The testudines + the shapes of distributions for individual species crocodilians show the most positive mean fl are in uenced not only by patterns of growth but kurtosis and the greatest mean CV of the three also by size and life history characteristics. For growth classes, while mean skew is close to zero. example, animals with larger body sizes tend to These patterns of skew and kurtosis are con- have relatively longer periods of juvenile growth sistent with slow juvenile growth and extended than smaller animals (Lee and Werning 2008; adult growth patterns (Fig. 1), in which neither Schrader et al. 2006), resulting in differences in a tail of testudine + crocodilian data distributions distribution of mandibular depths during is relatively truncated. Lepidosaurs show a ontogeny simply due to overall body size. mean kurtosis close to zero and have the most Similarly, a species that produces many negative mean skew of the three growth classes. offspring per year may have a longer left tail This is consistent with slow juvenile growth and (althoughsuchaneffectwouldbefurther determinate adult growth, in which only the fl in uenced by other factors such as juvenile right tails of the lepidosaur data distributions are mortality), and longevity may be expected to relatively truncated (Fig. 1). fl in uence the length of the right tail. It is Thus, general patterns of data distribution importantthatthemembersofdifferentgrowth conform to expectations for each growth class: classes used in this study have a relatively even unskewed but negatively kurtotic distributions distribution of size and different life history for mammals + birds, negatively skewed fi strategies, otherwise it would be dif cult to distributions with no strong kurtosis for determine whether consistent differences in lepidosaurs, and unskewed distributions with skew, kurtosis, or CV are due to the differences large CVs for testudines + crocodilians (Fig. 1). in growth pattern or to consistent differences in size or life history variables between groups. It is beyond the scope of this study to model Discriminant Analysis of Distribution Shape the effects of all aspects of life history, but mean Differences between growth classes were number of offspring per year and maximum assessed by stepwise discriminant analysis using longevity were included to at least partially test three predictor variables to assign membership whether differences in life history confound the to three groups. The three predictors were

TABLE 1. Means and standard deviations of original and transformed predictor variables (skew, kurtosis, and CV) for each growth class.

Predictor Mean of original SD of original Mean of transformed SD of transformed Growth class variable variables variables variables variables Mammals + birds Skew −0.10 0.15 2.0981 0.172 Kurtosis −0.97 0.33 0.6245 0.155 CV 12.42 5.36 1.0093 0.002 Testudines + Skew 0.06 0.36 2.2772 0.408 crocodilians Kurtosis 0.80 1.49 0.2692 0.097 CV 33.86 15.53 1.0132 0.002 Lepidosaurs Skew −0.49 0.23 1.6552 0.259 Kurtosis 0.04 0.91 0.3540 0.099 CV 26.91 7.00 1.0125 0.001

variables relating to the shape of the size- (Table 2A) indicate that they account for 69.8% frequency distribution of each species: the skew, and 63.5%, respectively, of the total relation- the kurtosis, and the CV. ship between groups and predictors. During Following Box-Cox power transformations stepwise entry of variables, all three predictors of variables (Sokal and Rohlf 2012; see Supple- were entered with significance of F < 0.01, in mentary Material S2) significant heterogeneity the order kurtosis, skew, CV. This shows that of variance–covariance matrices was found the model that best predicts group member- (Box’s M test, p < 0.05). Heterogeneity of ship includes all three predictors, with kurtosis variance–covariance matrices (which measures as the single best predictor. multivariate dispersion) may not cause The structure matrix (Table 2C), consisting of problems with inference but can do so for pooled within-group correlations between the classification (Tabachnick and Fidell 2007). discriminant functions and the predictor vari- Therefore, we performed classification based ables (skew, kurtosis, and CV), indicates which on separate covariance matrices for each variables most reliably distinguish between group, rather than the pooled within-group groups along a particular discriminant func- variance–covariance matrix, as recommended tion. It shows that the first discriminant by Tabachnick and Fidell (2007). This proce- function is most strongly correlated with dure may lead to overfitting, in which classifi- kurtosis and the CV (although there is also cation functions, as estimates of group some correlation with skew). Figure 3 illus- membership, work well for the sample trates that this first function principally sepa- from which they were derived but do not rates mammals + birds from the lepidosaur generalize across the whole population. There- group and (to a slightly lesser extent) the fore, cross-validation was also carried out to testudine + crocodilian groups. Mammals + test how well classification functions derived birds have more negative measures of kurtosis from only a subset of the data could classify (Table 1), suggesting that their distributions of withheld data. mandibular depth have relatively more trun- Stepwise discriminant analysis extracted cated tails than distributions of testudine + two discriminant functions (Table 2B; com- crocodilian or lepidosaur mandibular depth ’ = χ2 = bined Wilks s lambda 0.111, (6) 68.3, (Fig. 1), while greater CV values in testudines + p < 0.001). There remains a significant associa- crocodilians and lepidosaurs compared with tion between groups and predictors after mammals (Table 1) indicate that the diapsid removal of the first function (Table 2B; Wilks’s mandibular depths are dispersed across a = χ2 = < lambda 0.365, (2) 31.2, p 0.001), indicat- relatively greater size range than those of ing that both functions may be considered mammals + birds. The second discriminant reliable discriminants of the groups. The first function correlates most strongly with skew, and second discriminant functions account for and to a lesser extent with CV, and chiefly 57.0% and 43.0%, respectively, of the between- discriminates testudines + crocodilians from group variability, while canonical R2 values mammals + birds and lepidosaurs, with

TABLE 2. Stepwise discriminant analysis with all species included.

A. Eigenvalues and canonical correlations of predictor variables with groups for each function Discriminant % of Between-group Canonical Canonical 95% Conﬁdence function Eigenvalue variance correlation R2 limits 1 2.305 57.0 0.835 0.6975 0.420–0.815 2 1.737 43.0 0.797 0.6346 0.328–0.772

B. Wilks’s lambda and signiﬁcance of functions

Test of Wilks’s Degrees of Partial η2 95% Conﬁdence function(s) lambda χ2 freedom p-Value (effect size) limits

1 through 2 0.111 68.274 6 0.000000 0.5713 0.184–0.688 2 0.365 31.210 2 0.000000 ——

C. Structure matrix of correlations of predictor variables with the discriminant functions and their effect sizes

Correlations of predictor variables with discriminant functions Correlation effect size

12 12

Transformed −0.698 0.379 0.487 0.144 kurtosis Transformed CV 0.707 −0.332 0.501 0.111 Transformed −0.556 −0.461 0.309 0.212 skew

testudines + crocodilians showing greater predictor for each group were contrasted with values of skew and CV than mammals + birds pooled means for the other two groups (Table 3). and lepidosaurs (Table 1). Skew is close to zero FDR corrections were applied to p-values for the in testudine + crocodilian distributions, while nine contrasts. When contrasting mammals + skew of mammals and lepidosaurs distributions birds with the pooled testudines + crocodilians is negative, with that of lepidosaurs the most and lepidosaurs and adjusting for all other negative. This is because a few individual predictors, we found mammals + birds to be testudines and crocodilians with an extended significantly separated from the other groups by pattern of adult growth grow to extreme size, kurtosis and CV. Kurtosis and skew were found increasing the proportion of data in the right tail to significantly separate testudines + crocodi- of their mandibular depth distributions. This lians from the other groups; and kurtosis, CV, increases the CV of their distributions and also and skew significantly separated lepidosaurs results in more even left and right tails to their from the other groups. Therefore, all three mandibular depth distributions than in deter- predictor variables are important in discriminat- minately growing mammals + birds and ing between the three different growth classes. lepidosaurs (Fig. 1). Lepidosaurs, in contrast, Mandibular depth distributions for mammals + have the most unevenly distributed left and birds are characterized by having a more right tails, since they have determinate growth negative kurtosis and lower CVs, reflecting both (truncated right tail) and slow juvenile growth rapid juvenile growth and determinate, trun- (longer left tail), and hence the most negative cated adult growth (Fig. 1). Testudines + skew. crocodilians have more positive values of To support the interpretation of structure kurtosis and values of skew that are close to matrix correlations and assess which predictors zero, which is consistent with their mandibular reliably separate each group from the other two depth distributions having two relatively long groups after adjustment for the other predictor tails due to both slow juvenile growth and variables, we performed nine general linear extended adult growth (Fig. 1). Finally, lepido- model (GLM) runs in which means for each saur distributions are characterized by more

FIGURE 3. Canonical discriminant function plot. Discriminant function analysis separated three growth classes (mammal + bird, lepidosaur, and testudine + crocodilian) on the basis of three predictor variables (skew, kurtosis, and CV) that relate to the shape of size distributions of mandibular depth for each growth-class member. The ﬁrst function principally separates amniotes with rapid juvenile growth (mammals + birds) from those with slow juvenile growth (testudines + crocodilians and lepidosaurs) and correlates most strongly with kurtosis and CV. The second function principally separates amniotes with extended growth (testudines + crocodilians) from those with determinate, truncated growth (mammals + birds and lepidosaurs) and correlates most strongly with skew. Classiﬁcation functions derived from this analysis were used to predict growth-class membership for three fossil species of unknown growth class (Morganucodon, Oligokyphus, and Gephyrosaurus). The marsupials Didelphis and Dasyurus are positioned close to the lepidosaur growth class.

negative values of skew and CVsandkurtosis then summed and added to a constant to find intermediate between mammals + birds and classification scores. Classification scores can testudines + crocodilians, which is consistent then be compared for each species across with their determinate, truncated adult growth groups to assess group membership. Here, and slow juvenile growth. these equations were modified to take account of the differences in group size by using growth-class sample proportions as prior Classification of Species into Growth probabilities when assigning species to their Categories growth classes. Posterior probabilities, or the Classification equations allow a species to be conditional probability of growth-class mem- assigned to a particular group and were bership under this model given the values of derived for each growth class in the discrimi- predictor variables, were calculated for all nant function analysis. In these equations, species. Of all original nonfossil species from predictor variable values for each subject which classification functions were derived, are first multiplied by classification function 100% were correctly classified, in comparison coefficients (Tabachnick and Fidell 2007) and with the 41.5% expected by chance alone.

TABLE 3. General linear model (GLM) contrasts of the mean of each predictor variable for each growth class against the pooled means for the other two growth classes. p-Values adjusted for multiple comparisons by FDR correction.

Predictor (adjusted for all others) Contrast Transformed kurtosis Transformed CV Transformed skew

Mammals + birds vs. others F(1,30) 7.47 5.01 0.47 p-Value (after FDR) 0.015 0.042 0.533 Effect size (partial η2) 0.199 0.143 0.016 Testudines + crocodilians vs. others F(1,30) 25.86 0.40 26.73 p-Value (after FDR) 0.000 0.533 0.000 Effect size (partial η2) 0.463 0.013 0.471 Lepidosaurs vs. others F(1,30) 7.92 10.68 44.82 p-Value (after FDR) 0.015 0.007 0.000 Effect size (partial η2) 0.209 0.263 0.599

TABLE 4. Posterior probabilities of group membership for fossil species and marsupial species in different discriminant function analyses. M/B, mammals + birds; T/C, testudines + crocodilians; L, lepidosaurs.

Posterior probability of group membership Marsupials Didelphis only All taxa Marsupials excluded All taxa excluded excluded (size corrected) (size corrected) M/B T/C L M/B T/C L M/B T/C L M/B T/C L M/B T/C L Morganucodon 1.000 0.000 0.000 1.000 0.000 0.000 1.000 0.000 0.000 1.000 0.000 0.000 1.000 0.000 0.000 Oligokyphus 0.815 0.012 0.173 0.690 0.015 0.294 0.783 0.005 0.212 0.664 0.324 0.012 0.516 0.460 0.024 Gephyrosaurus 0.261 0.016 0.723 0.036 0.030 0.934 0.121 0.033 0.847 0.053 0.000 0.947 0.007 0.000 0.993 Dasyurus 0.900 0.100 0.000 ———0.871 0.128 0.000 0.705 0.285 0.010 ——— Didelphis 0.550 0.004 0.446 ——————0.022 0.000 0.978 ———

All extant species were classified to their correct although this is lower than mammal-group groups with posterior probabilities greater probabilities exhibited by Morganucodon and than 0.85, with the exception of Didelphis, all placental species. Gephyrosaurus is classified which was classified correctly as a mammal with highest posterior probability (pp = 0.732; but with very low probability (pp = 0.550; Table 4) as a lepidosaur and occupies a position Table 4). All five species of birds were classified in the discriminant function plot (Fig. 3) very correctly in the mammal + bird growth class close to that group. with posterior probabilities in excess of A cross-validation run was performed to 0.999. In the canonical discriminant plot assess the stability of the classification proce- (Fig. 3), birds appear to form a small cluster dure. Classification functions, from which somewhat overlapping with placental group memberships of unknown fossil species mammals and distant from both lepidosaurs are estimated, were derived from approxi- and testudines + crocodilians. mately 75% of the extant species selected at Of the three fossil species with unknown random, while the remainder were withheld as growth patterns, Morganucodon was classified cross-validation data. For the species used to in the mammal group (pp = 1.000; Table 4) and derive classification functions (training data), occupies a position in the canonical discrimi- correct classification rate was 96.2%, while nant function plot (Fig. 3) that is close to but for the withheld cross-validation species, not within the cluster of placental mammal correct classification was 100%, indicating species. Oligokyphus occupies an intermediate that the classification procedure has high position between all three groups in the plot of consistency. Didelphis, which was classified as canonical discriminant functions (Fig. 3). It has a lepidosaur rather than as mammal, was the the greatest posterior probability of member- only incorrectly classified taxon among the ship in the mammal group (pp = 0.815; Table 4), training data.

Additional Discriminant Function Analyses CV, which discriminate between growth The entire discriminant function analysis was classes, are due to growth or to consistent repeated, excluding Canis, Dasyurus, Fringilla, differences in the life history variables. and Columba, to test whether problems relating Duetothesmallsamplesizeofthetestudine+ to their sample sizes biased results. Their crocodilian group and the fact that the number exclusion alters the results of the analysis very of predictor variables cannot exceed the size of little (Supplementary Material S4) and does not the smallest group in a discriminant analysis change the conclusions of this study. Repeating (Tabachnick and Fidell 2007), it was necessary to the analysis using only those measurements collapse the lepidosaur group with testudines + from greyhounds as Canis data also results in crocodilians into one diapsid group (which minimal changes to the results, with Canis differsingrowthstrategyfrommammals+ classified as a mammal with pp = 1.000 in birds in having slow, rather than rapid, juvenile both cases, whether using all dogs or only growth). Species for which life history data were greyhounds. missing were excluded. The analysis was also repeated excluding the Only one function is extracted by this marsupials Didelphis and Dasyurus. These taxa analysis, since only two groups are discrimi- are located closer to the lepidosaurs than nated. This function is highly significant ’ = χ2 = < placental mammals in the canonical discrimi- (Wilks s lambda 0.462, (6) 19.7, p 0.001; nant function plot (Fig. 3), suggesting that see Supplementary Material S6.1), indicating marsupials may form a growth class distinct that it reliably discriminates between mam- 2 from placental mammals by having slower mals and diapsids, and its canonical R value juvenile growth. They were therefore excluded shows that it explains 53.8% of the total to test whether this alters the positions of relationship between groups and predictors. Morganucodon and Oligokyphus in discriminant During stepwise entry of variables, only CV function plots. Again, exclusion does not was entered into the analysis with significance significantly alter overall results of the analysis of F < 0.05. This shows that the model that best (Supplementary Material S3.1). Morganucodon predicts mammal + bird versus nonavian and Oligokyphus occupy similar positions in the diapsid group membership only requires CV discriminant function plot in comparison with and is not improved by the addition of other the analysis with marsupials included (Fig. 3). variables. This function separates mammals + However, the classification of Oligokyphus birds from diapsids on the basis of the more changes; the posterior probability of mammal restricted distributions of the former and + bird group membership drops from pp = reflects rapid juvenile growth and determinate, 0.815 with marsupials included to pp = 0.6690 truncated adult growth in mammals, and when marsupials are excluded (Table 4). This slower juvenile growth in diapsids. This is not underscores the differences in growth patterns surprising, since this function corresponds between Oligokyphus and Morganucodon; the with the first discriminant function of the main latter taxon remains classified with the placen- analysis (Fig. 3, x-axis), which separates mam- tal mammal group at pp = 1.000 (Table 4) when mals from lepidosaurs and testudines + marsupials are excluded. crocodilians (i.e., diapsids) chiefly on the basis of CV and kurtosis. Since none of the size or life history variables were included in the stepwise The Effects of Body-Size and Life History Data analysis, this suggests that they do not reliably Three size and life history variables were discriminate between groups. included in another stepwise discriminant When testudines + crocodilians are col- analysis to assess whether any discriminant lapsed with the mammal + bird group and function correlates strongly with these vari- contrasted against lepidosaurs, conclusions ables (in addition to skew, kurtosis, or CV). If differ little from those described above for so, this would confound the effects of growth, diapsids versus mammals. One function was as it would be difficult to distinguish whether extracted, and stepwise entry of variables consistent differences in skew, kurtosis, and resulted in three variables being included in

the analysis with significance of F < 0.05. These growth: mammal + bird (rapid juvenile growth, were entered in the order skew, CV, size. The determinate, truncated adult growth), lepido- structure matrix of correlations between the saur (slow juvenile growth, determinate, discriminant function and the predictor vari- truncated adult growth), and testudine + ables (Supplementary Material S6.2.3) shows crocodilian (slow juvenile growth, extended that of the three entered variables, the function adult growth). Marsupials appear to have a correlates most strongly with skew. The corre- pattern of growth distinct from placental mam- lation of the size variable with the function is mals and may comprise a fourth pattern, while very weak (−0.140) and shares less than 2% of some species of birds exhibit juvenile growth variance with the function. This is below the that is even more rapid than that of most minimum level of correlation (0.32; sharing placental mammals. Growth in Morganucodon 10% of variance) recommended by Comrey is very similar to that of extant small placental and Lee (1992) for meaningful interpretation. mammals, with both determinate, truncated Again, this suggests that neither size nor any adult growth and rapid juvenile growth. life history variable reliably discriminates Oligokyphus is intermediate between placental between the groups. It is therefore unlikely mammals and diapsids; in comparison with that consistent differences in life history vari- Morganucodon and placental mammals ables are causing the consistent differences in Oligokyphus shows somewhat slower juvenile the combinations of skew, kurtosis, and CV. growth and somewhat more extended adult Rather, these differences in skew, kurtosis, and growth. CV are due to differences in growth pattern between groups. These analyses test for the effects of body Using Distribution Shape to Discriminate size and life history on the extant taxa with between Growth Patterns known growth patterns. While data regarding The two discriminant functions extracted life history variables are not available for the from the main discriminant analysis were fossil taxa, their body-size data can be highly significant, indicating that they both included. To assess the effect of body size on reliably discriminated between members of the classification of the fossil taxa while also different growth classes, with relatively high retaining three growth classes (rather than effect sizes (canonical correlations; Table 2A) collapsing two together), we performed linear (Tabachnick and Fidell 2007). regression of the three predictor variables The first discriminant function (Fig. 3) pri- against body size. The residuals from these marily separates amniotes with rapid juvenile regressions were then used as size-corrected growth (mammals + birds) from those with skew, kurtosis, and CV variables in a further slower juvenile growth on the basis of more discriminant function analysis. The results of negatively kurtotic distributions, with lower CV this analysis differ very little from the main in the mammal + bird group. The second analysis, with only minor changes in interpre- discriminant function primarily separates mem- tation of correlations of the discriminant func- bers of the testudine + crocodilian growth class, tions (e.g., a slightly higher correlation of with extended adult growth, from the other two kurtosis with the second discriminant function; groups, which have determinate, truncated Supplementary Material S7), which do not adult growth. This function correlates most alter any conclusions drawn from the main strongly with the skew and CV of individual analysis. species’ data distributions. Together with GLM analysis, this shows that the combinations of predictors for discriminating between different Discussion groups reflect the expected differences between Discriminant function analysis on skew, these groups given their respective growth kurtosis, and CV of mandibular depth distribu- strategies. tions showed that these measures reliably Broad within-group phylogenetic diversity, discriminate between at least three patterns of permitted by the inclusion of species with

convergently acquired characters, reduces the lower CVs than placentals (Fig. 3; Supplemen- confounding effects of phylogeny on func- tary Material S1), consistent with even more tional associations in multivariate approaches rapid juvenile growth in many bird species (Chen and Wilson 2015). Thus, while it is (Case 1978). possible that phylogenetic signal in both This analysis therefore derives discriminant predictor variables and growth classes may functions that reliably distinguish between underlie some of our observed pattern (Harvey growth classes on the basis of predictor vari- and Pagel 1991), the clustering of species with ables relating to the shape of mandibular depth convergently acquired growth strategies sug- distributions, and although a phylogenetic gests that functional effects of growth explain signal may be present, the functional effect of these patterns better than phylogenetic signal growth is clearly the most important driver alone. Birds, which convergently acquired separating classes. rapid juvenile growth and determinate, truncated adult growth, cluster within the same growth class as mammals with very high The Effects of Life History and Body Size posterior probabilities (all species > 0.999), If certain attributes of size or life history somewhat overlapping with placentals (Fig. 3), strategy were clumped in one particular and very distant from lepidosaurs and testu- growth class, it would be difficult to disen- dines + crocodilians (which are all more tangle whether the differences in distribution closely related to birds than are mammals; shape for this group were due to its different Fig. 1). Marsupials cluster more closely to growth strategy or influenced by size or life distantly related lepidosaurs than to placental history strategy. However, the inclusion of size mammals, possibly owing to their slower and life history variables in further discrimi- juvenile growth (see “Growth Patterns of nant function analyses showed that these Didelphis” section). variables do not discriminate reliably between If skew, kurtosis, and CV of mandibular diapsids and mammals or between lepidosaurs distributions were influenced primarily by and a collapsed mammal + bird + testudine + inherited characteristics (other than growth crocodilian group (Supplementary Material S6). pattern), there would be no particular reason This suggests that size and life history variables for combinations of characteristic skew, are relatively evenly spread through the three kurtosis, and CV patterns produced by such a different groups and are therefore unlikely to be phylogenetic signal to coincide so closely with causing the consistent differences in patterns those expected from growth. This is particu- of skew, kurtosis, and CV that distinguish larly evident in those cases in which species do between the growth classes. not cluster with other members of their clade Furthermore, discriminant function analysis but to a more distantly related group with carried out on the three predictor variables which they share particular growth character- after correction for size made very little istics; in these species, not only do their difference to results in comparison with the predictor variable values differ from those of main analysis (Supplementary Material S7.5). their closer relatives, but the predictor vari- Morganucodon and Oligokyphus are both still ables differ in exactly the way one would classified with highest posterior probability in expect given their differing growth patterns. the mammal group (Morganucodon: pp = 1.000; Not only do marsupials not cluster with Oligokyphus: pp = 0.664; Table 4), although the placental mammals, but differences in skew, posterior probability of mammal group mem- kurtosis, and CV imply much slower juvenile bership of Oligokyphus is somewhat reduced in growth in marsupials than in placentals, which comparison with the main analysis (pp = 0.815; is consistent with known growth differences Table 4), and Oligokyphus has a slightly closer between placentals and marsupials (Tyndale- relationship with both the lepidosaur and Biscoe 2001). Similarly, birds resemble placen- testudine + crocodilian groups in the discrimi- tals rather than other diapsids, and several nant function plot. However, this alters none of species also show more negative kurtosis and the conclusions of this study and suggests that

size differences have not greatly affected this is lower than the posterior probability of any analysis. Exclusion of the largest mammals placental mammal, which for all species (Canis and Dasyurus) did not alter the conclu- exceeds 0.999. In addition, when Didelphis sions either (Supplementary Material S4), nor alone was excluded from the analysis, did use of only greyhound data rather than Dasyurus had a somewhat reduced posterior data from all dogs. Nonetheless, given the probability of mammal + bird growth-class more prolonged growth period in larger membership (pp = 0.871 in comparison with mammals such as elephants and ruminants pp > 0.99 for all placental mammals; Table 4). (Lee and Werning 2008; Köhler et al. 2012), far This suggests that inclusion of Didelphis within larger in size than the fossils of relevance to this the placental mammal + bird growth class may study, future investigations could profitably have artificially raised the probability of inclu- focus on the effects of including a greater sion of Dasyurus in this growth class and that number of large-bodied taxa. marsupials represent a growth class distinct from placental mammals. However, robust testing of this hypothesis would require a Predicting Group Membership—Growth greater sample size of marsupial taxa. Patterns of Didelphis Classification functions from the main analysis (not including size and life history vari- Growth Patterns in Morganucodon and ables) predict group membership well, with Oligokyphus 100% of all original grouped cases being Morganucodon and Oligokyphus were assigned correctly classified in comparison with the to growth classes using classification functions 41.5% expected by chance alone. A cross- derived from the extant and extinct species of validation run indicated that the classification known growth patterns. Morganucodon exhibits procedure had high consistency. While all placental mammal-like growth on the basis of species were classified correctly, one mammal skew, kurtosis, and CV, with a posterior species, Didelphis, was classified with much probability of mammal + bird class member- lower posterior probability than any other ship of 1.000. Oligokyphus was classified with (pp = 0.550 in comparison with pp > 0.90 for all the mammal + bird growth class with a placental mammals; Table 4). relatively high posterior probability (pp = 0.815). One hypothesis to account for this is that, in The question arises as to whether a statistical common with other marsupials, Didelphis model derived from data distributions of extant exhibits growth patterns that differ from those species can be used to predict group member- of placental mammals, a hypothesis supported ship of extinct species whose data distributions by the close position of our other sampled may be subject to different biases, most notably marsupial, Dasyurus, to the lepidosaur group preservation bias. The truncation of the left tail in the discriminant function plot (Fig. 3). of Morganucodon’s data distribution may be due Epiphyseal growth plate closure is consistently to placental-like rapid juvenile growth, or it delayed or lacking in many marsupials, and may be due to poor preservation of smaller growth may continue throughout life (Geiger juvenile individuals with less ossified skeletons. et al. 2014). Marsupials also have a very To avoid conflating the effects of growth and derived reproductive strategy, with a pro- preservation bias, we included Gephyrosaurus in longed period of lactation resulting in slower our study. Gephyrosaurus is an extinct rhyncho- and more prolonged juvenile growth (Tyndale- cephalian that likely had lepidosaur growth Biscoe 2001), which may explain why the patterns (Chinsamy and Hurum 2006). It is of growth patterns of marsupials such as Didel- the same age and size and from the same phis and Dasyurus more closely resemble the Glamorgan fissure-fill deposits as Morganuco- lepidosaur growth pattern than that of placen- don (Evans 1980; Evans and Kermack 1994). tal mammals. Unlike Didelphis, Dasyurus was Oligokyphus, although from a slightly more classified as a mammal with relatively high recent locality, is from fissure-fill deposits probability (pp = 0.900; Table 4). However, this similar to those at Glamorgan; both deposits

were likely formed by predator-accumulated differences in growth in Morganucodon are not skeletal material being washed into an under- principally due to it having a slightly more ground water system (Kühne 1956; Evans and extended growth pattern than most extant Kermack 1994). placentals. Rather, it suggests that Morganuco- As expected, Gephyrosaurus is classified with don has slightly less rapid juvenile growth, extant lepidosaurs (slow juvenile growth, leading to data dispersed over a greater range determinate, truncated adult growth) with and with less negative kurtosis than in most high posterior probability (pp = 0.732). Its dis- placental mammals (indeed, Morganucodon has tribution is strongly negatively skewed with a less negative kurtosis than any placental long left tail, suggesting that the absence of mammal), and hence a more extreme position such a tail in the Morganucodon distribution is of Morganucodon in the first discriminant not due to preservation bias but to differences function. Nevertheless, Morganucodon also has in growth between Morganucodon and Gephyr- relatively low values in the second discrimi- osaurus. Thus, we conclude that Morganucodon nant function, suggesting that both a slightly has rapid juvenile growth in contrast with less rapid juvenile growth combined with a slower juvenile growth in Gephyrosaurus. slightly more extended adult growth pattern The classification of Morganucodon in the position Morganucodon at the extreme edge of mammal + bird growth class is based on its the extant placental mammal group. placental mammal–like values of skew, kurto- Oligokyphus occupies a position that is inter- sis, and CV. While its kurtosis is less negative mediate between all three major growth classes than that of placental mammals, it is still more in the canonical discriminant function plot negative than that of any testudine + crocodi- (Fig. 3), regardless of the inclusion or exclusion lian or lepidosaur (Supplementary Material of marsupials. It is positioned closer to the S1). This suggests that Morganucodon is likely testudine + crocodilian and lepidosaur growth to have had an almost typically placental classes than is Morganucodon. This suggests growth pattern of both rapid juvenile growth that growth in Oligokyphus may have and determinate, truncated adult growth. approached the placental mammalian condi- However, growth patterns in Morganucodon tion, while still differing from growth patterns are not identical with those observed in the seen in most extant mammals and Morganuco- sample of modern placentals. In the canonical don, for example, by having less rapid juvenile discriminant function plot (Fig. 3), Morganuco- growth or adult growth that did not terminate don is situated on the edge of the placental so abruptly as in extant mammals. mammal group; of all the placental mammals Oligokyphus differs from extant placental and birds, it is among the closest to either of the mammals to a greater extent in the first diapsid groups. Less rapid juvenile growth discriminant function than in the second. This may be the more important underlying differ- may suggest that slower juvenile growth pat- ence separating Morganucodon from extant terns exerted a strong influence in separating it placentals. In the canonical discriminant func- from Morganucodon and extant mammals. How- tion plot (Fig. 3), Morganucodon is on the most ever, the position of Oligokyphus in the discri- extreme edge of the placental mammal group minant function plot is also very close to the in the first discriminant function direction. In testudine + crocodilian group (Fig. 3). Indeed, comparison it is well within the range of extant when size is corrected for, the position of placentals in the second discriminant function. Oligokyphus is extremely close to that of the The second function separates chelonians + green turtle, Chelonia,andOligokyphus has a crocodilians from the other groups chiefly much higher posterior probability of member- because their more extended growth patterns ship in the testudines + crocodilian group cause longer right tails in the distributions, and (pp = 0.324) than the lepidosaur group (pp = so skew is closer to zero than in the other 0.012). This difference is even more marked groups. The fact that Morganucodon does not (testudine + crocodilian membership: pp = differ so greatly from most other mammals in 0.460; lepidosaur membership: pp = 0.024) the second discriminant function indicates that when the two marsupial species are removed

from the analysis, since they artiﬁcially enlarge This suggests that the evolution of rapid the discriminant function space occupied by the growth occurred in synapsids more basal than mammal + bird group. This suggests that Oligokyphus and that truncated adult growth Oligokyphus may have had somewhat less rapid evolved from morganucodontans crownward, juvenile growth than extant placental mammals subsequent to the evolution of key mammalia- but differed more prominently from placentals form traits such as the squamosal-dentary jaw and Morganucodon in having a more extended articulation. Thus, the origin of a determinate, growth period. This is consistent with evidence truncated pattern of adult growth may have from bone histology; tritylodontids had sus- followed the evolution of rapid juvenile tained, uninterrupted growth that slowed later growth. The origin of determinate truncated in ontogeny (Botha-Brink et al. 2012), but fully adult growth may then have permitted reduc- grown Oligokyphus specimens with peripheral tion of tooth replacement to diphyodont rest lines have yet to be sampled, so it is possible patterns. These conclusions are consistent with that growth was more extended in Oligokyphus existing hypotheses that link the evolution of than Morganucodon. Further study incorporat- determinate growth and of rapid juvenile ing more lepidosaurs and testudines + croco- growth with the origin of diphyodonty (Luo dilians of a variety of sizes would help to further et al. 2004). interpret how growth in Oligokyphus differs Most nonmammaliaform cynodonts have from Morganucodon. multiple, alternate dental replacements across As previously noted, we assume that the the entire dentition (Crompton 1963; Osborn sampled Oligokyphus specimens derive from a and Crompton 1973; Kielan-Jaworowska et al. single species (Kühne 1956); any conclusions 2004; Abdala et al. 2013). Replacement pat- about growth in this species must be recon- terns, especially of the postcanines, are some- sidered if our sample does in fact comprise two what reduced in more crownward taxa such as species. Probainognathus (Crompton and Jenkins 1979), Brasilodon (Martinelli and Bonaparte 2011), tritylodontids, and Sinoconodon (Zhang et al. Growth Patterns and the Evolution of 1998; Luo et al. 2004; Abdala et al. 2013). Such a Mammalian Biology reduction in tooth replacement may have been In combination with other evidence from permitted by more rapid rates of juvenile skull size ranges (Luo et al. 2001), ratios of growth. Morganucodon is the most basal known juvenile to adult specimens (Parrington 1971; synapsid to have a diphyodont replacement Kermack et al. 1973, 1981; Gow 1985), and bone pattern typical of extant mammals (Luo et al. histology (Chinsamy and Hurum 2006), the 2004). The placental-like truncated growth results of this study support determinate, patterns of Morganucodon would have truncated adult growth and rapid juvenile restricted the time at which the jaw was at an growth patterns in Morganucodon, as suggested intermediate size, hence reducing the require- for M. oehleri by Luo et al. (2004). Oligokyphus ment for multiple replacements of teeth (Zhang differed from Morganucodon in growth, possi- et al. 1998) and permitting a diphyodont bly in having slightly less rapid juvenile pattern of tooth replacement. growth but more likely in having a somewhat Applying the techniques used in this study more extended period of growth. This is to other mammaliaform and cynodont taxa indicated by its closer afﬁliation with the could further test this hypothesis of the testudines + crocodilian group than the dependence of diphyodonty on the evolution lepidosaur group. Supporting evidence for of both rapid juvenile growth and determinate, such growth patterns in Oligokyphus is pro- truncated growth. This hypothesis would vided by bone histology, which suggests that predict that relatively placental-like patterns juvenile growth is very rapid in Oligokyphus, of growth should occur in cynodonts with very with reproductive maturity reached within a reduced dental replacement. Hence, Sinocono- year, while growth after this may well have don, which has reduced postcanine replace- been extended relative to Morganudocon. ment (somewhat similar to tritylodontids),

should have growth patterns at least resem- molar occlusion (Crompton and Jenkins bling those of Oligokyphus, if not placental 1973; Pond 1977; Crompton 1995) in more mammals. Luo et al. (2001) inferred growth crownward mammaliaforms, as the relative patterns were less mammal-like in Sinoconodon positions of teeth could remain constant in than in Morganucodon, but further work is adult animals. These dental characteristics are required to assess growth in Sinoconodon in turn integrated with a suite of other relative to more basal cynodonts. It should be potentially correlated characteristics, such as noted that a hypothesis of placental-like mammalian masticatory function (Crompton growth enabling diphyodonty to evolve does 1995) and endothermy (Kemp 2005), which not necessarily exclude the possibility of rapid have been of vital importance in the subse- and truncated growth rates evolving more quent evolution of mammals. basally than the origin of diphyodonty. Given evidence from bone histology, it is possible that Acknowledgments this has occurred in several therapsid taxa, for example, therocephalians (Huttenlocker and The authors would like to thank two Botha-Brink 2014), Thrinaxodon (Botha and anonymous reviewers for their thoughtful Chinsamy 2005), and Galesaurus (Butler 2010). comments, which improved both the metho- Inclusion of more basal taxa in a similar dology and interpretation of results. We are analysis, permitting direct comparison with indebted to Ian Corfe for helpful advice those examined here, could be useful in under- regarding Oligokyphus that expanded the scope standing how growth evolved more basally in of this study and to Michel Laurin and David the synapsid lineage. Marjanović who provided helpful comments on the manuscript. Thanks go to John Aston and Brian McCabe for statistical advice. Summary Gephyrosaurus specimens were provided by Our results permit a more nuanced inter- Susan Evans (University College London), pretation of growth across the cynodont-to- while Alan Resetar (Field Museum of Natural mammaliaform transition than a dichotomy History, Chicago), Sylvia Humphries (Han- between determinate versus extended growth. cock Museum, Newcastle), Patrick Campbell Like other mammalian features, growth pat- (Natural History Museum, London), Sandra terns known today among placental mammals Chapman (Natural History Museum, London), evolved gradually (Kemp 2007). Growth in Roberto Portela Miguez (Natural History Morganucodon closely resembled extant placen- Museum London), Małgosia Nowak-Kemp tal mammals, while in Oligokyphus, growth (Oxford University Museum of Natural was intermediate with slightly less rapid History), Emma-Louise Nicholls (University juvenile growth and more extended adult College London, Grant Museum of Zoology), growth than in Morganucodon. Given that true and Matthew Lowe (University Museum of diphyodonty was present in Morganucodon but Zoology, Cambridge) facilitated access to not more stemward cynodonts (e.g., Oligoky- specimens at museum collections. R.N.O.’s phus, Sinoconodon), this is consistent with the work is funded by the Cambridge Home and hypothesis that placental-like growth enabled EU Scholarship Scheme. diphyodont replacement. Rapid juvenile growth combined with more truncated (determinate) adult growth in Literature Cited basal mammaliaforms enabled reduction of Abdala, F., S. C. Jasinoski, and V. Fernandez. 2013. Ontogeny of dental replacement and may also comprise the Early Triassic cynodont Thrinaxodon liorhinus (Therapsida): dental morphology and replacement. Journal of Vertebrate indirect evidence for the evolution of Paleontology 33:1408–1431. lactation (Zhang et al. 1998; Luo et al. 2004). Adolph, S. C., and W. P. Porter. 1996. Growth, seasonality, and – A reduction in tooth replacement, together lizard life histories: age and size at maturity. Oikos 77:267 278. Andrews, R. M. 1982. Patterns of growth in reptiles. Pp. 273–320 with truncated, determinate growth, may in C. Gans, and F. H. Pough, eds. Biology of the Reptilia, Vol. 13. have permitted the evolution of more precise Academic, New York.

Asher, R. J., and T. Lehmann. 2008. Dental eruption in afrotherian Ciancio, M. R., M. C. Castro, F. C. Galliari, A. A. Carlini, and mammals. BMC Biology 6:14. R. J. Asher. 2012. Evolutionary implications of dental eruption in Asher, R. J., and G. Olbricht. 2009. Dental ontogeny in Macroscelides Dasypus (Xenarthra). Journal of Mammalian Evolution 19:1–8. proboscideus (Afrotheria) and Erinaceus europaeus (Lipotyphla). Clemens, W. A. 1979. A problem in morganucodontid taxonomy. Journal of Mammalian Evolution 16:99–115. Zoological Journal of the Linnean Society 66:1–14. Balazs, G. H. 1980. Synopsis of biological data on the green turtle in Comrey, A. L., and H. B. Lee. 1992. A first course in factor analysis, the Hawaiian islands. NOAA Technical Memorandum NMFS, 2nd ed. Erlbaum, Hillsdale, N.J. NOAA-SWFC-7. U.S. Department of Commerce. Congdon, J. D., R. D. Nagle, O. M. Kinney, R. C. van Loben Sels, Barr, W. A., and R. S. Scott. 2014. Phylogenetic comparative meth- T. Quinter, and D. W. Tinkle. 2003. Testing hypotheses of aging ods complement discriminant function analysis in ecomorphol- in long-lived painted turtles (Chrysemys picta). Experimental ogy. American Journal of Physical Anthropology 153:663–674. Gerontology 38:765–772. Benjamini, Y., and Y. Hochberg. 1995. Controlling the false Congdon, J. D., J. Whitfield Gibbons, R. J. Brooks, N. Rollinson, and discovery rate: a practical and powerful approach to multiple R. N. Tsaliagos. 2013. Indeterminate growth in long-lived fresh- testing. Journal of the Royal Statistical Society B 57:289–300. water turtles as a component of individual fitness. Evolutionary Bjorndal, K. A., J. Parsons, W. Mustin, and A. B. Bolten. 2013. Ecology 27:445–459. Threshold to maturity in a long-lived reptile: interactions of age, Cothran, E. G., M. J. Aivaliotis, and J. L. Vandeberg. 1985. The size, and growth. Marine Biology 160:607–616. effects of diet on growth and reproduction in grey short-tailed Botha, J., and A. Chinsamy. 2000. Growth patterns deduced from opossums, Monodelphis domestica. Journal of Experimental the histology of the cynodonts Diademodon and Cynognathus. Zoology 236:103–114. Journal of Vertebrate Paleontology 20:705–711. Cott, H. B. 1961. Scientific results of an inquiry into the ecology and ——. 2005. Growth patterns of Thrinaxodon liorhinus, a non- economic status of the Nile crocodile (Crocodylus niloticus)in mammalian cynodont from the Lower Triassic of South Africa. Uganda and northern Rhodesia. Transactions of the Zoological Palaeontology 48:385–394. Society of London 29:211–256. Botha-Brink, J., F. Abdala, and A. Chinsamy-Turan. 2012. The Crawford, N. G., J. F. Parham, A. B. Sellas, B. C. Faircloth, radiation and osteohistology of nonmammaliaform cynodonts. T. C. Glenn, T. J. Papenfuss, J. B. Henderson, M. H. Hansen, Pp. 222–246 in A. Chinsamy-Turan, ed. Forerunners of mam- and W. B. Simison. 2015. A phylogenomic analysis of turtles. mals: radiation, histology, biology. Indiana University Press, Molecular Phylogenetics and Evolution 83:250–257. Bloomington. Crompton, A. W. 1963. Tooth replacement in the cynodont Butler, E. 2010. The post-cranial skeleton of the Early Triassic non- Thrinaxodon liorhinus Seeley. Annals of the South African mammalian cynodont Galesaurus planiceps: implications for Museum 46:479–521. biology and lifestyle. Master’s dissertation, University of the Free ——. 1995. Masticatory function in nonmammalian cynodonts and State, Bloemfontein, South Africa. early mammals. Pp. 55–75 in J. J. Thomason, ed. Functional Butler, P. M. 1995. Ontogenetic aspects of dental evolution. Inter- morphology in vertebrate paleontology. Cambridge University national Journal of Developmental Biology 39:25–34. Press, Cambridge. Carr, A., and D. Goodman. 1970. Ecologic implications of size and Crompton, A. W., and F. A. Jenkins. 1973. Mammals from reptiles: growth in Chelonia. Copeia 4:783–786. a review of mammalian origins. Annual Review of Earth and Case, T. J. 1978. On the evolution and adaptive significance of Planetary Sciences 1:131–155. postnatal growth rates in the terrestrial vertebrates. Quarterly ——. 1979. Origin of mammals. Pp. 59–73 in J. Lillegraven, Review of Biology 53:243–282. Z. Kielan-Jaworowska, and W. Clemens, eds. Mesozoic Castanet, J., and M. Báez. 1991. Adaptation and evolution in Gallotia mammals: the first two thirds of mammalian history. University lizards from the Canary Islands: age, growth, maturity and of California Press, Berkeley. longevity. Amphibia-Reptilia 12:81–102. Crompton, A. W., and Z.-X. Luo. 1993. Relationships of the Liassic Castanet, J., D. G. Newman, and H. Saint Girons. 1988. Skeleto- mammals Sinoconodon, Morganucodon,andDinnetherium. chronological data on the growth, age and population structure Pp. 30–44 in F. S. Szalay, M. J. Novacek, and M. C. McKenna, of the tuatara, Sphenodon punctatus, on the Stephens and Lady eds. Mammal phylogeny: mesozoic differentiation, multi- Alice islands, New Zealand. Herpetologica 44:25–37. tuberculates, monotremes, early therians, and marsupials. Charnov, E. L., T. F. Turner, and K. O. Winemiller. 2001. Repro- Springer, New York. ductive constraints and the evolution of life histories with Crompton, A. W., and P. Parker. 1978. Evolution of the mammalian indeterminate growth. Proceedings of the National Academy of masticatory apparatus: the fossil record shows how mammals Sciences USA 98:9460–9464. evolved both complex chewing mechanisms and an effective Chen, M., and G. P. Wilson. 2015. A multivariate approach to middle ear, two structures that distinguish them from reptiles. infer locomotor modes in Mesozoic mammals. Paleobiology 41: American Scientist 66:192–201. 280–312. Crompton, A. W., C. B. Wood, and D. N. Stern. 1994. Differential Chiari, Y., V. Cahais, N. Galtier, and F. Delsuc. 2012. Phylogenomic wear of enamel: a mechanism for maintaining sharp analyses support the position of turtles as the sister group of cutting edges. Advances in Comparative and Environmental birds and crocodiles (Archosauria). BMC Biology 10:65. Physiology 18:321–346. Chinsamy, A., and F. Abdala. 2008. Palaeobiological implications of Curran-Everett, D. 2000. Multiple comparisons: philosophies and the bone microstructure of South American traversodontids illustrations. American Journal of Physiology: Regulatory, (Therapsida: Cynodontia). South African Journal of Science Integrative and Comparative Physiology 279:1–8. 104:225–230. Dawbin, W. H. 1982. The tuatara Sphenodon punctatus: aspects Chinsamy, A., and J. H. Hurum. 2006. Bone microstructure and of life history, growth and longevity. In D. G. Newman, ed. growth patterns of early mammals. Acta Palaeontologica New Zealand herpetology. New Zealand Wildlife Service, Polonica 51:325–338. Department of Internal Affairs, Occasional Publications 2: Chinsamy, A., S. A. Hanrahan, R. M. Neto, and M. Seely. 1995. 237–250. Skeletochronological assessment of age in Angolosaurus skoogi,a de Buffrénil, V., I. Ineich, and W. Böhme. 2004. Comparative data cordylid lizard living in an aseasonal environment. Journal of on epiphyseal development in the family Varanidae. Journal of Herpetology 29:457–460. Herpetology 37:328–335.

de Magalhaes, J. P., and J. Costa. 2009. A database of vertebrate Hopson, J. A. 1971. Postcanine replacement in the gomphodont longevity records and their relation to other life-history traits. cynodont Diademodon. Pp. 1–21 in D. M. Kermack, and Journal of Evolutionary Biology 22:1770–1774. K. A. Kermack, eds. Early mammals. Academic, London. de Ricqlès, A. 1969. Recherches paléohistologiques sur les os longs ——. 1973. Endothermy, small size and the origin of mammalian des Tétrapodes. II, Quelques observations sur la structure des reproduction. American Naturalist 107:446–452. longs des Thériodontes. Annales de Paléontologie (Vertébrés) Hurum, J. H., and A. Chinsamy-Turan. 2012. The radiation, bone 55:1–52. histology, and biology of early mammals. Pp. 248–270 in ——. 1976. On bone histology of fossil and living reptiles, with A. Chinsamy-Turan, ed. Forerunners of mammals: radiation, comments on its functional and evolutionary significance. histology, biology. Indiana University Press, Bloomington. Pp. 123–150 in A. A. Bellairs, and C. B. Cox, eds. Morphology and Huttenlocker, A. K., and J. Botha-Brink. 2014. Bone microstructure biology of reptiles (Linnean Society Symposium Series No. 3). and the evolution of growth patterns in Permo-Triassic ther- Academic, London. ocephalians (Amniota, Therapsida) of South Africa. PeerJ 2:e325. Dice, L. R., and R. M. Bradley. 1942. Growth in the deer-mouse, Jackson, C. M., and L. G. Lowrey. 1912. On the relative growth of Peromyscus maniculatus. Journal of Mammalogy 23:416–427. the component parts (head, trunk and extremities) and systems Dunham, A. E., and J. W. Gibbons. 1990. Growth of the slider turtle. (skin, skeleton, musculature and viscera) of the albino rat. Ana- Pp. 135–145 in J. W. Gibbons, ed. Life history and ecology of the tomical Record 6:449–474. slider turtle. Smithsonian Institution Press, Washington, D.C. Jenkins, F. A., and C. R. Schaff. 1988. The Early Cretaceous mammal Edmund, A. G. 1960. Tooth replacement phenomena in the lower Gobiconodon (Mammalia, Triconodonta) from the Cloverly For- vertebrates. Contributions of Royal Ontario Museum, Life mation in Montana. Journal of Vertebrate Paleontology 8:1–24. Science Division 52:1–190. Kemp, T. S. 2005. The origin and evolution of mammals. Oxford Eisen, E. J. 1976. Results of growth curve analyses in mice and rats. University Press, Oxford. Journal of Animal Science 42:1008–1023. ——. 2007. The concept of correlated progression as the basis of a Erickson, G. M. 2005. Assessing dinosaur growth patterns: a micro- model for the evolutionary origin of major new taxa. Proceedings scopic revolution. Trends in Ecology and Evolution 20:677–684. of the Royal Society of London B 274:1667–1673. Erickson, G. M., K. Curry Rogers, and S. A. Yerby. 2001. Kermack, K. A., and D. M. Kermack. 1984. Evolution of mammalian Dinosaurian growth patterns and rapid avian growth rates. characters. Croom Helm, London. Nature 412:429–433. Kermack, K. A., F. Mussett, and H. W. Rigney. 1973. The lower jaw Evans, S. E. 1980. The skull of a new eosuchian reptile from the of Morganucodon. Zoological Journal of the Linnean Society Lower Jurassic of South Wales. Zoological Journal of the Linnean 53:87–175. Society 70:203–264. ——. 1981. The skull of Morganucodon. Zoological Journal of the Evans, S. E., and M. E. H. Jones. 2010. The origin, early history and Linnean Society 71:1–158. diversification of lepidosauromorph reptiles. In S. Bandyo- Kielan-Jaworowska, Z., and D. Dashzeveg. 1998. Early Cretaceous padhyay, ed. New aspects of Mesozoic biodiversity. Lecture amphilestid (‘triconodont’) mammals from Mongolia. Acta Notes in Earth Sciences 132:27–44. Springer, Berlin. Palaeontologica Polonica 43:413–438. Evans, S. E., and K. A. Kermack. 1994. Assemblages of small Kielan-Jaworowska, Z., R. L. Cifelli, and Z.-X. Luo. 2004. Mammals tetrapods from the Early Jurassic of Britain. Pp. 271–283 in from the age of dinosaurs: origins, evolution and structure. N. C. Fraser, and H.-D. Sues, eds. In the shadow of the dinosaurs. Columbia University Press, New York. Cambridge University Press, Cambridge. Köhler, M., N. Marín-Moratalla, X. Jordana, and R. Aanes. 2012. Ewer, R. F. 1963. Reptilian tooth replacement. News Bulletin of the Seasonal bone growth and physiology in endotherms shed light Zoological Society of South Africa 4:4–9. on dinosaur physiology. Nature 487:358–361. Fernandez, S. 1998. Age, growth and calving season of bottlenose Kolarov, T., K. Ljubisavljević, L. Polović,G.Džukić,and dolphins, Tursiops truncatus, off coastal Texas. Fishery Bulletin M. L. Kalezić. 2010. The body size, age structure and growth 96:357–365. pattern of the endemic Balkan Mosor rock lizard (Dinarolacerta Frazer, N. B., and R. C. Ladner. 1986. A growth curve for green sea mosorensis, Kolombatović, 1886). Acta Zoologica Academiae turtles, Chelonia mydas, in the U.S. Virgin Islands, 1913–14. Scientiarum Hungaricae 56:55–71. Copeia 3:798–802. Krogman, W. M. 1931. Growth changes in the skull and face of the Geiger, M., A. M. Forasiepi, D. Koyabu, and M. R. Sánchez-Villagra. gorilla. American Journal of Anatomy 47:89–115. 2014. Heterochrony and post-natal growth in mammals—an Kühne, W. G. 1956. The Liassic therapsid Oligokyphus. Trustees of examination of growth plates in limbs. Journal of Evolutionary the British Museum, London. Biology 27:98–115. Lee, A. H., and S. Werning. 2008. Sexual maturity in growing Godfrey, L. R., K. E. Samonds, P.C. Wright, and S. J. King. 2005. dinosaurs does not fit reptilian growth models. Proceedings of Schultz’s unruly rule: dental developmental sequences and the National Academy of Sciences USA 105:582–587. schedules in small-bodied, folivorous lemurs. Folia Primatolo- Lee, A. H., A. K. Huttenlocker, K. Padian, and H. N. Woodward. gica 76:77–99. 2013. Analysis of growth rates. Pp. 217–251 in K. Padian, and Gow, C. E. 1985. Apomorphies of the Mammalia. South African E.-T. Lamm, eds. Bone histology of fossil tetrapods: advancing Journal of Science 81:558–560. methods, analysis and interpretation. University of California Grine, F. E., and E. S. Vrba. 1980. Prismatic enamel: a pre- Press, Berkeley. adaptation for mammalian diphyodonty? South African Journal Lovich, J. E., C. H. Ernst, and J. F. McBreen. 1990. Growth, maturity, of Science 76:139–141. and sexual dimorphism in the wood turtle, Clemmys insculpta. Haines, R. W. 1969. Epiphyses and sesamoids. Pp. 81–115 in Canadian Journal Zoology 68:672–677. C. Gans, A. d’A. Bellairs, and T. S. Parsons, eds. Biology of the Luo, Z.-X. 1994. Sister-group relationships of mammals and trans- Reptilia, Vol. 1A. Morphology. Academic, London. formations of diagnostic mammalian characters. Pp. 98–128 in Harvey, P. H., and M. D. Pagel. 1991. The comparative method in N. C. Fraser, and H.-D. Sues, eds. In the shadow of the dinosaurs. evolutionary biology. Oxford University Press, Oxford. Cambridge University Press, Cambridge. Helmink, S. K., R. D. Shanks, and E. A. Leighton. 2000. Breed and Luo, Z.-X., A. W. Crompton, and A.-L. Sun. 2001. A new mammal sex differences in growth curves for two breeds of dog guides. from the Early Jurassic and evolution of mammalian character- Journal of Animal Science 78:27–32. istics. Science 292:1535–1540.

Luo, Z.-X., Z. Kielan-Jaworowska, and R. L. Cifelli. 2002. In quest Rootes, W. L., R. H. Chabreck, V. L. Wright, B. W. Brown, for a phylogeny of Mesozoic mammals. Acta Palaeontologica and T. J. Hess. 1991. Growth rates of American alligators Polonica 47:1–78. in estuarine and palustrine wetlands in Louisiana. Estuaries ——. 2004. Evolution of dental replacement in mammals. Bulletin 14:489–494. of the Carnegie Museum of Natural History 36:159–175. Rowe, T. B. 1998. Definition, diagnosis, and origin of Mammalia. Maisano, J. A. 2002. Terminal fusions of skeletal elements as Journal of Vertebrate Paleontology 8:241–264. indicators of maturity in squamates. Journal of Vertebrate Säilä, L. K. 2005. A new species of the sphenodontian reptile Paleontology 22:268–275. Clevosaurus, from the Lower Jurassic of South Wales. Palaeon- Martin, T., and M. Nowotny. 2000. The docodont Haldanodon from tology 48:817–831. the Guimarota mine. Pp. 91–96 in T. Martin, and B. Krebs, eds. Sander, P. M., and N. Klein. 2005. Developmental plasticity in the Guimarota—a Jurassic ecosystem. Verlag Dr. Friedrich Pfeil, life history of a prosauropod dinosaur. Science 310:1800–1802. Munich. Scheyer, T. M., N. Klein, and M. Sander. 2010. Developmental Martinelli, A. G., and J. F. Bonaparte. 2011. Postcanine replacement palaeontology of Reptilia as revealed by histological studies. in Brasilodon and Brasilitherium (Cynodontia, Probainognathia) Seminars in Cell and Developmental Biology 21:462–470. and its bearing in cynodont evolution. Pp. 179–186 in J. Calvo, Schrader, A. M., S. M. Ferreira, M. E. McElveen, P.C. Lee, C. J. Moss, J. Porfiri,B.GonzalesRiga,andD.DosSantos,eds.Paleontologíay and R. J. van Aarde. 2006. Growth and age determination of Dinosaurios desde América Latina Editora de la Universidad de African savanna elephants. Journal of Zoology 270:40–48. Cuyo. Mendoza, Argentina. Sebens, K. P. 1987. The ecology of indeterminate growth in animals. Moss, M. L., and M. J. Baer. 1956. Differential growth of the Annual Review of Ecology and Systematics 18:71–407. rat skull. Growth 20:107–120. Seminoff, J. A., A. Resendiz, W. J. Nichols, and T. T. Jones. 2002. Mills, J. R. E. 1971. The dentition of Morganucodon. Pp. 29–63 in Growth rates of wild green turtles (Chelonia mydas)ata D. M. Kermack, and K. A. Kermack, eds. Early mammals. Aca- temperate foraging area in the Gulf of California, México. Copeia demic, London. 3:610–617. Münkemüller, T., S. Lavergne, B. Bzeznik, S. Dray, T. Jombart, K. Shine, R., and E. L. Charnov. 1992. Patterns of survival, growth, and Schiffers, and W. Thuiller. 2012. How to measure and test maturation in snakes and lizards. American Naturalist 39: phylogenetic signal. Methods in Ecology and Evolution 3:743–756. 1257–1269. Nesterenko, V., and S. Ohdachi. 2001. Postnatal growth and Shine, R., and J. B. Iverson. 1995. Patterns of survival, growth and development in Sorex unguiculatus. Mammal Study 26:145–148. maturation in turtles. Oikos 72:343–348. Nowotny, M., T. Martin, and M. S. Fischer. 2001. Dental anatomy Sokal, R. R., and F. J. Rohlf. 2012. Biometry, 4th ed. Freeman, and tooth replacement of Haldanodon exspectatus (Docodonta, New York. Mammalia) from the Upper Jurassic of Portugal. Journal of Tabachnick, B. G., and L. S. Fidell. 2007. Using Multivariate Morphology 248:268. Statistics, 5th ed. Pearson Education, Boston. Osborn, J. W. 1971. The ontogeny of tooth succession in Lacerta Tucker, A. D., C. J. Limpus, K. R. McDonald, and H. I. McCallum. vivipara, Jacquine (1787). Proceedings of the Royal Society of 2006. Growth dynamics of freshwater crocodiles (Crocodylus London B 179:261–289. johnstoni) in the Lynd River, Queensland. Australian Journal of ——. 1974. On the control of tooth replacement in reptiles and its Zoology 54:409–415. relationship to growth. Journal of Theoretical Biology 46:509–527. Tyndale-Biscoe, C. H. 2001. Australasian marsupials—to cherish Osborn, J. W., and A. W. Crompton. 1973. The evolution of mam- and to hold. Reproduction, Fertility and Development 13: malian from reptilian dentitions. Breviora 399:1–18. 477–485. Padian, K., A. J. de Ricqlès, and J. R. Horner. 2001. Dinosaurian van Devender, R. W. 1978. Growth ecology of a tropical lizard, growth rates and bird origins. Nature 412:405–408. Basiliscus basiliscus. Ecology 59:1031–1038. Parrington, F. R. 1971. On the Upper Triassic mammals. Philoso- Westergaard, B., and M. W. J. Ferguson. 1986. Development of the phical Transactions of the Royal Society of London B 261:231–272. dentition in Alligator mississippiensis. Early embryonic develop- ——. 1973. The dentitions of the earliest mammals. Zoological ment in the lower jaw. Journal of Zoology 210:575–597. Journal of the Linnean Society 52:85–95. ——. 1987. Development of the dentition in Alligator mis- ——. 1978. A further account of the Triassic mammals. Philoso- sissippiensis. Later development in the lower jaws of embryos, phical Transactions of the Royal Society of London B 282: hatchlings and young juveniles. Journal of Zoology 212:199–222. 177–204. Wilkinson, P. M., and W. E. Rhodes. 1997. Growth rates of Amer- Pond, C. M. 1977. The significance of lactation in the evolution of ican alligators in coastal South Carolina. Journal of Wildlife mammals. Evolution 31:177–199. Management 61:397–402. Porter, K. R. 1972. Herpetology. Saunders, Philadelphia. Woodward, H. N., J. R. Horner, and J. O. Farlow. 2011. Osteohis- Ray, S., S. Bandyopadhyay, and D. Bhawal. 2009. Growth patterns tological evidence for determinate growth in the American as deduced from bone microstructure of some selected neother- alligator. Journal of Herpetology 45:339–342. apsids with special emphasis on dicynodonts: phylogenetic Zhang, F.-K., A. W. Crompton, Z.-X. Luo, and C. R. Schaff. 1998. implications. Palaeoworld 18:53–66. Pattern of dental replacement of Sinoconodon and its implications Ray, S., J. Botha, and A. Chinsamy. 2004. Bone histology and for evolution of mammals. Vertebrata PalAsiatica 36:197–217. growth patterns of some nonmammalian therapsids. Journal of Zug, G. R., A. H. Wynn, and C. Ruckdeschel. 1986. Age determi- Vertebrate Paleontology 24:634–648. nation of loggerhead sea turtles, Caretta caretta, by incremental R Core Team. 2012. R: a language and environment for statistical growth marks in the skeleton. Smithsonian Contributions to computing. R Foundation for Statistical Computing, Vienna, Zoology 427:1–34. Austria. http://www.R-project.org. Zúñiga-Vega, J. J., R. I. Rojas-González, J. A. Lemos-Espinal, Robinson, P. L. 1957. The Mesozoic fissures of the Bristol Channel and M. E. Pérez-Trejo. 2005. Growth ecology of the lizard area and their vertebrate faunas. Zoological Journal of the Xenosaurus grandis in Veracruz, México. Journal of Herpetology Linnean Society 43:260–282. 39:433–443.