Beyond Gorilla and Pongo Alternative models for evaluating variation and sexual dimorphism in fossil hominoid samples.код для вставкиСкачать
AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 140:253–264 (2009) Beyond Gorilla and Pongo: Alternative Models for Evaluating Variation and Sexual Dimorphism in Fossil Hominoid Samples Jeremiah E. Scott,1* Caitlin M. Schrein,1 and Jay Kelley2 1 School of Human Evolution and Social Change, Institute of Human Origins, Arizona State University, Tempe, AZ 85287-4101 2 Department of Oral Biology, College of Dentistry, University of Illinois at Chicago, Chicago, IL 60612 KEY WORDS bootstrap; dental variation; Lufengpithecus; Ouranopithecus; Sivapithecus ABSTRACT Sexual size dimorphism in the postcanine dentition of the late Miocene hominoid Lufengpithecus lufengensis exceeds that in Pongo pygmaeus, demonstrating that the maximum degree of molar size dimorphism in apes is not represented among the extant Hominoidea. It has not been established, however, that the molars of Pongo are more dimorphic than those of any other living primate. In this study, we used resampling-based methods to compare molar dimorphism in Gorilla, Pongo, and Lufengpithecus to that in the papionin Mandrillus leucophaeus to test two hypotheses: (1) Pongo possesses the most size-dimorphic molars among living primates and (2) molar size dimorphism in Lufengpithecus is greater than that in the most dimorphic living primates. Our results show that M. leucophaeus exceeds great apes in its overall level of dimorphism and that L. lufengensis is more dimorphic than the extant spe- cies. Using these samples, we also evaluated molar dimorphism and taxonomic composition in two other Miocene ape samples—Ouranopithecus macedoniensis from Greece, specimens of which can be sexed based on associated canines and P3s, and the Sivapithecus sample from Haritalyangar, India. Ouranopithecus is more dimorphic than the extant taxa but is similar to Lufengpithecus, demonstrating that the level of molar dimorphism required for the Greek fossil sample under the single-species taxonomy is not unprecedented when the comparative framework is expanded to include extinct primates. In contrast, the Haritalyangar Sivapithecus sample, if it represents a single species, exhibits substantially greater molar dimorphism than does Lufengpithecus. Given these results, the taxonomic status of this sample remains equivocal. Am J Phys Anthropol 140:253–264, 2009. V 2009 Wiley-Liss, Inc. A frequently encountered problem in hominoid paleontology is identiﬁcation of the source of high levels of size variation in a fossil sample (e.g., Kay 1982a,b; Lieberman et al., 1988; Cope and Lacy, 1992; Albrecht and Miller, 1993; Kramer, 1993; Martin and Andrews, 1993; Richmond and Jungers, 1995; Lockwood et al., 1996, 2000; Plavcan and Cope, 2001; Silverman et al., 2001; Scott and Lockwood, 2004; Villmoare, 2005). While some sources are relatively easily identiﬁed and controlled (e.g., variation due to ontogeny or pathology), others present greater difﬁculty. For example, high variation in a single fossil sample can be interpreted as evidence of the presence of multiple species, changes in size over time, or marked sexual dimorphism, or some combination of these factors. Determining which of these alternatives is responsible for the pattern of variation in a given fossil assemblage is important because each has different implications regarding species diversity, modes of evolutionary change (i.e., anagenesis vs. cladogenesis), and social behavior. One perspective on fossil hominoid taxonomy speciﬁes that the degree of variation in extinct species should not be greater than that in Gorilla and Pongo, the most sexually dimorphic extant hominoids, which logically requires rejection of a single-species hypothesis in cases where a temporally and geographically restricted fossil sample is more variable than these great apes (e.g., Kay, 1982a,b; Lieberman et al., 1988; Martin and Andrews et al., 1993; Teaford et al., 1993; Walker et al., 1993; see also Cope and Lacy, 1992; Cope, 1993; Plavcan, 1993). However, adopting a multiple-species taxonomy for a fossil sample solely on the basis of excessive size variation relative to Gorilla and Pongo is problematic for two reasons. First, it is not clear that the upper limit of intraspeciﬁc variation in extant primates is represented by these taxa. Among living primates, Gorilla and Pongo are exceeded in body-mass dimorphism (and presumably intraspeciﬁc variation in body mass) by the African papionin Mandrillus sphinx (Jungers and Smith, 1997; Setchell et al., 2001). Although it has not been established whether this difference is reﬂected in aspects of skeletal or dental size variation and dimorphism, data from other papionins, particularly Papio, indicate that at least some of the members of this clade may be more skeletally and dentally dimorphic than the great apes (e.g., Wood, 1976; Uchida, 1996a,b; Plavcan, 2002, 2003). Second, the upper limit of intraspeciﬁc variation may not be represented by any extant primate. Among fossil primates, the hominoid sample from the late Miocene C 2009 V WILEY-LISS, INC. C *Correspondence to: Jeremiah E. Scott, School of Human Evolution and Social Change, Institute of Human Origins, Arizona State University, Tempe, AZ 85287-4101, USA. E-mail: firstname.lastname@example.org Received 3 July 2008; accepted 28 January 2009 DOI 10.1002/ajpa.21059 Published online 8 April 2009 in Wiley InterScience (www.interscience.wiley.com). 254 J.E. SCOTT ET AL. site of Lufeng, China, represents a single species— Lufengpithecus lufengensis—that exceeds Gorilla and Pongo in its degree of postcanine sexual dimorphism (Kelley and Xu, 1991; Kelley, 1993; Kelley and Plavcan, 1998). Establishing that the Lufeng sample represents a single highly dimorphic species was made possible by two key characteristics of the assemblage: the sample is large, comprising hundreds of teeth (e.g., Kelley and Etler, 1989; Wood and Xu, 1991), and a number of postcanine dentitions have been conﬁdently sexed using associated canines and P3s (e.g., Kelley and Xu, 1991; Kelley, 1993; Kelley, 1995a,b). Using the sexed specimens (n 16 for each molar position), Kelley and colleagues (Kelley and Xu, 1991; Kelley, 1993; Kelley and Plavcan, 1998) demonstrated that molar dimorphism in L. lufengensis is so high that there is no overlap between male and female individuals in bivariate plots of mesiodistal and buccolingual dimensions. Several researchers have argued that the Lufeng sample contains multiple species (e.g., Wu and Oxnard, 1983a,b; Martin, 1991; Cope and Lacy, 1992; Plavcan, 1993), but a mixture of two or more species is unlikely to have produced the pattern of variation observed in the sample, unless one appeals to highly improbable sampling events (Kelley and Plavcan, 1998). Thus, L. lufengensis extends the known range of intraspeciﬁc size variation and sexual dimorphism in the Hominoidea, at least with respect to the postcanine dentition. Despite initial objections based on both ontological and epistemological grounds (e.g., Ruff et al., 1989; Martin, 1991; Cope and Lacy, 1992; Martin and Andrews, 1993; Plavcan, 1993; Teaford et al., 1993; Walker et al., 1993), the idea that some fossil hominoid species were more dimorphic than living great apes has gained wider acceptance, and many researchers now acknowledge extreme dimorphism as a potential source of high measures of variation that must be considered when evaluating fossil samples (e.g., Plavcan, 2001; Plavcan and Cope, 2001; Scott and Lockwood, 2004; Schrein, 2006; Skinner et al., 2006; Simons et al., 2007; Humphrey and Andrews, 2008).1 This is not to say that extreme dimorphism should be regarded as the null hypothesis for Miocene hominoids; rather, we are suggesting that extreme dimorphism is a viable alternative to the hypothesis that high levels of size variation in a fossil sample indicate the presence of multiple species. Acceptance of L. lufengensis as a single highly dimorphic species highlights the need to incorporate other comparative species—in addition to the living great apes—when evaluating fossil samples. One option is to use the highly dimorphic papionins as analogues, which some studies have done (e.g., Ruff et al., 1989; Teaford et al., 1993; Uchida 1996b; Harvati et al., 2004; Baab, 2008). Another option is to use L. lufengensis as an analogue (Kelley, 2005). The use of fossil species to model intraspeciﬁc variation in other fossil assemblages was suggested by Wood (1991), who used Australopithecus boisei to determine whether variation in A. africanus and A. robustus indicated the presence of multiple species in each of these hypodigms (for other examples of the use of extinct species to evaluate variation in fossil samples, see Kelley, 2005; Skinner et al., 2006; Baab, 2008). Although Wood’s (1991) intent in taking this approach was to control for temporal variation, the purpose of using L. lufengensis as an analogue would be to include a reference sample that possesses a level of intraspeciﬁc variation not represented among extant hominoids. Although the amount of American Journal of Physical Anthropology time represented by the hominoid-bearing deposits at Lufeng is unknown, temporal variation is unlikely to be a major component of the high level of size variation in L. lufengensis, given that intrasexual variation in the sample is within the range of modern species (Kelley and Plavcan, 1998). The fact that L. lufengensis exceeds Pongo in its level of molar dimorphism means that it is potentially more dimorphic in the molar dentition than any extant primate, as Pongo is commonly thought to possess the greatest level of molar dimorphism among living primates (e.g., Mahler, 1973; Kelley and Xu, 1991; Kelley and Plavcan, 1998). If true, then including the Lufeng sample as part of the comparative framework for assessing variation in fossil primate samples becomes even more critical. In fact, it has not been quantitatively veriﬁed that Pongo expresses the greatest degree of molar dimorphism among living primates, and therefore the claim that the degree of molar dimorphism documented in L. lufengensis falls outside the range observed in living primate species has not been adequately tested. Thus, in this study, we test two hypotheses regarding molar size dimorphism in primates: (1) Pongo represents the uppermost extreme of molar dimorphism among living primates, and (2) molar dimorphism in L. lufengensis is greater than that in the most dimorphic living primate species. We then apply the results of these analyses to other potential instances of extreme dimorphism in the late Miocene hominoid fossil record—the Sivapithecus material from Haritalyangar, India, and the Ouranopithecus macedoniensis material from Greece (Kelley, 2005; Schrein, 2006). Speciﬁcally, we evaluate whether levels of apparent sexual dimorphism (i.e., the level of dimorphism required if the distinct large and small size clusters evident in the Sivapithecus and O. macedoniensis molar samples represent conspeciﬁc males and females, respectively) in these fossil samples fall within the limits of dimorphism established for living primates and L. lufengensis. MATERIALS AND METHODS Three extant species were included in the analysis: the western lowland gorilla (Gorilla gorilla), the Bornean orangutan (Pongo pygmaeus), and the drill (Mandrillus leucophaeus) (Table 1). The drill was chosen to represent papionins because Plavcan’s (1990) data set indicates that Mandrillus probably has the most dimorphic postcanine teeth of any extant papionin. Mandrillus leucophaeus is smaller in body size than M. sphinx and may not be as sexually dimorphic in body mass (Jungers and Smith, 1997), but the two species have similar degrees of postcanine dimorphism. This assessment is based on a comparison of Plavcan’s (1990) M. leucophaeus data set to unpublished data for M. sphinx collected by S. Frost, R. Nuger, and M. Singleton. The M. leucophaeus data were used in order to avoid the potential for interobserver error in the M. sphinx data. For each of the extant species, maximum length (mesiodistal, MD) and width (buccolingual, BL) dimensions of the mandibular molars were taken from the literature (for G. gorilla: Mahler, 1973; for P. pygmaeus and M. leucophaeus: Plavcan, 1990). Maxillary molars were not included in the analysis because sample sizes for these teeth are not as large as those for the mandibular molars in the fossil samples. MODELING SEXUAL DIMORPHISM IN MIOCENE APES TABLE 1. Sample sizes for the extant comparative taxa and L. lufengensis M1 M2 M3 Male Female Male Female Male Female G. gorilla P. pygmaeus M. leucophaeus L. lufengensis 43 20 23 10 43 20 18 12 40 20 24 11 40 20 18 11 34 18 24 6 34 18 16 10 Data are from the following sources: G. gorilla, Mahler (1973); P. pygmaeus, Plavcan (1990); M. leucophaeus, Plavcan (1990); L. lufengensis, provided by Xu Qinghua. The L. lufengensis sample is identical to the one used by Kelley and Plavcan (1998; Table 1), with the exception of one additional female M3 (identiﬁed by JK after reexamining the Lufeng data). This sample includes only molars from associated dentitions, thus making tooth position (i.e., M1, M2, M3) unambiguous and making it possible to sex teeth using associated canines and P3s (see Kelley, 1993). These two factors are important for obtaining an accurate estimation of sexual dimorphism in L. lufengensis (Kelley and Plavcan, 1998). Inclusion of isolated and unsexed molars has the potential to bias estimates of dimorphism upwards, either by mixing M1s and M2s or by including large females in the male sample and small males in the female sample (e.g., Kelley and Etler, 1989; Kelley and Plavcan, 1998). Sexual dimorphism in Lufengpithecus lufengensis and the extant species, quantiﬁed using log-transformed (base e) indices of sexual dimorphism (following Smith, 1999), was compared in two ways: (1) by combining the individual molars into a single measure (i.e., multivariate molar size dimorphism) and (2) by analyzing each molar position separately. This allowed us to evaluate overall dimorphism in the molar row and to account for the fact that comparisons among individual teeth are not independent (i.e., species with highly dimorphic M1s are also likely to have highly dimorphic M2s), while also examining the differences at each molar position. For both analyses, molar size was represented by the geometric mean of the MD and BL dimensions [i.e., (MD 3 BL)1/2]. For the analysis of multivariate molar size dimorphism, we used the geometric-mean-based method developed by Gordon et al. (2008), which is useful for examining the overall dimorphism in a series of variables (molar dimensions in this case) and has the beneﬁt that specimens with missing data (e.g., incomplete fossil specimens) can be included. This approach takes advantage of the fact that the ratio of two geometric means is mathematically equivalent to the geometric mean of the individual ratios for each of the variables that constitute the geometric means (Gordon et al., 2008): GM1 h x1 y1 z1 i1=3 ¼ 3 3 ; GM2 x2 y2 z2 ð1Þ where GM1 is the geometric mean of the means (i.e., the cube root of the product of x1, y1, and z1) for a set of variables measured on individuals in Group 1 (e.g., males of a particular species) and GM2 is the geometric mean of the means for the same set of variables (i.e., x2, y2, and z2) measured on individuals in Group 2 (e.g., females of the same species). 255 Thus, multivariate molar size dimorphism can be calculated in two ways. The ﬁrst way is to calculate the ratio of GMs. For each sex, a measure of multivariate molar size can be computed as follows: GM#ALL ¼ ðGM#1 3 GM#2 3 . . . 3 GM#n Þ1=n ; ð2Þ where GM#1 is the geometric mean of M1, M2, and M3 size [i.e., (M1 3 M2 3 M3)1/3] for the ﬁrst male, GM#2 is the geometric mean of M1, M2, and M3 size for the second male, etc., and thus GM#ALL is the geometric mean of the geometric means of all male individuals. The female geometric mean (GM$ALL) is computed in the same way. The index of sexual dimorphism (ISD) for multivariate molar size can then be calculated as ISD 5 GM#ALL/GM$ALL (i.e., the ratio of GMs). The second way to calculate multivariate molar size dimorphism is to use the GM of ratios: ISD ¼ ðM1ISD 3 M2ISD 3 M3ISD Þ1=3 ; ð3Þ where M1ISD is the ISD for M1 (i.e., mean M1 size for males divided by mean M1 size for females), M2ISD is the ISD for M2, and M3ISD is the ISD for M3. Note that Equations 3 and 1 are equivalent. When using the ratio of GMs (i.e., GM#ALL/GM$ALL) to calculate multivariate molar size dimorphism, all of the specimens in the analysis must possess each molar; those lacking one or more molars must be excluded. However, using the GM of ratios [i.e., (M1ISD 3 M2ISD 3 M3ISD)1/3], specimens with missing data can be retained because the ISD for each molar position is calculated independently of the other positions (Gordon et al., 2008), and thus fossil specimens that do not preserve the entire molar row can be included in the analysis. For this study, the GM of ratios was used to calculate ISDs for each sample in order to account for the fact that withinsex sample sizes for each molar position were not equal for any of the species or fossil samples used in the analysis (Table 1). To statistically evaluate differences between sample ISDs, we used the bootstrap (i.e., resampling with replacement) to generate 95% conﬁdence intervals for each pairwise difference as follows: 1. For each molar position, Sample A (e.g., G. gorilla) was resampled with replacement 2000 times,2 with the sample size and sex ratio for each bootstrap sample being identical to those of the original sample. Note that, because we resampled with replacement, a specimen could be included in each bootstrap sample multiple times or not included at all, and thus each iteration was highly unlikely to produce a sample that was identical to the original sample in specimen composition. 2. The ISD for each bootstrap sample was then computed. For the analysis of multivariate molar size dimorphism, bootstrap samples for each molar position were randomly grouped together (i.e., one bootstrap sample of M1s, one bootstrap sample of M2s, and one bootstrap sample of M3s), and multivariate molar dimorphism was calculated as the GM mean of the ISDs for each molar position. Note that we did not resample entire molar rows at once. Thus, in the case of the G. gorilla sample, for each iteration, an M1 ISD calculated using 43 males and 43 females was American Journal of Physical Anthropology 256 J.E. SCOTT ET AL. between Sample A and Sample B (disregarding the sign of the difference). 3. Finally, we divided the value obtained from Step 2 by the total number of bootstrap samples. The observed difference between Samples A and B was included in the latter calculations, such that P 5 (M 1 1)/(N 1 1), where M is the number of bootstrap differences (absolute values) greater than or equal to the observed difference, N is the total number of bootstrap differences, and one is added to M and N to include the observed difference. Fig. 1. An example of the procedure used to derive P-values for pairwise differences among the extant species and L. lufengensis. The top image shows the distribution of pairwise differences obtained from bootstrapping two samples. The observed difference between the ISDs of the two samples is 0.06; accordingly, the distribution is centered on 0.06. In the bottom image, the bootstrap distribution has been recentered on zero. The observed difference (0.06), represented by the vertical line, does not fall within the zero-centered distribution. Thus, the P-value for this comparison is P 5 0.0005 (i.e., 1/2001; see text for further details). combined with an M2 ISD calculated using 40 males and 40 females, and these were combined with an M3 ISD calculated using 34 males and 34 females (see Table 1). 3. Steps 1 and 2 were performed for Sample B (e.g., L. lufengensis), with each bootstrap sample containing the same number of males and females as in Sample B. 4. The bootstrapped ISDs for Sample A were then randomly paired with those for Sample B, and the difference between the ISDs for each pairing was calculated, creating a distribution of 2000 ISD differences. The middle 95% of this distribution represents the 95% conﬁdence interval for the pairwise comparison. A pairwise difference with a 95% conﬁdence interval that does not overlap zero (i.e., no difference) can be considered statistically signiﬁcant at the a 5 0.05 level. However, we obtained more precise P-values in the following way: 1. First, we recentered the distribution of pairwise differences between Sample A and Sample B on zero (see Fig. 1), as outlined by Manly (1997, p 99–100). This step was necessary because the distribution of pairwise differences will be centered on the observed difference between Sample A and Sample B. In order to derive a P-value for the observed difference between Samples A and B, the distribution must be recentered on (i.e., the mean of the distribution must equal) zero. According to Manly (1997, p 99), ‘‘the idea with this approach is to use bootstrapping to approximate the distribution of a suitable test statistic when the null hypothesis is true’’ (i.e., no difference between samples). 2. Next, using the recentered distribution, we counted the number of values that were as extreme as or more extreme than the observed ISD difference American Journal of Physical Anthropology Note that this test is two tailed. Although the questions of interest are (1) whether M. leucophaeus exceeds P. pygmaeus and G. gorilla in molar size dimorphism and (2) whether L. lufengensis exceeds all of the extant comparative species in molar size dimorphism, specifying a directional alternative to the statistical null hypothesis of no difference in sexual dimorphism requires a priori justiﬁcation (i.e., evidence independent of the sample estimates of molar dimorphism; see also Scott and Stroik, 2006). For example, if it were known that postcranial size dimorphism in L. lufengensis is greater than in any extant primate, then one could reasonably hypothesize that other aspects of the Lufeng hominoid are also extremely dimorphic, thus justifying a one-tailed test. This resampling procedure differs from previous applications of the bootstrap (e.g., Lockwood et al., 1996, 2000; Lockwood, 1999; Silverman et al., 2001; Reno et al., 2003; Villmoare, 2005; Harmon, 2006; Schrein, 2006; Gordon et al., 2008; see also Cope and Lacy, 1992) in two important ways. First, the latter studies are generally concerned with determining the probability of obtaining from the comparative samples a sample with characteristics (e.g., size, variation, sexual dimorphism) identical to that of a fossil sample. In the present case, however, because we are dealing with a fossil assemblage (the sexed Lufeng specimens) that is large in comparison to other such assemblages, we are able to use the bootstrap to generate conﬁdence intervals for the fossil ISD, allowing us to make inferences about population parameters. Thus, we are able to incorporate the uncertainty in the sample ISDs for the comparative taxa and for the fossil species, resulting in more robust statistical testing than is typically the case for small fossil samples (see also Gordon et al., 2008). The second notable difference between our resampling procedure and those used in previous studies of variation in fossil samples is that the bootstrap samples obtained from the comparative taxa were not reduced to match the size of the fossil sample. In most of the studies cited above, the statistic for the fossil sample (e.g., coefﬁcient of variation, the index of sexual dimorphism) is used as a point estimate for comparison with distributions generated from the comparative samples. Such distributions are composed of bootstrap samples that are identical in size to the fossil sample. When only a point estimate is used for the fossil sample, it is necessary for the samples produced from resampling the comparative samples to be the same size as the fossil sample because conﬁdence intervals for the fossil sample are not generated. In contrast, because we resampled the comparative samples and the L. lufengensis sample—and thus generated conﬁdence intervals for all of the samples—matching the sample size of the fossil sample was unnecessary and MODELING SEXUAL DIMORPHISM IN MIOCENE APES 257 TABLE 2. The Sivapithecus and Ouranopithecus samples Taxon Specimen a Ouranopithecus RPl-55 RPl-56 RPl-75 RPl-76 RPl-89* NKT-21 RPl-54 RPl-79* RPl-84* RPl-88* Sivapithecus GSI D. 197 YPM 13828 ONGC/v/790 PUA 1052-69 GSI 18039 GSI 18042 GSI D. 199 YPM 13806 YPM 13825 GSI 18041 GSI 18067 PUA 760-69 Sex assignmentb Male** Male Male** Male Male Female Female** Female Female Female Male Male Male Male Male Male Female Female Female Female Female Female Tooth sizec C P3 M1 M2 M3 11.7 10.9 12.7 13.2d 13.0 8.5 8.5 9 – 8.8 11.6 11.3 11.6 – 11.7 9.8 10.1 10.1 9.6 9.5 14.2 14.6 15.3 – 14.5 11.6 12.3 12.2 11.6 12.8 15.9 15.6 16.7 – 16.0 13.6 13.6 14.1 13.7 14.0 17.8 16.6 17.4 18.1 18.0 13.8 14.2 14.5 14.1 14.3 – – – – – – – – – – – – – – – – – – – – – – – – 11.7 14.5 – 12.6 14.6 14.9 13.0 – – – – 13.9 14.9 11.3 – – – 11.5 12.0 – 10.6 9.9 10.1 11.3 – 10.7 – – – – 10.3 9.6 – – a Data for Ouranopithecus were taken from Koufos (1993) and Koufos and de Bonis (2004); specimens marked with an asterisk (*) were not included in Schrein’s (2006) analysis. The Sivapithecus data were compiled by JK from various sources. b For Ouranopithecus, sex assignment is based on canine and P3 size (see also Fig. 2); specimens marked with double asterisks (**) were sexed by Koufos (1995) using canine shape. For Sivapithecus, sex assignment is based on molar size (see text for further discussion). c Tooth size was calculated as the square root of the product of MD and BL diameters. d Only the MD dimension [maximum length, identiﬁed by Koufos (1993) as ‘‘transverse diameter’’] is available for this canine. would have actually reduced the power of the test to detect differences, making it overly conservative. After establishing the rank order of molar dimorphism in the extant species and L. lufengensis, we evaluated apparent dimorphism in the Ouranopithecus macedoniensis and Haritalyangar Sivapithecus samples. The O. macedoniensis data used for this study were taken from the literature (Koufos, 1993; Koufos and de Bonis, 2004), while the Sivapithecus data were provided by JK. All of the O. macedoniensis specimens used here can be conﬁdently sexed based on associations with canines and P3s (Table 2; Fig. 2; see also Schrein, 2006). This sample includes newly published specimens from Ravin de la Pluie (Koufos and de Bonis, 2004) that were not used in the most recent analysis of variation and sexual dimorphism in this fossil ape (Schrein, 2006), and that expand the sample from n 5 5–6 sexed individuals per molar position to n 5 9–10, including the addition of three complete female molar rows (for a total of ﬁve) and one complete male molar row (for a total of four) (Table 2). The sample of Sivapithecus mandibular molars from Haritalyangar is smaller, with n 5 5–7 individuals per molar position (Table 2), and none of these specimens can be sexed based on associations with canines or P3s. However, the M2 and M3 samples are each characterized by the presence of two markedly disjunct size clusters. If the Haritalyangar assemblage samples a single species, Fig. 2. Bivariate plots of canine size vs. M2 size (top) and P3 size vs. M2 size (bottom) in Ouranopithecus macedoniensis. Tooth size is the geometric mean of the MD and BL dimensions. Specimens that were sexed based on canine shape by Koufos (1995) are indicated by male (#) and female ($) symbols. Note that (1) large and small canines and P3s cluster with the male and female specimens, respectively, and (2) specimens with large molars are associated with large (male) canines and P3s, whereas specimens with small molars are associated with small (female) canines and P3s. The ﬁrst and third molars exhibit a similar pattern. then the cluster of large specimens must be composed of males and the cluster of small specimens must be composed of females (Kelley, 2005). In contrast, the distribution of Haritalyangar M1s is continuous, making sex assignment more arbitrary. Based on associations with M2s, three of the seven M1s can be tentatively allocated to ‘‘male’’ and ‘‘female’’ clusters, while the largest (ONGC/v/790) and smallest (PUA 760-69) M1s can also be assigned to the ‘‘male’’ and ‘‘female’’ groupings, respectively. Two teeth—GSI 18041 and GSI 18042—fall in the middle of the M1 size range. If no overlap between males and females is assumed, then the index of apparent sexual dimorphism (ISDA) is between 1.19 and 1.21, depending on whether both specimens are assigned to one sex or if the larger GSI 18042 is grouped with presumed males and the smaller GSI 18041 is grouped with presumed females. If females and males do overlap in size (with the smaller GSI 18041 placed with presumed males and the larger GSI 18042 placed with presumed females), then the ISDA would be 1.16. We examined the effect of these alternative assignments and found that they did not substantively inﬂuence the results. Thus, we report only the results of the analyses in which GSI 18042 was considered male and GSI 18041 was considered female. Note that these sex assignments American Journal of Physical Anthropology 258 J.E. SCOTT ET AL. are identical to those that would have been obtained had we simply used the mean method [i.e., dividing the sample into ‘‘males’’ and ‘‘females’’ about the mean (Plavcan, 1994; Gordon et al., 2008)]. The Sivapithecus and O. macedoniensis samples were evaluated using resampling methods, but because these samples are small (n 10 for all molar positions), they were treated as point estimates for the purpose of comparing them to the extant taxa and L. lufengensis. Following previous studies (e.g., Lockwood et al., 1996, 2000; Lockwood, 1999; Silverman et al., 2001; Reno et al., 2003; Villmoare, 2005; Harmon, 2006; Schrein, 2006), we bootstrapped the comparative species (including L. lufengensis) to obtain samples that were identical to the Sivapithecus and O. macedoniensis samples in size and sex ratio, creating distributions for determining the probability of obtaining a sample from G. gorilla, P. pygmaeus, M. leucophaeus, and L. lufengensis with the same level of molar dimorphism observed in the Sivapithecus and O. macedoniensis samples. In the procedure describe above, resampling without replacement can be used instead of bootstrapping (e.g., Gordon et al., 2008). In fact, resampling without replacement is more likely to produce lower P-values than resampling with replacement given that, at small sample sizes (e.g., n 5 5–7 in the case of the Sivapithecus analysis), the latter can, in principle, produce samples composed only of multiple entries of the largest male and smallest female, or samples composed only of multiple entries of the smallest male and largest female. Clearly, such samples would produce wider bootstrap distributions (i.e., with very high and very low ISDs) that will be more likely to encompass the fossil value. However, Cope and Lacy (1992, p. 361), in their study of the use of the coefﬁcient of variation (CV) for evaluating variation in fossil samples, noted that a comparative sample ‘‘of hundreds or thousands is needed to properly simulate CV sample distributions.’’ This problem motivated them to develop a method in which a very large (n 5 10,000) simulated ‘‘population’’ is generated using descriptive statistics from samples of extant species. This simulated population is then resampled without replacement at a sample size equal to the fossil assemblage in order to determine the probability of sampling the CV observed in the fossil sample from the simulated population. As an alternative for overcoming the intractable problem of limited comparative material, Lockwood et al. (1996) used the bootstrap to generate samples equal in size to fossil samples directly from the comparative samples. In this study, we preferred the bootstrap over resampling without replacement because it is not clear that our comparative samples are sufﬁciently large. For each molar position, two sets of 1000 bootstrap samples were drawn from each of the extant species samples and from the Lufengpithecus sample, with one set matching the composition of the Sivapithecus sample and the other matching the composition of the O. macedoniensis sample.3 For example, in the Sivapithecus analysis, each bootstrap sample contained seven M1s (four males, three females), six M2s (three males, three females), and ﬁve M3s (two males, three females). For each bootstrap sample, log-transformed (base e) ISDs were calculated as described above. The Sivapithecus and O. macedoniensis ISDAs (log-transformed) were then compared to the bootstrap distributions; if the values for these two fossil samples fell outside the middle 95% of the bootstrap distributions, then the null hypothesis of American Journal of Physical Anthropology no difference was considered falsiﬁed at the a 5 0.05 level. For these tests, two-tailed P-values were obtained by counting the total number of bootstrap ISD values that were as extreme as or more extreme than the Sivapithecus and O. macedoniensis values (including the values for the two fossil samples) and dividing that number by the total number of ISDs (i.e., 1001). In this case, ‘‘extreme’’ refers to values that when subtracted from the comparative sample’s ISD produce a difference (regardless of sign) as large as or larger than the difference produced by subtracting the fossil sample’s ISDA from the comparative sample’s ISD. Because our division of the Sivapithecus sample into sexes was based solely on size, we also analyzed this sample using a sex-blind statistic—the CV—to estimate dimorphism. For each molar position, we bootstrapped the comparative samples 1000 times each at a sample size equal to the Sivapithecus sample but without regard to sex (i.e., the sex ratios of the bootstrapped samples did not necessarily match the hypothesized sex ratio of the Sivapithecus sample) and calculated the CV for each. For this part of the analysis, the comparative samples (including the Lufeng sample) were modiﬁed so that the sex ratios for each tooth were balanced prior to being bootstrapped. We then compared the CVs for the Sivapithecus molars to the resulting distributions and determined the statistical signiﬁcance of the sample differences as described above. For this analysis, we only examined the individual molar positions, as there are currently no methods for dealing with missing data in the calculation of the CV. The results of these analyses did not differ substantively from the analyses in which the specimens were sexed, and thus only the ISD-based results are reported. Finally, it is important to note that, because our comparative samples are not composed entirely of complete molar rows, the P-values reported for the analyses of multivariate molar dimorphism should be considered approximate. For example, consider a case in which the molars of a species are identical in their degree of dimorphism. If a sample of 40 males and 40 females is collected in which the ten largest males are missing their M3s, then the estimate of dimorphism for the M3 will be lower than in the other teeth. When the teeth are combined and multivariate molar dimorphism is estimated, the estimate will be biased due to the missing M3 data. Such a sample will produce a bootstrap distribution that is shifted to the left (i.e., toward monomorphism), resulting in an artiﬁcially low P-value—and a potential type II error—in a pairwise comparison with a fossil sample. However, this problem is unlikely to be an issue in our analysis because the missing teeth in our samples are not size-biased. Thus, the effects of missing data on the P-values for the analysis of multivariate molar dimorphism are likely to be minimal. Therefore, in order to use samples that are as large as possible, we have chosen not to limit the comparative samples to only those individuals that preserve complete molar rows. RESULTS The ISDs for the extant taxa and L. lufengensis are presented in Table 3. For multivariate molar size, sample dimorphism is greatest in L. lufengensis, followed in rank order by M. leucophaeus, P. pygmaeus, and G. gorilla. This pattern is repeated at each individual molar position with one exception: M3 sample dimorphism is greater in G. gorilla than in P. pygmaeus. The bootstrap tests for multivariate molar size dimorphism MODELING SEXUAL DIMORPHISM IN MIOCENE APES 259 TABLE 3. Indices of sexual dimorphism for the extant taxa and L. lufengensis G. gorilla P. pygmaeus M. leucophaeus L. lufengensis MALLa M1 M2 M3 1.08 1.10 1.13 1.19 1.06 1.09 1.12 1.18 1.07 1.11 1.14 1.19 1.11 1.09 1.15 1.19 a The abbreviation ‘‘MALL’’ refers to multivariate molar size here and in subsequent tables. TABLE 4. Results of the bootstrap tests for interspeciﬁc differences in multivariate molar size dimorphism Gorilla Pongo Mandrillus Pongo 5 (0.1119) Mandrillus M [ G (0.0005) M [ P (0.004) Lufengpithecus L [ G (0.0005) L [ P (0.0005) L [ M (0.001) Nonsigniﬁcant differences are indicated by an equality symbol; greater-than symbols indicate signiﬁcance and the direction of difference. P-values for each comparison are given in parentheses (probabilities are two-tailed). Abbreviations: G, Gorilla; P, Pongo; M, Mandrillus; L, Lufengpithecus. reveal that G. gorilla and P. pygmaeus are not signiﬁcantly different, whereas M. leucophaeus is signiﬁcantly more dimorphic than the two extant apes, and L. lufengensis is signiﬁcantly more dimorphic than all of the living species (Table 4, Fig. 3). When dimorphism is examined by molar position (Table 5), P. pygmaeus and G. gorilla differ statistically only at M2, with P. pygmaeus being more dimorphic at this position. Mandrillus leucophaeus is signiﬁcantly more dimorphic than G. gorilla at M1 and M2—but not at M3—and is signiﬁcantly different from P. pygmaeus only at M3. Lufengpithecus lufengensis is signiﬁcantly more dimorphic than the living apes at all molar positions, but is signiﬁcantly more dimorphic than M. leucophaeus only at M1 and M2. Some of these differences are nonsigniﬁcant after adjusting a-levels for multiple comparisons using the sequential Bonferroni method (e.g., Rice, 1989); the results that remain signiﬁcant are: M. leucophaeus more dimorphic than G. gorilla for M1 and M2, L. lufengensis more dimorphic than the living great apes for all molar positions, and L. lufengensis more dimorphic than M. leucophaeus for M1. Application of the sequential Bonferroni adjustment to the comparisons of multivariate molar size dimorphism does not alter the results. The results for the analysis of the O. macedoniensis sample are given in Table 6. For multivariate molar size, O. macedoniensis is more dimorphic than all of the extant taxa, but it is not signiﬁcantly different from L. lufengensis (Fig. 4A). The results for M1 and M3 are similar to those for multivariate molar size, but for M2, O. macedoniensis is only signiﬁcantly more dimorphic than G. gorilla. Sequential Bonferroni adjustment renders only the latter difference nonsigniﬁcant. In contrast to the O. macedoniensis sample, apparent dimorphism in the Sivapithecus assemblage is signiﬁcantly greater than in any of the comparative taxa, including L. lufengensis, even after sequential Bonferroni adjustment (Table 7, Fig. 4B). The only exception is apparent dimorphism in the M1 sample, which cannot be statistically distinguished from M1 dimorphism in L. lufengensis. Thus, the Haritalyangar M2 and M3 Fig. 3. Bootstrap distributions for multivariate molar size dimorphism for the extant species and L. lufengensis. The middle 95% of each distribution is equivalent to the 95% conﬁdence interval for multivariate molar size dimorphism. Gorilla gorilla and P. pygmaeus are not signiﬁcantly different, M. leucophaeus is more dimorphic than the living apes, and L. lufengensis is more dimorphic than all of the extant taxa. dimensions indicate that if this assemblage samples a single species, then the distal molars of that species are even more dimorphic than those of L. lufengensis. This is true for multivariate molar dimorphism as well. DISCUSSION Identifying levels of sexual dimorphism in fossil species that are extreme in comparison to living species requires knowledge of the limits of dimorphism in extant taxa. In the case of L. lufengensis, previous studies have used extant Pongo to represent the upper limit of molar dimorphism in living primates (Kelley and Xu, 1991; Kelley, 1993: Kelley and Plavcan, 1998). However, the results of this study demonstrate that the molars of P. pygmaeus are not the most size-dimorphic among extant primates; in fact, our samples do not allow us to unequivocally establish that P. pygmaeus is even the most dimorphic living hominoid in this respect. Mandrillus leucophaeus emerges as the most dimorphic extant primate when the molar row is considered in its entirety, but the drill cannot be consistently distinguished statistically from either P. pygmaeus or G. gorilla at individual molar positions (though sample dimorphism is always greatest in the drill among the extant taxa). While the general lack of statistical differences between G. gorilla and P. pygmaeus in this study challenges the conventional assumption that the molars of the oranguAmerican Journal of Physical Anthropology 260 L [ M (0.012) 5 (0.1339) L [ P (0.0005) 5 (0.1009) M [ G (0.0015) L [ G (0.0005) Pongo Mandrillus Lufengpithecus Nonsigniﬁcant differences are indicated by an equality symbol; greater-than symbols indicate signiﬁcance and the direction of difference. P-values for each comparison are given in parentheses (probabilities are two-tailed). Abbreviations: G, Gorilla; P, Pongo; M, Mandrillus; L, Lufengpithecus. An asterisk (*) indicates that the comparison is not signiﬁcant after sequential Bonferroni adjustment (applied within each variable). 5 (0.0885) M [ P* (0.0305) L [ P (0.001) L [ M* (0.0195) 5 (0.4448) 5 (0.1149) L [ G (0.0005) 5 (0.2214) L [ P (0.0005) P [ G* (0.0325) M [ G (0.0005) L [ G (0.0005) Pongo Gorilla Mandrillus M2 Pongo Gorilla Mandrillus M1 Pongo Gorilla TABLE 5. Results of the bootstrap tests for interspeciﬁc differences at individual molar positions M3 Mandrillus J.E. SCOTT ET AL. American Journal of Physical Anthropology tan are more dimorphic than those of the gorilla, Uchida (1996a) documented intrageneric variation in molar dimorphism in both Pongo and Gorilla. Thus, a more complete analysis that includes material from eastern lowland gorillas, mountain gorillas, and Sumatran orangutans could reveal differences between these two genera. It is also important to point out that our ability to detect differences among the living taxa is hampered in some respects. First, ratios such as the ISD generally have wider conﬁdence intervals than the variables from which they are derived due to the fact that there is measurement error in both the numerator (male mean) and denominator (female mean) (see discussion in Smith, 1999). Second, because males and females constitute separate components of the ISD, the effective sample sizes for each species are about half the total sample sizes. Thus, given that the differences in molar sample ISDs among G. gorilla, P. pygmaeus, and M. leucophaeus are relatively small, especially when compared to differences in canine, craniofacial, and body-mass dimorphism across the Anthropoidea (Plavcan, 2001), it is not surprising that many of the comparisons in this study are nonsigniﬁcant. Future studies will require larger samples to establish whether the differences in sample ISDs observed between G. gorilla and P. pygmaeus and between P. pygmaeus and M. leucophaeus at individual molar positions reﬂect true population differences. In spite of the conservative nature of the statistical tests, our results conﬁrm that the molars of L. lufengensis are more dimorphic than those of living apes. Our analysis of the Lufeng hominoid also demonstrates that it was more dimorphic than M. leucophaeus (at least with respect to the molar row in its entirety and M1, and probably M2 as well). That we were able to detect signiﬁcant differences between L. lufengensis and the extant species despite the fact that the Lufeng sample contains only n 5 16–22 individuals per molar position highlights just how much greater dimorphism is in the molar teeth of this fossil ape. Notably, the analysis of multivariate molar size dimorphism indicates that M. leucophaeus is intermediate between the great apes and L. lufengensis (see Fig. 3). Thus, although molar dimorphism in L. lufengensis is extreme relative to living primates, comparison to the drill reveals that it is not as extreme as it appears to be when only extant great apes are considered. Despite the drill’s higher level of overall molar dimorphism compared to extant apes, its inclusion in our analysis of the O. macedoniensis material does not alter previous conclusions that a single-species interpretation of this fossil assemblage necessitates a level of dimorphism that exceeds that observed in living primates (Schrein, 2006). Although the addition of the more recent Ravin de la Pluie specimens (Koufos and de Bonis, 2004) results in slightly lower indices of apparent sexual dimorphism (ISDAs) for O. macedoniensis in comparison to those for the smaller sample used by Schrein (2006), there is still no overlap in size between specimens identiﬁed as male and those identiﬁed as female on the basis of canine or P3 size/morphology (see Table 2, Fig. 2), an attribute also evident in the L. lufengensis sample (Kelley and Plavcan, 1998). In our analysis, M2 is the only O. macedoniensis variable for which size dimorphism cannot be statistically distinguished from that of any of the extant species, except for G. gorilla prior to sequential Bonferroni adjustment. Schrein (2006) obtained somewhat different results for her comparisons MODELING SEXUAL DIMORPHISM IN MIOCENE APES 261 TABLE 6. Bootstrap results for the Ouranopithecus comparisons Ouranopithecus Gorilla Pongo Mandrillus Lufengpithecus MALL (ISD 5 1.20) M1 (ISD 5 1.21) M2 (ISD 5 1.16) M3 (ISD 5 1.24) O [ G (0.001) O [ P (0.001) O [ M (0.001) 5 (0.3407) O [ G (0.002) O [ P (0.002) O [ M (0.006) 5 (0.3996) O [ G* (0.018) 5 (0.1339) 5 (0.4336) 5 (0.2987) O [ G (0.004) O [ P (0.001) O [ M (0.004) 5 (0.0939) Nonsigniﬁcant differences are indicated by an equality symbol; greater-than symbols indicate signiﬁcance and the direction of difference. P-values for each comparison are given in parentheses (probabilities are two-tailed). Abbreviations: G, Gorilla; P, Pongo; M, Mandrillus; O, Ouranopithecus. An asterisk (*) indicates that the comparison is not signiﬁcant after sequential Bonferroni adjustment (applied within each variable). between O. macedoniensis and the great apes (i.e., only the M1 of Ouranopithecus could be conﬁdently identiﬁed as being more dimorphic than in gorillas and orangutans), which is probably attributable to the smaller sample of O. macedoniensis used in her study and the fact that the compositions of the Gorilla and Pongo samples were different from those used in the present analysis. Note also that Schrein (2006) examined MD and BL dimensions separately, whereas we combined them [i.e., (MD 3 BL)1/2]. Nevertheless, the pattern of results in the two studies is broadly similar. Under the assumption that fossil species could not have been more dimorphic than extant species, our results could be interpreted as supporting the presence of multiple species in the O. macedoniensis sample (e.g., Kay, 1982a). However, the fact that molar size dimorphism in O. macedoniensis cannot be statistically distinguished from that in L. lufengensis demonstrates that the level of dimorphism required for O. macedoniensis under a single-species taxonomy is not unprecedented among late Miocene hominoids. Thus, the inclusion of L. lufengensis in the comparative framework demonstrates that, although O. macedoniensis does not ﬁt expectations regarding sexual dimorphism among extant taxa, it can be accommodated within known models of intraspeciﬁc variation and sexual dimorphism when other fossil species are used as analogues. Schrein (2006) reviewed several lines of evidence pointing to the existence of only a single species within the O. macedoniensis dental sample: large specimens are male, small specimens are female; the Ravin de la Pluie specimens, which constitute the bulk of the sample, are from individuals that were sympatric and probably synchronic; and molar morphology is homogeneous. The results presented here strengthen the case for recognizing a single species among the hominoid remains from Ravin de la Pluie, Xirochori, and Nikiti, one characterized by an extreme degree of molar dimorphism relative to living primates. The results of the Sivapithecus analysis, on the other hand, do not lend themselves to easy interpretation. Kelley (2005) found that measures of variation for the Haritalyangar M2s and M3s are statistically signiﬁcantly higher than those for L. lufengensis, suggesting an even greater level of sexual dimorphism than that exhibited by L. lufengensis if these specimens represent a single species. Our results conﬁrm that the level of apparent dimorphism in the Haritalyangar M2 and M3 samples is highly unlikely to have come from a species as dimorphic as L. lufengensis; none of the samples bootstrapped from the Lufeng sample produced ISDs as high as the ISDAs for the Haritalyangar M2, M3, or multivariate molar size. In contrast, the ISDA for M1 falls well within the Fig. 4. Bootstrap distributions for multivariate molar size dimorphism generated by bootstrapping the extant taxa at a sample size and sex ratio identical to that of the (A) Ouranopithecus and (B) Sivapithecus samples. Only the M. leucophaeus and L. lufengensis distributions are shown; the G. gorilla and P. pygmaeus distributions would be to the left of the Mandrillus distribution. The solid vertical line in A indicates the ISDA for the O. macedoniensis sample; the dashed vertical line in B indicates the ISDA for the Sivapithecus sample. Lufeng distribution, and Kelley’s (2005) analysis of variation in the Haritalyangar maxillary molars indicates that the same would certainly be true for M1, M2, and M3, as levels of apparent dimorphism in these teeth are slightly lower than or similar to those of L. lufengensis (M2 ISDA 5 1.16; M3 ISDA 5 1.19; an ISDA cannot be calculated for M1 due to the fact that the specimens American Journal of Physical Anthropology 262 J.E. SCOTT ET AL. TABLE 7. Bootstrap results for the Sivapithecus comparisons Sivapithecus MALL (ISDA 5 1.29) Gorilla Pongo Mandrillus Lufengpithecus S [ G (0.001) S [ P (0.001) S [ M (0.001) S [ L (0.001) M1 (ISDA 5 1.20) M2 (ISDA 5 1.32) M3 (ISDA 5 1.34) S [ G (0.001) S [ P (0.004) S [ M (0.01) 5 (0.6533) S [ G (0.001) S [ P (0.001) S [ M (0.001) S [ L (0.001) S [ G (0.003) S [ P (0.001) S [ M (0.001) S [ L (0.001) Nonsigniﬁcant differences are indicated by an equality symbol; greater-than symbols indicate signiﬁcance and the direction of difference. P-values for each comparison are given in parentheses (probabilities are two-tailed). Abbreviations: G, Gorilla; P, Pongo; M, Mandrillus; L, Lufengpithecus; S, Sivapithecus. form a fairly tight cluster, precluding the use of size as a criterion for sex assignment; see Fig. 8.3 in Kelley, 2005). If we accept that fossil species are not constrained by currently known limits of intraspeciﬁc variation and sexual dimorphism (Kelley, 1993; Kelley and Plavcan, 1998; Plavcan and Cope, 2001; Schrein, 2006), then the singlespecies hypothesis cannot be deﬁnitively ruled out for the Haritalyangar sample, despite the fact that such a species would have to be even more dimorphic than L. lufengensis. While the high levels of size variation and apparent sexual dimorphism in the Haritalyangar second and third mandibular molars can be used to argue for the presence of two species (Kelley, 2005), such evidence cannot be used as the sole basis for rejecting the single-species hypothesis (Kelley and Plavcan, 1998; Plavcan and Cope, 2001; Schrein, 2006). Presumably, there is a limit to the amount of molar dimorphism that can be expressed in primates, but whether or not L. lufengensis (and O. macedoniensis) represents that limit is currently unknown. Other recently reported cases of extreme dimorphism, including the middle Miocene hominoid Griphopithecus alpani from Pas alar, Turkey [apparent even though a second species has been identiﬁed in the Pas alar assemblage (Humphrey and Andrews, 2008; Kelley et al., 2008)], and the Oligocene early catarrhine Aegyptopithecus zeuxis from the Fayum, Egypt (Simons et al., 2007), could provide insight into this issue. On the other hand, given that the Haritalyangar second and third mandibular molars do not ﬁt any of our comparative models of sexual dimorphism, additional lines of evidence are required before accepting a singlespecies taxonomy for this sample, as the two-species taxonomy cannot be rejected based on current evidence either. In this context, demonstration that the size clusters evident in the M2 and M3 samples are truly homogeneous with respect to sex using canine and/or P3 size and morphology, as was done for the L. lufengensis and O. macedoniensis samples (Kelley and Xu, 1991; Kelley, 1993; Schrein, 2006; see Fig. 2), would provide support for the single-species hypothesis. Conversely, a two-species hypothesis—with each size cluster representing a different species—would be supported if it is shown that males and females are present in both clusters. Unfortunately, the current sex assignments are based on size because there are no associated canines or P3s, which precludes unequivocally linking the high levels of variation in the sample to sex differences. Finally, it is important to note that the temporal span for Sivapithecus at Haritalyangar, at approximately 400,000 years (Pillans et al., 2005), is certainly greater than for either the Lufengpithecus or Ouranopithecus samples, but how much of this range is represented in the portion of the Haritalyangar sample analyzed here is American Journal of Physical Anthropology unknown. Thus, based on the current evidence, the taxonomy of the Haritalyangar Sivapithecus material remains ambiguous (see also Kelley, 2005). CONCLUSIONS Our analysis of sexual dimorphism in molar size in great apes and the drill demonstrates that the latter species exceeds the extant hominoids in some aspects of molar dimorphism. Thus, Pongo does not possess the most dimorphic molars among living primates, though they are among the most dimorphic. These results indicate that Mandrillus leucophaeus (and perhaps other papionins) should be included in extant comparative samples when evaluating variation in fossil hominoid assemblages, particularly when variation appears to exceed that in gorillas and orangutans. We conﬁrmed the extreme degree of molar dimorphism in the Lufengpithecus lufengensis sample relative to extant species, thereby establishing the importance of using this species as a comparative analogue to represent levels of intraspeciﬁc variation and sexual dimorphism not sampled among living primates (e.g., Kelley, 2005). Using the drill and L. lufengensis samples as part of our comparative framework, we analyzed apparent size dimorphism in the molars of two other late Miocene hominoid assemblages that have been identiﬁed as possibly comprising single highly dimorphic species. Our results for the Haritalyangar Sivapithecus sample show that, if only one species is present at this site, then it is more dimorphic than L. lufengensis for at least some teeth. Given the uncertainties concerning the sex of the individuals in this sample, and because the sample as a whole does not ﬁt any of our comparative models, we are unable to choose with conﬁdence between the hypotheses that the sample contains (1) a single, extremely sizedimorphic species or (2) two species, differing primarily in size. On the other hand, in the case of Ouranopithecus macedoniensis, our analysis shows that the level of molar dimorphism required under a single-species taxonomy is fully compatible with the degree of sexual dimorphism in the molars of L. lufengensis, thus demonstrating that, while a single-species taxonomy for the O. macedoniensis sample requires a degree of molar dimorphism that is extreme compared to that in living anthropoids, it is not extreme in comparison to at least one other hominoid species from the late Miocene of Eurasia. ACKNOWLEDGMENTS We thank Xu Qinghua of the Institute of Vertebrate Paleontology and Paleoanthropology, Beijing, China, for MODELING SEXUAL DIMORPHISM IN MIOCENE APES providing access to the Lufengpithecus dental data while sponsored by grants from the National Academy of Sciences and the Leakey Foundation to JK. We are grateful to Michael Plavcan for answering questions regarding his Mandrillus leucophaeus data, and Stephen Frost kindly allowed us to examine Mandrillus sphinx data that he, Rachel Nuger, and Michelle Singleton collected. Dennis Young provided invaluable statistical advice. This manuscript beneﬁtted from thoughtful comments and suggestions by Editor-in-Chief Christopher Ruff, the associate editor, and two anonymous reviewers. The bootstrap tests were performed using Microsoft Excel macros written by Charles Lockwood—friend, mentor, and colleague. He is missed. LITERATURE CITED Albrecht GH, Miller JMA. 1993. Geographic variation in primates: a review with implications for interpreting fossils. In: Kimbel WH, Martin LB, editors. Species, species concepts, and primate evolution. New York: Plenum. p 123–161. Baab KL. 2008. The taxonomic implications of cranial shape variation in Homo erectus. J Hum Evol 54:827–847. 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