Recognizing Sexual Dimorphism in the Fossil Record: Lessons from Nonavian Dinosaurs

Paleobiology, page 1 of 13 DOI: 10.1017/pab.2016.51

Recognizing sexual dimorphism in the fossil record: lessons from nonavian dinosaurs

Jordan C. Mallon

Abstract.—The demonstration of sexual dimorphism in the fossil record can provide vital information about the role that sexual selection has played in the evolution of life. However, statistically robust inferences of sexual dimorphism in fossil organisms are exceedingly difficult to establish, owing to issues of sample size, experimental control, and methodology. This is particularly so in the case of dinosaurs, for which sexual dimorphism has been posited in many species, yet quantifiable data are often lacking. This study presents the first statistical investigation of sexual dimorphism across Dinosauria. It revisits prior analyses that purport to find quantitative evidence for sexual dimorphism in nine dinosaur species. After the available morphological data were subjected to a suite of statistical tests (normality and unimodality tests and mixture modeling), no evidence for sexual dimorphism was found in any of the examined taxa, contrary to conventional wisdom. This is not to say that dinosaurs were not sexually dimorphic (phylogenetic inference suggests they may well have been), only that the available evidence precludes its detection. A priori knowledge of the sexes would greatly facilitate the assessment of sexual dimorphism in the fossil record, and it is sug- gested that unambiguous indicators of sex (e.g., presence of eggs, embryos, medullary bone) be used to this end.

Jordan C. Mallon. Palaeobiology, Canadian Museum of Nature, Post Ofﬁce Box 3663, Station D, Ottawa, Ontario K1P 6P4, Canada. E-mail: [email protected]

Accepted: 21 November 2016 Data available from the Dryad Digital Repository: http://dx.doi.org/10.5061/dryad.8f6d2

Introduction Andersson 1994), so it is used here for strictly pragmatic reasons. Sexual dimorphism is broadly defined as the The semantic debate about sexual dimor- phenomenon in which the sexes of a species are phism has likewise sparked disagreement phenotypically different. Such differences typi- concerning what counts as evidence for sexual cally become more pronounced with maturity, selection. Assuming a strict definition of sexual and are usually manifested in the morphology dimorphism, only the documentation of dis- of the reproductive organs, but may also continuous character states counts toward an include variation in the shapes of display (e.g., argument for sexual selection (Padian and horns and crests) and feeding structures, in Horner 2011a,b, 2013, 2014a,b). However, color, in body size, and in behavior. Recent assuming sexual dimorphism sensu lato, the debate has centered on the semantics of sexual requirements are not nearly so strict, and a dimorphism, with some (Padian and Horner simple demonstration of positive allometry 2011a,b, 2013, 2014a,b) arguing that the term be may be admissible (Tomkins et al. 2010; Knell limited to describing discrete (presence/ et al. 2013b; Hone et al. 2016b). Positive absence) features, and others (Knell and allometry in the absence of dimorphism has Sampson 2011; Knell et al. 2013a,b; Mendelson been attributed to mutual sexual selection and Shaw 2013; Borkovic and Russell 2014) (Hone et al. 2012). arguing for a more inclusive definition that In spite of these prior disputes, what remains encompasses continuous variation. The latter uncontroversial is that sexual dimorphism definition is the more commonly and widely (however defined) typically results from sexual employed (e.g., Cunningham 1900; Schoener selection. Therefore, the identification of sexual 1967; Hedrick and Temeles 1989; Shine 1989; dimorphism in the fossil record can yield

© 2017 The Paleontological Society. All rights reserved. 0094-8373/17 Downloaded from https:/www.cambridge.org/core. IP address: 97.115.205.50, on 30 Mar 2017 at 01:45:35, subject to the Cambridge Core terms of use, available at https:/www.cambridge.org/core/terms. https://doi.org/10.1017/pab.2016.51 2 JORDAN C. MALLON

important insights into the role that sexual dimorphic character, ideally more often than selection has played in the history of life. would be expected due to chance alone. Sexual dimorphism has, indeed, been attri- Issues of Control.—The ability to convincingly buted to various fossil metazoans, including demonstrate sexual dimorphism in the fossil trilobites (Knell and Fortey 2005), ammonites record is contingent on the control of (Callomon 1963), mammals (Van Valkenburgh confounding sources of variation, including and Sacco 2002), and birds (Chinsamy et al. interspecific and individual differences, 2013; Handley et al. 2016), among others ontogeny, taphonomic processes and (Westermann 1969). However, recognizing diagenesis, geography, and pathology. sexual dimorphism in fossil organisms is However, with few exceptions, this is rarely replete with difficulties, owing to the limita- done, leading to spurious claims of sexual tions of a priori sexual identification and issues dimorphism. Examples of such claims may of ruling out confounding sources of morpho- include instances of vertebral fusion logical variation. What follows is an investiga- (Rothschild and Berman 1991; Rinehart et al. tion into some of the common approaches used 2009) and variation in vertebral count (Galton to identify sexual dimorphism in the fossil 1999), both of which are known to vary record, using nonavian dinosaurs (hereafter, individually in modern taxa (Danforth 1930; simply “dinosaurs”) as a study model. Dating Asher et al. 2011; VanBuren and Evans in back to the early considerations of Nopcsa press). Claims of sexual dimorphism in (1929), dinosaurs have featured prominently in ceratopsids (Sternberg 1927; Lehman 1990) discussions about sexual dimorphism in the and hadrosaurids (Nopsca 1929; Dodson fossil record (Chapman et al. 1997; Isles 1975; Hopson 1975; Weishampel 1981) have 2009; Dodson 2011; Table 1) and serve to been shown to be untenable due to the highlight the methodological shortcomings stratigraphic isolation of the dimorphs, underpinning many common approaches. suggesting species differences instead (Ryan These issues are briefly discussed in the and Evans 2005; Evans 2007; Mallon and following sections, before a more rigorous Holmes 2006). Ontogeny is particularly approach is presented. This approach reveals important to consider, because individuals just how difficult it can be to detect sexual can continue to gain mass even after having dimorphism in the fossil record, and highlights reached skeletal maturity, conceivably the need for more integrative approaches resulting in size dimorphism (Padian and going forward. Horner 2013). Many studies account for Issues of Sample Size.—Sample size matters ontogeny using a superficial age proxy (e.g., when attempting to positively identify sexual body size, osteological fusion, bone surface dimorphism in a fossil species (Rozhdestvensky texture), but none of these proxies are foolproof 1965; Plavcan 1994; Kościński and Pietraszewski (Hone et al. 2016a). No study of sexual 2004). Some purported examples of sexual dimorphism in dinosaurs to date has dimorphism in fossil taxa have relied on incorporated skeletochronological age sample sizes of just two (e.g., Sternberg 1927; determination; those studies that have Carpenter et al. 2011; Persons et al. 2015). determined the skeletochronological age of However, given that no two individuals are specimens (e.g, Horner and Padian 2004; exactly alike, it is a truism that two individuals Klein and Sander 2007; Woodward et al. 2015) will be dimorphic. Many more alleged have not identified gross skeletal features that examples of sexual dimorphism are based on would help to establish the sex to which the sample sizes of less than 10 (e.g., Gingerich specimens belonged. 1981; Deng 2005; Sanchez et al. 2010; Lü et al. Issues of Methodology.—A problem common 2011; Table 1), which is insufficient for statistical to many quantitative studies of fossil taxa is purposes (Kościński and Pietraszewski 2004). that they inherently assume dimorphism rather To validate the dimorphism hypothesis, a than test for it. This is true of some of the most sample must be composed of multiple common and widely advocated methods used specimens that consistently express the for detecting sexual dimorphism in

Downloaded from https:/www.cambridge.org/core. IP address: 97.115.205.50, on 30 Mar 2017 at 01:45:35, subject to the Cambridge Core terms of use, available at https:/www.cambridge.org/core/terms. https://doi.org/10.1017/pab.2016.51 at Downloaded from https:/www.cambridge.org/core/terms

TABLE 1. Purported examples of sexual dimorphism in the fossil record of Dinosauria. Asterisk (*) denotes study formally reevaluated here. Abbreviations: ANOVA, analysis of variance; MANOVA, multivariate analysis of variance; PCA, principal components analysis; PCO, principal coordinates analysis; RMA, reduced major axis regression.

https:/www.cambridge.org/core Discrete or continuous Parent taxon Species Purported dimorphic character(s) character(s)? n Methods Reference Coelophysidae Coelophysis bauri Skull length, neck length, forelimb length, Continuous, discrete None Colbert (1989, 1990) fusion of sacral neural spines Skull length, neck length, fusion of sacral Continuous, discrete 122 Regression analysis, Rinehart et al. (2009)* vertebrae 4 + 5, femur head width analysis of variance C. (‘Syntarsus’) Femoral lesser trochanter shape Continuous >30 Bivariate plots Raath (1990)* rhodesiensis . https://doi.org/10.1017/pab.2016.51 C. (‘Syntarsus’) Skeletal robustness, muscle attachment size Continuous 17 None Rowe (1989) kayentakatae Allosauridae Allosaurus fragilis Jaw shape, tooth count Continuous 37–45 None Thulborn (1994) . IPaddress: Size of dentary, femur, pedal phalanx I-1 Continuous 35-54 PCA, histograms, Smith (1998)* Shapiro-Wilk test Tyrannosauridae Aublysodon mirandus Premaxillary tooth shape Discrete Unspecified None Currie et al. (1990) Tyrannosaurus rex Skeletal robustness, ischium orientation Continuous 2, 3 None Carpenter (1990a) fi fi

97.115.205.50 Position and shape of rst chevron Continuous Unspeci ed None Larson (1994, 1997) Skeletal robustness Continuous 30 Bivariate plots Larson (1994, 1997, 2008*) T. rex, Tarbosaurus bataar Humeral curvature Continuous 2 (Tyrannosaurus), None Carpenter and Smith (2001) 2(Tarbosaurus) Caenagnathidae Chirostenotes pergracilis Pes robustness Continuous 3 None Currie and Russell (1988)

, on Oviraptoridae Khaan mckennai Proximal hemal spine shape Continuous 2 None Persons et al. (2015) Troodontidae Saurornithoides sp. Skeletal robustness, first chevron shape and Continuous Unspecified None Larson (1994) 30 Mar2017 at01:45:35 position Sauropodomorpha Sellosaurus gracilis Sacral count (2 vs. 3) Discrete 9 None Galton (1999) Plateosaurus sp. Distal femoral breadth, fourth trochanter width Continuous 22 PCA, RMA Weishampel and Chapman (1990)*; Galton (1997) Massospondylus carinatus Dorsal orbital rim thickening, maxillary depth Continuous 8 None Gow et al. (1990) Melanosaurus readi Skeletal robustness Continuous 2 None Galton (1997) Thecodontosaurus antiquus Skeletal robustness Continuous Unspecified None Galton (1997); Benton et al. (2000)

, subjectto theCambridgeCore termsofuse,available Neosauropoda Apatosaurus sp., Diplodocus Caudal vertebrae fusion Discrete 4 (Apatosaurus), None Rothschild and Berman sp., Camarasaurus sp. 6(Diplodocus), (1991) 8(Camarasaurus) Macronaria Camarasaurus spp. Body size Continuous 16 Histological staging, Klein and Sander (2008) bivariate plot Diplodocidae Tornieria africana Growth rate Continuous 15 Histological staging, Sander (2000) bivariate plot Heterodontosauridae Abrictosaurus consors Tusk presence/absence Discontinuous Unspeciﬁed None Thulborn (1974) Stegosauria Kentrosaurus aethiopicus, Sacral rib count Discrete Unspeciﬁed None Galton (1982a,b, 1991); Dacentrurus armatus, Galton and Upchurch Chungkingosaurus (2004) jiangheiensis, Stegosaurus stenops Lexovisaurus durobrivensis Shoulder plate size Continuous 2 None Galton (1985, 1990) Stegosauridae Stegosaurus mjosi Dorsal plate shape Continuous 40 PCA Saitta (2015)* Kentrosaurus aethiopicus Proximal femur shape Continuous 49 PCA, MANOVA, Barden and Maidment k-means cluster (2011)* analysis at Downloaded from https:/www.cambridge.org/core/terms

TABLE 1. Continued

Discrete or continuous https:/www.cambridge.org/core Parent taxon Species Purported dimorphic character(s) character(s)? n Methods Reference Ankylosauridae Euoplocephalus tutus Occipital condyle, squamosal horn size, Continuous, discrete 17 PCA Penkalski (2001) cervical half-ring scute count Saichania chulsanensis Humeral robustness Continuous 2 None Carpenter et al. (2011) Nodosauridae Edmontonia rugosidens Spine size/bifurcation Continuous, discrete 3 None Carpenter (1990b) Panoplosaurus mirus Muzzle length Continuous 3 None Carpenter (1990b) Edmontonia sp. Cranial proportions, cranial vault inﬂation, Continuous 4 None Gangloff (1995)

. cranial dermal plate patterns https://doi.org/10.1017/pab.2016.51 Pachycephalosauridae Stegoceras validum Dome curvature, dome smoothness Continuous 17 None Brown and Schlaikjer (1943) Dome size relative to braincase Continuous 29 PCA, RMA Chapman et al. (1981)* . IPaddress: Protoceratopsidae Protoceratops andrewsi Frill width, frontoparietal fossa size, facial Continuous >70 None Gregory and Mook (1925); depth, nasal height Brown and Schlaikjer (1940) Frill erection and expansion angle, orbit angle Continuous Unspeciﬁed Kurzanov (1972)

97.115.205.50 Postorbital width, frill height and width, Continuous 24 RMA, PCO Dodson (1976)* nasal height Handa et al. (2012) P. hellenikorhinus Postorbital width, frill height and width, Continuous 5 None Lambert et al. (2001) nasal height

, on Various Vertebral morphology, ilium curvature, Continuous 18 None Tereshchenko (2001) ischium curvature 30 Mar2017 at01:45:35 Chasmosaurinae Chasmosaurus belli Skeletal robustness Continuous 2 None Sternberg (1927) Triceratops horridus Postorbital horn stoutness Continuous 10 Regression Farlow (1990) Various Postorbital horncore orientation Continuous Unspecified None Lehman (1990) Centrosaurinae Pachyrhinosaurus lakustai Nasal boss concavity, midline parietal spike Continuous, discrete Unspecified None Currie et al. (2008) Centrosaurus apertus, Skull size, robustness, horn development Continuous, discrete Unspecified None Dodson (1990) Monoclonius crassus, Styracosaurus albertensis

, subjectto theCambridgeCore termsofuse,available Hadrosauriformes Various Skull proportions, crest development, neural Continuous, discrete Unspecified None Nopsca (1929) spine length, antebrachial length, sacral count, distal ischium shape Iguanodon bernissartensis Skeletal robustness Continuous Unspecified None Carpenter (1999) Lambeosaurinae Various Crest shape Continuous Unspecified None Hopson (1975); Weisham- pel (1981) Various Crest shape Continuous 36 RMA, PCO Dodson (1975) SEXUAL DIMORPHISM IN DINOSAURS 5

anthropology (e.g., means method, coefficient nonsexual sources of dimorphism (see earlier of variation method, assigned resampling section “Issues of Control”). method) (Plavcan 1994), where dimorphism is Institutional Abbreviations.—DMNS, Denver presupposed on grounds of phylogenetic Museum of Nature and Science, Denver, inference (Bryant and Russell 1992; Witmer Colorado, U.S.A.; NHMUK, Natural History 1995) and the degree to which it is manifested Museum, London, United Kingdom; USNM, is quantified. Although these methods are not Smithsonian Institution National Museum of often used outside anthropology, a comparable Natural History, Washington, D.C., U.S.A. approach has regularly been adopted within vertebrate paleontology (e.g., Dodson 1976; Cheng et al. 2009; Barden and Maidment 2011): Materials and Methods (1) plot the morphometric data in a histogram or a bivariate space (e.g., log-log or ordination Data.—Of the many studies that posit sexual plots); (2) visually inspect the data for evidence dimorphism in dinosaurs, only a handful of bimodal clustering (possibly with the aid of provide the data necessary to rigorously test cluster analysis); (3) if clustering is observed, this hypothesis (Table 1). These data form the subject the clusters to some statistical test (e.g., basis of the present analysis. The nine surveyed t-test, Mann-Whitney U-test, multivariate species correspond to various parts of the analysis of variance [MANOVA]) to confirm dinosaur phylogenetic tree, including theropods their disparity; (4) if significance is achieved, (Coelophysis bauri, C. rhodesiensis, Allosaurus conclude dimorphism. However, this fragilis, Tyrannosaurus rex), sauropodomorphs approach is inappropriate as a test of the (Plateosaurus sp.), stegosaurs (Stegosaurus mjosi, dimorphism hypothesis because even two Kentrosaurus aethiopicus), pachycephalosaurs arbitrary samples drawn from either tail of a (Stegoceras validum), and ceratopsians unimodal distribution can differ significantly (Protoceratops andrewsi). The data are derived (Fig. 1). What is needed, then, is to show that from both linear measurements and geometric the population is best modeled by a bimodal morphometrics and relate primarily to the skull distribution, for which mixture modeling is and appendicular skeleton. most suitable (Godfrey et al. 1993; Josephson Approach.—All of the aforementioned studies et al. 1996; Dong 1997). Of course, even if the include large compilations of linear sample is demonstrably dimorphic, there measurements or landmark data; however, the remains further testing to do to rule out hypothesized examples of sexual dimorphism are usually based on a subset of these data, such as particular linear variables or ordination scores. When testing these previous hypotheses, it is not enough to simply consider the same specific subset of data treated by the original study, because a failure to support its findings would only demonstrate that sexual dimorphism does not exist as posited by that study. The total data set must also be assessed more generally, should a truly dimorphic signal have gone unrecognized. Therefore, the published data were assessed in both the specific and general senses to more adequately test the hypothesis of sexual dimorphism. The data were generally log-transformed prior to testing, unless the purported FIGURE 1. Samples drawn from either side of an dimorphic signal specifically stemmed from arbitrarily divided (dashed line) unimodal distribution fi (n = 1000) can still differ significantly, as demonstrated untransformed data, in which case the bene tof here using a t-test. the doubt was granted, and the untransformed

data set was used. In cases involving bivariate evidence for dimorphism (sexual or otherwise) data, the residuals of reduced major axis in any of the nine species examined (Fig. 2). regression were used. In the general test cases, Several species (Plateosaurus sp., Stegoceras missing data were imputed using Bayesian validum, Pr. andrewsi, A. fragilis, Stegosaurus principal components analysis (PCA), which mjosi) are characterized by nonnormal functions well with morphological data (Brown distributions that are nevertheless unimodal. et al. 2012). The imputed data set was then More specific details for each species are subjected to PCA to facilitate study via reduced provided in Supplementary File 1, and the dimensionality. PCA of the variance– raw data are given in Supplementary File 2. covariance matrix was used when the variables General Tests.—Most of the surveyed taxa are were of the same unit; PCA of the correlation demonstrably nonnormal in at least one matrix was used when the units differed principal component (PC), but few pass (Hammer and Harper 2001). Only those princi- Hartigan’s dip test for unimodality (Fig. 2). pal components accounting for ≥5% of the total These results echo those recovered previously variance were subjected to statistical testing. for Pr. andrewsi (Maiorino et al. 2015) and Although all specimens were included in the Stegoceras validum (Goodwin 1990; Schott et al. regression and ordination calculations, imma- 2011). The Coelophysis bauri data set of Rinehart ture specimens (if identified a priori) were et al. (2009) is too incomplete to facilitate excluded from subsequent tests under the pre- general multivariate analysis. In A. fragilis, mise that sexual dimorphism was most likely to only dentary size (approximated by be expressed among mature individuals. PC 1, which is characteristically loaded A workflow was designed to test the sexual positively and subequally by all linear dimorphism hypothesis in sequential, com- variables) is demonstrably nonunimodal. plementary steps. First, the variable of interest Mixture modeling reveals that the population was tested for normality using the commonly is best modeled by three normally distributed employed Shapiro-Wilk (Shapiro and Wilk groups (AIC = 18.2), not two. This finding is 1965) and Anderson-Darling (Anderson and consistent with various interpretations, Darling 1952) tests. If nonnormality could not including a population consisting of three be rejected, the variable was then subjected to cohorts or one consisting of nonadults and Hartigan’s dip test for unimodality (Hartigan sexually dimorphic adults; these competing and Hartigan 1985). Dip-test p-values were hypotheses are presently underdetermined by computed using 10,000 Monte Carlo replicates. the available data. Notably, other studies of Failing rejection of unimodality, the number of variation in A. fragilis have failed to find normal distributions that best fit the data was evidence for sexual dimorphism (Loewen determined using mixture analysis paired with 2009; Carpenter 2010). the Akaike information criterion (AIC; Akaike Scrutiny of Saitta’s (2015) original PC scores 1973) for model selection. for Stegosaurus mjosi plate shape reveals that Missing value imputation was performed in only PC 2 is nonnormally distributed. This axis R, Version 3.1.2 (R Core Team 2014) using the is loaded most heavily by plate inclination. ‘pcaMethods’ package (Stacklies et al. 2007). Mixture analysis shows that the distribution of The normality and unimodality tests were PC 2 is best modeled by two normal curves conducted in R, Version 3.1.2 using the (AIC = −5.85) of highly disparate standard ‘nortest’ (Gross and Ligges 2015) and ‘diptest’ deviation (0.011 vs. 0.889) and group numbers packages (Maechler 2015), respectively. All (~3:1 ratio) (Fig. 3). These findings support the other analyses were run with PAST, Version hypothesis of dimorphism in the dermal plates 2.17b (Hammer et al. 2001). of Stegosaurus mjosi, but there is little reason to think that this dimorphism is sexual in nature. Results Rather, as shown by Saitta (2015: Supplemental Fig. S6), plate inclination shifts abruptly pos- Specific Tests.—Formal testing of those teriorly between plates 8 and 9 in Stegosaurus specific cases of sexual dimorphism reveals no stenops (Fig. 3), making this within-individual

FIGURE 2. Summary of results. Check mark (✓) indicates passed test (i.e., significantly nonnormal or nonunimodal distribution of morphometric data), X indicates failed test (i.e., not significantly nonnormal or nonunimodal distribution of morphometric data), question mark (?) indicates inability to perform test due to missing morphometric data. Numbers correspond to the number of normal distributions (i.e., groups) that best fit the data (using the Akaike information criterion). Silhouette credits: A. Farke (Protoceratops, Stegosaurus), S. Hartman (Allosaurus, Plateosaurus, Stegoceras, Tyrannosaurus), E. Willoughby (Coelophysis, Kentrosaurus).

variation the most probable source of the subject to type II error, but this is preferable to dimorphism in the Stegosaurus mjosi sample. attributing sexual dimorphism to every per- ceived instance of intraspecific variation in the fossil record, particularly if there is no compel- Discussion ling reason to think it should exist in the first place. Kościński and Pietraszewski (2004) docu- Although there is no support for sexual mented seven methods for measuring sexual dimorphism in any of the taxa examined here, dimorphism in the fossil record; however, it is fallacious to conclude that dinosaurs were many of these methods beg the question in therefore not sexually dimorphic. In fact, there favor of sexual dimorphism by working may be good reason to suspect they were, under the premise that it exists. Only mixture given the evidence for sexual dimorphism in modeling methods are free from this assump- crocodylians (Webb and Messel 1978; Allsteadt tion and should be used to study sexual and Lang 1995; Prieto-Marquez et al. 2007; dimorphism in the fossil record (unless there Platt et al. 2009) and birds (e.g., Darwin 1871; is sufficient warrant from phylogenetic Ward 1965; Livezey and Humphrey 1984; inference that sexual dimorphism should be Goymann et al. 2015), the closest living present). The use of model selection criteria, relatives of dinosaurs (Bryant and Russell such as the AIC used here, provides a statistical 1992; Witmer 1995). It is only true that sexual means to test the sexual dimorphism dimorphism has not yet been unambiguously hypothesis. Such a conservative approach is demonstrated in dinosaurs or in many other

FIGURE 3. Relationship between plate number and plate angle in Stegosaurus. If the data set of Saitta (2015) is truly dimorphic, this dimorphism likely represents within-individual variation, as plate angle shifts abruptly between plates 8 and 9 (indicated by arrow) in articulated specimens (NHMUK PV R36730, DMNS 2818, and USNM 4934). Solid gray line indicates kernel density estimate. Modiﬁed from Saitta (2015: Supplemental Fig. S6). Silhouette credit: A. Farke.

fossil vertebrates. Such a signal, if it exists, is priori knowledge of sex, the ability to detect undoubtedly masked by the obfuscating dimorphism in a fossil sample is likely only in effects of time-averaging, preservational cases of strongly expressed dimorphism (i.e., biases, diagenetic processes, and small sample well-separated peaks on a histogram or dis- sizes. Bonnan et al. (2008) demonstrated that crete character states); weakly expressed ontogeny and individual variation likewise dimorphism, where the sexes overlap consid- mask sexual dimorphism in the femur erably in morphospace, may be impossible to shape of Alligator mississippiensis (American discriminate in the fossil record (Kościński and alligator). Pietraszewski 2004). Mathematical modeling This raises the question: To what extent can by Godfrey et al. (1993) showed that sexual we expect to be able to identify sexual mean differences as great as 28% may not dimorphism in the fossil record, without the manifest as bimodality for sample sizes as beneﬁt of prior sexual determination? To large as 100. The situation is much worse address this question, mixture modeling was for small sample sizes (~10), in which sexual applied to a data set of A. mississippiensis pelvic mean differences of up to 47% may not be measurements (Prieto-Marquez et al. 2007) and detectable. Similar results were reported by Centropus superciliosus (white-browed coucal Plavcan (1994) using Cercopithecus (guenon) bird) body mass measurements (Goymann canine dimensions. et al. 2015), ignoring sex as a discriminant The ability to morphologically discriminate factor. Although these species are known to be the sexes is greatly enhanced if they are known sexually dimorphic with respect to these a priori. Unambiguous indicators of sex are characters, such dimorphism is undetectable known for various fossil groups by way of eggs using mixture modeling (Fig. 4), particularly in or embryos preserved within the body cavities the case of C. superciliosus, for which the of females (e.g., O’Harra 1930; Caldwell and histogram exhibits only a single obvious peak. Lee 2001; Cheng et al. 2004; Sato et al. 2005; It therefore follows that, in the absence of a Zelenitsky et al. 2008). However, such rare

FIGURE 4. Histograms depicting sexually dimorphic traits in (A) Alligator mississippiensis (data from Prieto-Marquez et al. 2007) and (B) Centropus superciliosus (data from Goymann et al. 2015). Although the ratio of pelvic canal depth: width is sexually dimorphic in A. mississippiensis, this dimorphism is difﬁcult to demonstrate if the sexes are not known a priori. The same is true of body mass distribution in C. superciliosus. Gray line indicates kernel density estimate of the entire distribution. Abbreviations: A-D, Anderson-Darling test; S-W, Shapiro-Wilk test.

finds are almost entirely dependent on chance. remains problematic. With a large enough Sex has recently become possible to determine sample size, it is conceivable that morphologies through histological and biochemical techni- consistently associated with gravid females ques. Schweitzer et al. (2005) reported on the might enable the development of a “search presence of medullary bone in the femur of image” that can then be used to separate the T. rex. Such endosteal tissue consists of vascu- remaining nongravid females from the males. larized, nonstructural woven bone and is known to occur definitively only in gravid Acknowledgments female birds (Schweitzer et al. 2007, 2016). It is likely used as a source of calcium during egg I thank N. Alfonso, B. Borkovic, N. production (Bonucci and Gherardi 1975). Campione, T. Cullen, P. Dodson, B. Hedrick, Schweitzer et al. (2016) have further cemented R. Holmes, P. Larson, K. Padian, and A. Russell the identification of this specialized tissue for valuable discussion. D. Hone commented in T. rex using molecular fingerprinting, on an early version of the paper. Thanks to all assuaging concerns that it may be pathological authors cited herein for making their data in origin (Chinsamy and Tumarkin-Deratzian available through either publication or perso- 2009). Examples of medullary bone have nal request. S. Rufolo painstakingly converted since been found in other dinosaurs (Lee published data into a usable format. D. Fraser and Werning 2008; Hübner 2012; Chinsamy helped with troubleshooting in R. Helpful et al. 2013). comments were provided by P. Barrett and A priori knowledge of sex facilitates the use two anonymous reviewers, and C. Badgley of more powerful analyses for detecting sexual offered valuable editorial assistance. Dinosaur dimorphism, such as discriminant function silhouettes were sourced from phylopic.org. analysis, and this combined approach may be This research was supported by funding from the way forward. Yet it is not without complica- the Canadian Museum of Nature. tion. The absence of eggs, embryos, or medullary bone in a fossil vertebrate is not positive Literature Cited evidence against its being female; only positive Akaike, H. 1973. Information theory and an extension of the maximum likelihood principle. Pp. 267–281 in B. N. Petrov, evidence against its being gravid. As such, and F. Csáki, eds. Proceedings of the Second International Sym- discriminating males from nongravid females posium on Information Theory. Akadémiai Kiadó, Budapest.

Allsteadt, J., and J. W. Lang. 1995. Sexual dimorphism in the genital K. Carpenter, eds. Mesozoic vertebrate life. Indiana University morphology of young American alligators, Alligator mis- Press, Bloomington. sissippiensis. Herpetologica 51:314–325. Carpenter, K., S. Hayashi, Y. Kobayashi, T. Maryańska, R. Barsbold, Anderson, T. W., and D. A. Darling. 1952. Asymptotic theory of K. Sato, and I. Obata. 2011. Saichania chulsanensis (Ornithischia, certain “goodness-of-fit” criteria based on stochastic processes. Ankylosauridae) from the Upper Cretaceous of Mongolia. Annals of Mathematical Statistics 23:193–212. Palaeontographica Abteilung A 294:1–61. Andersson, M. 1994. Sexual selection. Princeton University Press, Chapman, R. E., P. M. Galton, J. J. Sepkoski, Jr., and W. P. Wall. Princeton, N.J. 1981. A morphometric study of the cranium of the Asher, R. J., K. H. Lin, N. Kardjilov, and L. Hautier. 2011. Varia- pachycephalosaurid dinosaur Stegoceras. Journal of Paleontology bility and constraint in the mammalian vertebral column. Journal 55:608–618. of Evolutionary Biology 24:1080–1090. Chapman, R. E., D. B. Weishampel, G. Hunt, and D. Raskin- Barden, H. E., and S. C. R. Maidment. 2011. Evidence for sexual Gutman. 1997. Sexual dimorphism in dinosaurs. Pp. 83–93 dimorphism in the stegosaurian dinosaur Kentrosaurus aethiopi- in D. L. Wolberg, E. Stump, and G. D. Rosenberg, eds. Dinofest cus from the Upper Jurassic of Tanzania. Journal of Vertebrate International: Proceedings of a Symposium Sponsored by Ari- Paleontology 31:641–651. zona State University. Academy of Natural Sciences, Benton, M. J., L. Juul, G. W. Storrs, and P. M. Galton. 2000. Philadelphia. Anatomy and systematics of the prosauropod dinosaur Cheng, Y.-N., X.-C. Wu, and Q. Ji. 2004. Triassic marine reptiles Thecodontosaurus antiquus from the Upper Triassic of gave birth to live young. Nature 432:383–386. southwest England. Journal of Vertebrate Paleontology 20: Cheng, Y.-N., R. Holmes, X.-C. Wu, and N. Alfonso. 2009. Sexual 77–108. dimorphism and life history of Keichousaurus hui (Reptilia: Saur- Bonnan, M. F., J. O. Farlow, and S. L. Masters. 2008. Using linear opterygia). Journal of Vertebrate Paleontology 29:401–408. and geometric morphometrics to detect intraspecific variability Chinsamy, A., and A. Tumarkin‐Deratzian. 2009. Pathologic bone and sexual dimorphism in femoral shape in Alligator mis- tissues in a turkey vulture and a nonavian dinosaur: implications sissippiensis and its implications for sexing fossil archosaurs. for interpreting endosteal bone and radial fibrolamellar bone in Journal of Vertebrate Paleontology 28:422–431. fossil dinosaurs. Anatomical Record 292:1478–1484. Bonucci, E., and G. Gherardi. 1975. Histochemical and electron Chinsamy, A., L. M. Chiappe, J. Marugán-Lobón, G. Chunling, and microscope investigations on medullary bone. Cell and Tissue Z. Fengjiao. 2013. Gender identification of the Mesozoic bird Research 163:81–97. Confuciusornis sanctus. Nature Communications 4:1381. Borkovic, B., and A. Russell. 2014. Sexual selection according to Colbert, E. H. 1989. The Triassic dinosaur Coelophysis. Museum of Darwin: a response to Padian and Horner’s interpretation. Northern Arizona Bulletin 57:1–160. Comptes Rendus Palevol 13:701–707. ——. 1990. Variation in Coelophysis bauri. Pp. 81–90 in Carpenter Brown, B., and E. M. Schlaikjer. 1940. The structure and relation- and Currie 1990. ships of Protoceratops. Annals of the New York Academy of Sci- Cunningham, J. T. 1900. Sexual dimorphism in the animal king- ences 40:133–265. dom: a theory of the evolution of secondary sexual characters. ——. 1943. A study of the troodont dinosaurs with the description Adam and Charles Black, London. of a new genus and four new species. American Museum of Currie, P. J., and D. A. Russell. 1988. Osteology and relationships of Natural History Bulletin 82:121–149. Chirostenotes pergracilis (Saurischia, Theropoda) from the Judith Brown, C. M., J. H. Arbour, and D. A. Jackson. 2012. Testing of River (Oldman) Formation of Alberta, Canada. Canadian Journal the effect of missing data estimation and distribution in mor- of Earth Sciences 25:972–986. phometric multivariate data analyses. Systematic Biology Currie, P. J., J. K. Rigby, Jr., and R. E. Sloan. 1990. Theropod teeth 61:941–954. from the Judith River Formation of southern Alberta, Canada. Bryant, H. N., and A. P. Russell. 1992. The role of phylogenetic Pp. 107–125 in Carpenter and Currie 1990. analysis in the inference of unpreserved attributes of extinct taxa. Currie, P. J., W. Langston, Jr., and D. H. Tanke. 2008. A new species Philosophical Transactions of the Royal Society of London B of Pachyrhinosaurus (Dinosauria, Ceratopsidae) from the Upper 337:405–418. Cretaceous of Alberta, Canada. Pp. 1–108 in P. J. Currie, Caldwell, M. W., and M. S. Y. Lee. 2001. Live birth in Cretaceous W. Langston, Jr., and D. H. Tanke, eds. A new horned dinosaur marine lizards (mosasauroids). Proceedings of the Royal Society from an Upper Cretaceous bone bed in Alberta. NRC Research of London B 268:2397–2401. Press, Ottawa. Callomon, J. H. 1963. Sexual dimorphism in Jurassic ammonites. Danforth, C. H. 1930. Numerical variation and homologies in ver- Transactions of the Leicester Literary and Philosophical Society tebrae. American Journal of Physical Anthropology 14:463–481. 57:21–56. Darwin, C. 1871. The descent of man, and selection in relation to Carpenter, K. 1990a. Variation in Tyrannosaurus rex. Pp. 141–145 in sex. J. Murray, London. Carpenter and Currie 1990. Deng, T. 2005. New discovery of Iranotherium morgani (Perisso- ——. 1990b. Ankylosaur systematics: example using Panoplosaurus dactyla, Rhinocerotidae) from the late Miocene of the Linxia and Edmontonia (Ankylosauria: Nodosauridae). Pp. 281–298 in Basin in Gansu, China, and its sexual dimorphism. Journal of Carpenter and Currie 1990. Vertebrate Paleontology 25:442–450. ——. 1999. Eggs, nests, and baby dinosaurs: a look at dinosaur Dodson, P. 1975. Taxonomic implications of relative growth in reproduction. Indiana University Press, Bloomington. lambeosaurine hadrosaurs. Systematic Biology 24:37–54. ——. 2010. Variation in a population of Theropoda (Dinosauria): ——. 1976. Quantitative aspects of relative growth and sexual Allosaurus from the Cleveland-Lloyd Quarry (Upper Jurassic), dimorphism in Protoceratops. Journal of Paleontology 50:929–940. Utah, USA. Paleontological Research 14:250–259. ——. 1990. On the status of the ceratopsids Monoclonius and Carpenter, K., and P. J. Currie, eds. 1990. Dinosaur systematics: Centrosaurus. Pp. 231–243 in Carpenter and Currie 1990. approaches and perspectives. Cambridge University Press, ——. 2011. Sex in the Cretaceous—how to tell the girls from Cambridge. the boys. American Paleontologist 19(3):21–24. Carpenter, K., and M. Smith. 2001. Forelimb osteology and bio- Dong, Z. 1997. Mixture analysis and its preliminary application in mechanics of Tyrannosaurus rex. Pp. 90–116 in D. H. Tanke, and archaeology. Journal of Archaeological Science 24:141–161.

Evans, D. C. 2007. Ontogeny and evolution of lambeosaurine Handley, W. D., A. Chinsamy, A. M. Yates, and T. H. Worthy. 2016. dinosaurs (Ornithischia: Hadrosauridae). Unpublished Ph.D. Sexual dimorphism in the late Miocene mihirung Dromornis dissertation. University of Toronto, Toronto. stirtoni (Aves: Dromornithidae) from the Alcoota Local Fauna of Farlow, J. O. 1990. Review: dynamic dinosaurs. Paleobiology central Australia. Journal of Vertebrate Paleontology 36: 16:234–241. e1180298. doi: 10.1080/02724634.2016.1180298. Galton, P. M. 1982a. Juveniles of the stegosaurian dinosaur Stego- Hartigan, J. A., and P. M. Hartigan. 1985. The dip test of unim- saurus from the Upper Jurassic of North America. Journal of odality. Annals of Statistics 13:70–84. Vertebrate Paleontology 2:47–62. Hedrick, A. V., and E. J. Temeles. 1989. The evolution of sexual ——. 1982b. The postcranial anatomy of stegosaurian dinosaur dimorphism in animals: hypotheses and tests. Trends in Ecology Kentrosaurus from the upper Jurassic of Tanzania, East Africa. and Evolution 4:136–138. Geologica et Palaeontologica 15:139–160. Hone, D. W., D. Naish, and I. C. Cuthill. 2012. Does mutual sexual ——. 1985. British plated dinosaurs (Ornithischia, Stegosauridae). selection explain the evolution of head crests in pterosaurs and Journal of Vertebrate Paleontology 5:211–254. dinosaurs? Lethaia 45:139–156. ——. 1990. Stegosauria. Pp. 435–455 in D. B. Weishampel, Hone, D. W., A. A. Farke, and M. J. Wedel. 2016a. Ontogeny and the P. Dodson, and H. Osmólska, eds. The Dinosauria. University of fossil record: what, if anything, is an adult dinosaur? Biology California Press, Berkeley. Letters 12:20150947. doi: 10.1098/rsbl.2015.0947. ——. 1991. Postcranial remains of stegosaurian dinosaur Hone, D. W., D. Wood, and R. J. Knell. 2016b. Positive allometry for Dacentrurus armatus from upper Jurassic of France and Portugal. exaggerated structures in the ceratopsian dinosaur Protoceratops Geologica et Palaeontologica 25:299–327. andrewsi supports socio-sexual signaling. Palaeontologia Elec- ——. 1997. Comments on sexual dimorphism in the prosauropod tronica 19(1):1–13. dinosaur Plateosaurus engelhardti (Upper Triassic, Trossingen). Hopson, J. A. 1975. The evolution of cranial display structures in Neues Jahrbuch für Geologie und Paläontologie, Monatshefte hadrosaurian dinosaurs. Paleobiology 1:21–43. 1997:674–682. Horner, J. R., and K. Padian. 2004. Age and growth dynamics of ——. 1999. Sex, sacra and Sellosaurus gracilis (Saurischia, Saur- Tyrannosaurus rex. Proceedings of the Royal Society of London B opodomorpha, Upper Triassic, Germany)—or why the character 271:1875–1880. “two sacral vertebrae” is plesiomorphic for Dinosauria. Hübner, T. R. 2012. Bone histology in Dysalotosaurus lettowvorbecki Neues Jahrbuch fur Geologie und Palaontologie-Abhandlungen (Ornithischia: Iguanodontia)–variation, growth, and implica- 213:19–56. tions. PLoS ONE 7:e29958. doi: 10.1371/journal.pone.0029958. Galton, P. M., and P. Upchurch. 2004. Stegosauria. Pp. 343–362 in Isles, T. E. 2009. The socio-sexual behaviour of extant archosaurs: D. B. Weishampel, P. Dodson, and H. Osmólska, eds. The implications for understanding dinosaur behaviour. Historical Dinosauria, 2nd ed. University of California Press, Berkeley. Biology 21:139–214. Gangloff, R. A. 1995. Edmontonia sp., the ﬁrst record of an ankylo- Josephson, S. C., K. E. Juell, and A. R. Rogers. 1996. Estimating saur from Alaska. Journal of Vertebrate Paleontology 15:195–200. sexual dimorphism by method‐of‐moments. American Journal of Gingerich, P. 1981. Cranial morphology and adaptations in Eocene Physical Anthropology 100:191–206. Adapidae. 1. Sexual dimorphism in Adapis magnus and Klein, N., and P. M. Sander. 2007. Bone histology and growth of the Adapis parisiensis. American Journal of Physical Anthropology prosauropod dinosaur Plateosaurus engelhardti von Meyer, 1837 56:217–234. from the Norian bonebeds of Trossingen (Germany) and Frick Godfrey, L. R., S. K. Lyon, and M. R. Sutherland. 1993. Sexual (Switzerland). Special Papers in Palaeontology 77:169–206. dimorphism in large-bodied primates: the case of the ——. 2008. Ontogenetic stages in the long bone histology of saur- subfossil lemurs. American Journal of Physical Anthropology opod dinosaurs. Paleobiology 34:247–263. 90:315–334. Knell, R. J., and R. A. Fortey. 2005. Trilobite spines and beetle horns: Goodwin, W. B. 1990. Morphometric landmarks of pachycephalo- sexual selection in the Palaeozoic? Biology Letters 1:196–199. saurid cranial material from the Judith River Formation of Knell, R. J., and S. Sampson. 2011. Bizarre structures in dinosaurs: northcentral Montana. Pp. 189–201 in Carpenter and Currie 1990. species recognition or sexual selection? A response to Padian Gow, C. E., J. W. Kitching, and M. A. Raath. 1990. Skulls of the and Horner. Journal of Zoology 283:18–22. prosauropod dinosaur Massospondylus carinatus Owen in the Knell, R. J., D. Naish, J. L. Tomkins, and D. W. Hone. 2013a. Is collections of the Bernard Price Institute for Palaeontological sexual selection deﬁned by dimorphism alone? A reply to Padian Research. Palaeontologia africana 27:45–58. and Horner. Proceedings of the Zoological Society of London Goymann, W., M. Makomba, F. Urasa, and I. Schwabl. 2015. Social 35:491–562. monogamy vs. polyandry: ecological factors associated with sex ——. 2013b. Sexual selection in prehistoric animals: detection and roles in two closely related birds within the same habitat. Journal implications. Trends in Ecology and Evolution 28:38–47. of Evolutionary Biology 28:1335–1353. Kościński, K., and S. Pietraszewski. 2004. Methods to estimate Gregory, W. K., and C. C. Mook. 1925. On Protoceratops, a primitive sexual dimorphism from unsexed samples: a test with computer- ceratopsian dinosaur from the Lower Cretaceous of Mongolia. generated samples. Przegląd Antropologiczny—Anthro- American Museum Novitates 156:1–9. pological Review 67:33–55. Gross, J., and U. Ligges. 2015. nortest: tests for normality. R pack- Kurzanov, S. M. 1972. Sexual dimorphism in protoceratopsians. age, Version 1:0–4. Palaeontological Journal 1:91–97. Hammer, Ø., and D. A. Harper. 2001. Paleontological data analysis. Lambert, O., P. Godefroit, H. Li, C. Y. Shang, and Z.-M. Dong. 2001. Blackwell Publishing: Malden, Mass. A new species of Protoceratops (Dinosauria, Neoceratopsia) from Hammer, Ø., D. A. T. Harper, and P. D. Ryan. 2001. PAST: the Late Cretaceous of Inner Mongolia (PR China). Bulletin de Paleontological Statistics software package for education and l’Institut Royal des Sciences Naturelles de Belgique. Sciences de data analysis. Palaeontologia Electronica 4(1):1–9. http://palaeo- la Terre, Supplément 71:5–28. electronica.org/2001_1/past/issue1_01.htm. Larson, P. L. 1994. Tyrannosaurus sex. Paleontological Society Spe- Handa, N., M. Watabe, and K. Tsogtbaatar. 2012. New specimens cial Publication 7:139–155. of Protoceratops (Dinosauria: Neoceratopsia) from the Upper ——. 1997. The king’s new clothes: a fresh look at Tyrannosaurus Cretaceous in Udyn Sayr, southern Gobi area, Mongolia. rex. Pp. 65–71 in D. L. Wolberg, E. Stump, and G. D. Rosenberg, Paleontological Research 16:179–198. eds. Dinofest lnternational: Proceedings of a Symposium

Sponsored by Arizona State University. Academy of Natural extinct non-avian archosaurs. Journal of Vertebrate Paleontology Sciences, Philadelphia. 27:603–609. ——. 2008. Variation and sexual dimorphism in Tyrannosaurus rex. Raath, M. A. 1990. Morphological variation in small theropods and Pp. 103–128 in P. Larson, and K. Carpenter, eds. Tyrannosaurus its meaning in systematics: evidence from Syntarsus. rex: the tyrant king. Indiana University Press, Bloomington. Pp. 91–105 in Carpenter and Currie 1990. Lee, A. H., and S. Werning. 2008. Sexual maturity in Rinehart, L. F., S. G. Lucas, A. B. Heckert, J. A. Spielmann, and growing dinosaurs does not fit reptilian growth models. Pro- M. D. Celeskey. 2009. The paleobiology of Coelophysis bauri ceedings of the National Academy of Sciences of the USA (Cope) from the Upper Triassic (Apachean) Whitaker quarry, 105:582–587. New Mexico, with detailed analysis of a single quarry block. Lehman, T. M. 1990. The ceratopsian subfamily Chasmosaurinae: New Mexico Museum of Natural History and Science Bulletin sexual dimorphism and systematics. Pp. 211–229 in Carpenter 45:1–260. and Currie 1990. Rothschild, B. M., and D. S. Berman. 1991. Fusion of caudal ver- Livezey, B. C., and P. S. Humphrey. 1984. Sexual dimorphism in tebrae in Late Jurassic sauropods. Journal of Vertebrate Paleon- continental steamer-ducks. Condor 86:368–377. tology 11:29–36. Loewen, M. A. 2009. Variation in the late Jurassic theropod dino- Rowe, T. 1989. A new species of the theropod dinosaur Syntarsus saur Allosaurus: ontogenetic, functional, and taxonomic implica- from the Early Jurassic Kayenta Formation of Arizona. Journal of tions. Unpublished Ph.D. dissertation. University of Utah, Salt Vertebrate Paleontology 9:125–136. Lake City. Rozhdestvensky, A. K. 1965. Growth changes in Asian dinosaurs Lü, J., D. Unwin, D. C. Deeming, X. Jin, Y. Liu, and Q. Ji. 2011. An and some problems of their taxonomy. Paleontologičeskij Žurnal egg-adult association, gender and reproduction in pterosaurs. 3:95–109 [In Russian.] Science 331:321–324. R Core Team. 2014. R: a language and environment for statistical Maechler, M. 2015. diptest: Hartigan’s dip test statistic for unim- computing. R Foundation for Statistical Computing, Vienna. odality—corrected R Package. Version 0:75–77. https://www.R-project.org. Maiorino, L., A. A. Farke, T. Kotsakis, and P. Piras. 2015. Males Ryan, M. J., and D. C. Evans. 2005. Ornithischian dinosaurs. Pp. resemble females: re-evaluating sexual dimorphism in Proto- 312–348 in P. J. Currie, and E. B. Koppelhus, eds. Dinosaur Pro- ceratops andrewsi (Neoceratopsia, Protoceratopsidae). PLoS ONE vincial Park: a spectacular ancient ecosystem revealed. Indiana 10:e0126464. doi: 10.1371/journal.pone.0126464. University Press, Bloomington. Mallon, J. C., and R. B. Holmes. 2006. A reevaluation of sexual Saitta, E. T. 2015. Evidence for sexual dimorphism in the plated dimorphism in the postcranium of the chasmosaurine ceratopsid dinosaur Stegosaurus mjosi (Ornithischia, Stegosauria) from the Chasmosaurus belli (Dinosauria: Ornithischia). Canadian Field- Morrison Formation (Upper Jurassic) of western USA. PLoS ONE Naturalist 120:403–412. 10:e0123503. doi: 10.1371/journal.pone.0123503. Mendelson, T. C., and K. L. Shaw. 2013. Further misconceptions Sanchez, I., V. Quiralte, J. Morales, B. Azanza, and M. Pickford. about species recognition: a reply to Padian and Horner. Trends 2010. Sexual dimorphism of the frontal appendages of the early in Ecology and Evolution 28:252–253. Miocene African pecoran Prolibytherium Arambourg, 1961 Nopcsa, F.. 1929. Sexual differences in ornithopodous dinosaurs. (Mammalia, Ruminantia). Journal of Vertebrate Paleontology Palaeobiologica 2:187–201. 30:1306–1310. O’Harra, C. C. 1930. A fossil mammal with unborn twins. Science Sander, P. M. 2000. Long bone histology of the Tendaguru saur- 71:341–342. opods: implications for growth and biology. Paleobiology Padian, K., and J. R. Horner. 2011a. The evolution of “bizarre 26:466–488. structures” in dinosaurs: biomechanics, sexual selection, social Sato, T., Y.-N. Cheng, X.-C. Wu, D. K. Zelenitsky, and Y.-F. Hsiao. selection or species recognition? Journal of Zoology 283:3–17. 2005. A pair of shelled eggs inside a female dinosaur. Science ——. 2011b. The definition of sexual selection and its implications 308:375. for dinosaurian biology. Journal of Zoology 283:23–27. Schoener, T. W. 1967. The ecological significance of sexual ——. 2013. Misconceptions of sexual selection and species recog- dimorphism in size in the lizard Anolis conspersus. Science nition: a response to Knell et al. and to Mendelson and Shaw. 155:474–477. Trends in Ecology and Evolution 28:249–250. Schott, R. K., D. C. Evans, M. B. Goodwin, J. R. Horner, C. M. ——. 2014a. The species recognition hypothesis explains exag- Brown, and N. R. Longrich. 2011. Cranial ontogeny in gerated structures in non-avian dinosaurs better than sexual Stegoceras validum (Dinosauria: Pachycephalosauria): selection does. Comptes Rendus Palevol 13:97–107. a quantitative model of pachycephalosaur dome growth and ——. 2014b. Darwin’s sexual selection: understanding his ideas in variation. PLoS ONE 6:e21092. doi: 10.1371/journal.pone. context. Comptes Rendus Palevol 13:709–715. 0021092. Penkalski, P. 2001. Variation in specimens referred to Euoplocepha- Schweitzer, M. H., J. L. Wittmeyer, and J. R. Horner. 2005. Gender- lus tutus. Pp. 261–298 in K. Carpenter, ed. The armored dino- specific reproductive tissue in ratites and Tyrannosaurus rex. saurs. Indiana University Press, Bloomington. Science 308:1456–1460. Persons, W. S., IV, G. F. Funston, P. J. Currie, and M. A. Norell. Schweitzer, M. H., R. M. Elsey, C. G. Dacke, J. R. Horner, and 2015. A possible instance of sexual dimorphism in the tails of two E.-T. Lamm. 2007. Do egg-laying crocodilian (Alligator oviraptorosaur dinosaurs. Scientific Reports 5:9472. mississippiensis) archosaurs form medullary bone? Bone 40: Platt, S. G., T. R. Rainwater, J. B. Thorbjarnarson, A. G. Finger, T. A. 1152–1158. Anderson, and S. T. McMurry. 2009. Size estimation, morpho- Schweitzer, M. H., W. Zheng, L. Zanno, S. Werning, and metrics, sex ratio, sexual size dimorphism, and biomass of T. Sugiyama. 2016. Chemistry supports the identification of Morelet’s crocodile in northern Belize. Caribbean Journal of Sci- gender-specific reproductive tissue in Tyrannosaurus rex. ence 45:80–93. Scientific Reports 6:23099. Plavcan, J. M. 1994. Comparison of four simple methods for esti- Shapiro, S. S., and M. B. Wilk. 1965. An analysis of variance test for mating sexual dimorphism in fossils. American Journal of Phy- normality (complete samples). Biometrika 52:591–611. sical Anthropology 94:465–476. Shine, R. 1989. Ecological causes for the evolution of sexual Prieto-Marquez, A., P. M. Gignac, and S. Joshi. 2007. Neontological dimorphism: a review of the evidence. Quarterly Review of evaluation of pelvic skeletal attributes purported to reflect sex in Biology 64:419–461.

Smith, D. K. 1998. A morphometric analysis of Allosaurus. Journal Webb, G. J. W., and H. Messel. 1978. Morphometric analysis of of Vertebrate Paleontology 18:126–142. Crocodylus porosus from the north coast of Arnhem Land, north- Stacklies, W., H. Redestig, M. Scholz, D. Walther, and J. Selbig. ern Australia. Australian Journal of Zoology 26:1–27. 2007. pcaMethods—a bioconductor package providing PCA Weishampel, D. B. 1981. Acoustic analyses of potential vocalization methods for incomplete data. Bioinformatics 23:1164–1167. in lambeosaurine dinosaurs (Reptilia: Ornithischia). Paleobiol- Sternberg, C. M. 1927. Horned dinosaur group in the National ogy 7:252–261. – Museum of Canada. Canadian Field-Naturalist 41:67 73. Weishampel, D. B., and R. E. Chapman. 1990). Morphometric Tereshchenko, V. S. 2001. Sexual dimorphism in the postcranial study of Plateosaurus from Trossingen (Baden-Württemberg, skeleton of protoceratopsids (Neoceratopsia, Protoceratopsidae) Federal Republic of Germany). Pp. 43–51 in Carpenter and – from Mongolia. Paleontological Journal 35:415 425. Currie 1990. Thulborn, R. A. 1974. A new heterodontosaurid dinosaur (Reptilia: Westermann, G. E. G. ed. 1969. Sexual dimorphism in fossil Ornithischia) from the Upper Triassic Red Beds of Lesotho. Metazoa and taxonomic implications. E. Schweizerbart’sche Zoological Journal of the Linnean Society of London 55:151–175. Verlagsbuchhandlung, Stuttgart. ——. 1994. Dimorphic jaw bones in the theropod Allosaurus fragilis. Witmer, L. M. 1995. The extant phylogenetic bracket and the Association of Australian Palaeontologists, Sydney, Australasian importance of reconstructing soft tissues in fossils. Pp. 19–33 in Palaeontological Convention Abstracts and Programme 94:54. J. J. Thomason, ed. Functional morphology in vertebrate Tomkins, J. L., N. R. LeBas, M. P. Witton, D. M. Martill, and paleontology. Cambridge University Press, Cambridge. S. Humphries. 2010. Positive allometry and the prehistory of Woodward, H. N., E. A. Freedman Fowler, J. O. Farlow, and J. R. sexual selection. American Naturalist 176:141–148. Horner. 2015. Maiasaura, a model organism for extinct VanBuren, C. S., and D. C. Evans. In press. Evolution and function of anterior cervical vertebral fusion in tetrapods. Biological vertebrate population biology: a large sample statistical assess- Reviews. doi: 10.1111/brv.12245. ment of growth dynamics and survivorship. Paleobiology – Van Valkenburgh, B., and T. Sacco. 2002. Sexual dimorphism, social 41:503 527. behavior, and intrasexual competition in large Pleistocene car- Zelenitsky, D. K., F. Therrien, W. G. Joyce, and D. B. Brinkman. nivorans. Journal of Vertebrate Paleontology 22:164–169. 2008. First fossil gravid turtle provides insight into the Ward, P. 1965. Feeding ecology of the black‐faced dioch Quelea evolution of reproductive traits in turtles. Biology Letters quelea in Nigeria. Ibis 107:173–214. 4:715–718.