Comparative application of the coefficient of variation and range-based statistics for assessing the taxonomic composition of fossil samples

Dental variation has been used commonly to assess taxonomic composition in morphologically homogeneous fossil samples. While the coefficient of variation (CV) has been used traditionally, range-based measures of variation, such as the range as a percentage of the mean (R%) and the maximum/minimum index (I_max/min) have recently become popular alternatives. The current study compares the performance of these statistics when applied to single- and pooled-species dental samples of extant Cercopithecus species. A common methodology for such problems of species discrimination has been to simply compare the maximum value of a variation statistic observed in extant samples with that observed in the fossil sample. However, regardless of what statistic is used, this approach has an unknowable Type I error rate, and usually has low power to detect multiple species. A more appropriate method involves a formal hypothesis test. The null hypothesis is that the level of variation in the fossil sample does not exceed what might be expected in a sample drawn randomly from a reference population, taking into account sampling error and the size of the fossil sample. Previous research using this method with the CV has indicated that it offers considerable power at an acceptable Type I error rate. In the current study, the data of primary interest were posterior dental dimensions for single- and pooled species samples from extant Cercopithecus species. In addition, the study also investigated the relative performance of variation statistics when applied to highly dimorphic canine dimensions, since much recent work has employed sexually dimorphic dental dimensions for assessing single-species hypotheses. The results indicate that the CV consistently out-performed the range-based statistics when using posterior dental dimensions to test a single-species hypothesis. Regardless of which statistic was used, tests on sexually dimorphic dimensions offered minimal power. In consideration of these results and the problem of studywise Type I error rates, we recommend against the use of multiple measures of variation to test for multiple species composition, and advocate the CV as the statistic of choice when using the method of Cope & Lacy (1992). For similar reasons, we argue for careful selection of dental variables for inclusion in such analyses, and in particular recommend against including sexually dimorphic dimensions when testing for multiple species composition.     

A simulation test of hominoid species number at Lufeng, China: implications for the use of the coefficient of variation in paleotaxonomy

High dental metric variation in the large hominoid sample from the late Miocene site of Lufeng, China has been interpreted in two ways: (1) there are two morphologically similar species that broadly overlap in size, and (2) there is one species that is more highly sexually dimorphic in dental size, and perhaps in body size, than any extant primate. It has been claimed that the high levels of dental metric variation falsify the single-species hypothesis, which has been viewed implicitly as corroboration of the two-species hypothesis. However, the two-species hypothesis has not been subjected to testing. Here we test the two-species hypothesis using computer simulations to attempt to reproduce the unusual pattern of intrasexual and intersexual dental metric variation observed in the Lufeng postcanine dentition. Conditions of the simulation experiments were optimized to favor the two-species hypothesis. It was found that, although the Lufeng pattern of metric variation could be reproduced by sampling two species, the likelihood of this occurrence was very low even when the conditions were optimized to the point of improbability. We conclude that the likelihood is very high that the Lufeng sample is composed of one species that is more highly sexually dimorphic in the postcanine dentition than any extent primate species. If so, then the high levels of sexual dimorphism and intraspecific dental metric variation in this species violate the central assumption of methods that employ the coefficient of variation (CV) for paleotaxonomy, namely, that neither can lie outside the ranges observed among extant species. Thus, we further conclude that the CV must be used with caution when evaluating the taxonomic composition of fossil samples and, further, that it cannot be used to falsify a single-species hypothesis in any meaningful way. Other fossil hominoid samples with high measures of dental variation may indicate that considerable sexual size dimorphism typified many Eurasian middle–late Miocene hominoids.     

Metric variation and sexual dimorphism in the dentition of Ouranopithecus macedoniensis

The fossil sample attributed to the late Miocene hominoid taxon Ouranopithecus macedoniensis is characterized by a high degree of dental metric variation. As a result, some researchers support a multiple-species taxonomy for this sample. Other researchers do not think that the sample variation is too great to be accommodated within one species. This study examines variation and sexual dimorphism in mandibular canine and postcanine dental metrics of an Ouranopithecus sample. Bootstrapping (resampling with replacement) of extant hominoid dental metric data is performed to test the hypothesis that the coefficients of variation (CV) and the indices of sexual dimorphism (ISD) of the fossil sample are not significantly different from those of modern great apes. Variation and sexual dimorphism in Ouranopithecus M(1) dimensions were statistically different from those of all extant ape samples; however, most of the dental metrics of Ouranopithecus were neither more variable nor more sexually dimorphic than those of Gorilla and Pongo. Similarly high levels of mandibular molar variation are known to characterize other fossil hominoid species. The Ouranopithecus specimens are morphologically homogeneous and it is probable that all but one specimen included in this study are from a single population. It is unlikely that the sample includes specimens of two sympatric large-bodied hominoid species. For these reasons, a single-species hypothesis is not rejected for the Ouranopithecus macedoniensis material. Correlations between mandibular first molar tooth size dimorphism and body size dimorphism indicate that O. macedoniensis and other extinct hominoids were more sexually size dimorphic than any living great apes, which suggests that social behaviors and life history profiles of these species may have been different from those of living species.     

Metric variation in the postcanine teeth from Paşalar, Turkey

The coefficient of variation (CV) has frequently been used to evaluate variation in a morphologically homogeneous fossil assemblage and to make inferences about its species composition. Comparisons of coefficients of variation in single- and mixed-species assemblages have typically involved mixed-species assemblages made up of an equal number of data points from two or more different species, but in reality, a fossil assemblage may be biased in favor of one or more of the component species. In this paper, we evaluate the effects of unequal species composition in mixed-species assemblages on CV distributions by carrying out an extensive series of resampling experiments. The experiments were designed to replicate a paleontological situation in which the species affiliation of particular specimens is not known. We use this technique to explore the pattern of metric variation in the postcanine dental assemblage from the middle Miocene site of Pa?alar in a comparative context. The distributions of CVs from mixed assemblages that are heavily biased toward one species may be characterized by a greater range of CVs, increased skewing, and a tail of low values, but only heavily biased assemblages comprising species that differ markedly in size could be reliably identified on this basis. Evidence from the simulated CV distributions supports nonmetric evidence in indicating that the Pa?alar assemblage represents a heavily biased assemblage of two species that are similar in size but not entirely overlapping in the size distributions of their postcanine teeth.     

Metric and non-metric randomization methods, geographic variation, and the single-species hypothesis for Asian and African Homo erectus

This paper proposes a statistical test of the single-species hypothesis using non-metric characters as a complement to statistical tests using more traditional metric characters. The sample examined is that of Asian and African Homo erectus. The paleoanthropological community is divided on the taxonomic distinction of these fossils, with workers arguing both for and against the species-level distinction between Asian and African populations. Previous arguments have focused on patterns of apparent morphological differentiation between the African and Asian cranial samples. To assess this question, three tests were performed that compared the range of variation in the fossil sample to a single-species group with a similar geographic distribution; this comparative sample was composed of 221 modern humans from Africa and Asia. For the first test, 23 metric characters were analyzed on the fossil and comparative samples. Using resampling procedures, the variation for these characters was examined, recreating 1000 samples from the human analogs and comparing the CV distributions of these samples to the CVs of the fossil group. The second test used the metric data to calculate a Euclidean distance between the African and Asian fossil samples. This distance was compared to a distribution of Euclidean distances calculated between 1000 randomly selected samples of African and Asian modern humans. For the third test, a grading scale was created for ten non-metric characters that encompassed the total morphological variation found in the fossil and modern human samples. The Manhattan distance between the Asian and African fossil samples was calculated and compared to a distribution of distances calculated between 1000 randomly selected samples of African and Asian moderns. The first two tests, using the metric data, failed to falsify the null hypothesis. However, in the third test, using non-metric data, the total Manhattan distance for the fossil sample approached the 100th percentile of the resampled distances calculated from the moderns. The implications of the contrasting results are discussed.     

Does brain size variability provide evidence of multiple species in Homo habilis?

Endocranial volume (ECV) variability as measured by the coefficient of variation (CV) has been important in supporting the view that more than one species is represented in Homo habilis. Supporters of this view used a CV of 10 as a standard to determine that 1) the H. habilis CV of 12.7 indicates multiple species and 2) there is a low probability of H. habilis specimens KNM-ER 1470 and KNM-ER 1813 being members of the same taxon. This study examines published data for ECVs of fossil and extant hominoids to determine whether CV yields any information regarding species number in H. habilis. Results indicate that there is no empirical basis for using a CV of 10 as a standard to detect multiple species in H. habilis. Also, geography, time, sample choice, sex ratio, and measurement technique are complicating factors that must be considered when interpreting CVs for fossil samples. Additionally, the broad 95% statistical confidence limits (5.1-20.3) indicate that the CV estimate of 12.7 for H. habilis is not sufficiently reliable to allow biologically meaningful interpretation. However, if the CV for H. habilis is actually 12.7, it still falls within the range of variation for single species of modern hominoids. The evidence from ECV variability does not support the argument for multiple species in H. habilis.     

An odontometric assessment of variability inAustralopithecus afarensis

Odontometric data are utilized to investigate both the extent of variation in the Pliocene hominid remains from Hadar and Laetoli and whether this variation is best explained as resulting from sexual dimorphism or from the presence of more than one species in the sample. Coefficients of variation for the Hadar/Laetoli dental elements are compared with those from other established Plio-Pleistocene hominid taxa and extant pongids. Results indicate that while CVs for the central cheek teeth (M1/1 and M2/2) tend to be rather high, the variability does not consistently exceed ranges of variability for extant anthropoids and other primate species. Thus odontometric data do not disprove the null hypothesis that the Hadar/Laetoli sample can be accommodated within a single species. Therefore, although the Hadar/Laetoli sample tends to exhibit less canine variability than is found among sexually dimorphic apes, odontometric variation in this sample is more likely due to sexual dimorphism than the presence of multiple taxa in the sample.     

Testing the taxonomic integrity of Paranthropus boisei sensu stricto

The craniodental hypodigm of Paranthropus boisei sensu stricto is morphologically distinctive, but it has been suggested that the substantial variation in mandibular and dental size in that hypodigm may exceed that which is reasonable to subsume within a single hominin species. In this study, Fligner and Killeen, coefficient of variation (CV)-based and average taxonomic distance (ATD)-based bootstrap tests, were used to compare variation in size and shape of the mandibular corpus remains attributed to P. boisei s.s. with the variation observed in samples of great apes and modern humans. The degree of size variation in the P. boisei s.s. mandibular hypodigm is never observed in human and chimpanzee samples, is rare in gorillas, but is not uncommon in orangutans. However, the shape variation in the fossil group is comparable to the variation in the extant reference groups. Although the size variation in P. boisei s.s. is substantial, it is exaggerated by the effects of taphonomy. The small mandibles are more often abraded, whereas the large mandibles are more likely to have been infiltrated with matrix. On the basis of the results of this investigation of the mandibular corpus, there are no grounds for rejecting the "single-species" hypothesis for P. boisei s.s. When Sokal and Braumann's adjusted CV values were used to predict the index of sexual dimorphism (ISD) for the P. boisei s.s., despite the substantial geological time embraced by the mandibular corpus hypodigm, the predicted value of lnISD, when corrected for taphonomic factors, is comparable to the sexual dimorphism observed within Gorilla.     

Human taxonomic diversity in the pleistocene: Does Homo erectus represent multiple hominid species?

Recently, nomina such as “Homo heidelbergensis” and “H. ergaster” have been resurrected to refer to fossil hominids that are perceived to be specifically distinct from Homo sapiens and Homo erectus. This results in a later human fossil record that is nearly as speciose as that documenting the earlier history of the family Hominidae. However, it is agreed that there remains only one extant hominid species: H. sapiens. Has human taxonomic diversity been significantly pruned over the last few hundred millennia, or have the number of taxa been seriously overestimated? To answer this question, the following null hypothesis is tested: polytypism was established relatively early and the species H. erectus can accommodate all spatio-temporal variation from ca. 1.7 to 0.5 Ma. A disproof of this hypothesis would suggest that modern human polytypism is a very recent phenomenon and that speciation throughout the course of human evolution was the norm and not the exception. Cranial variation in a taxonomically mixed sample of fossil hominids, and in a modern human sample, is analyzed with regard to the variation present in the fossils attributed to H. erectus. The data are examined using both univariate (coefficient of variation) and multivariate (determinant) analyses. Employing randomization methodology to offset the small size and non-normal distribution of the fossil samples, the CV and determinant results reveal a pattern and degree of variation in H. erectus that most closely approximates that of the single species H. sapiens. It is therefore concluded that the null hypothesis cannot be rejected. © 1993 Wiley-Liss, Inc.     

Analysis of the probability of multiple taxa in a combined sample of swartkrans and kromdraai dental material

It has been argued (Grine, [1988] Evolutionary History of the “Robust” Australopithecines [New York. Aldine de Gruyter], pp. 223–243) that the australopithecine material from Swartkrans and Kromdraai represents distinct species. In an attempt to test the validity of separate taxa at Swartkrans and Kromdraai, Cope's (Cope [1989] Systematic Variation in Cercopithecus Dental Samples [Austin: University of Texas]) method of analysis was adapted and utilized. This procedure includes an analysis of the coefficients of variation (CVs) of the individual posterior teeth (buccal-lingual breadth) of a combined fossil sample compared with the CVs of several known single taxon reference groups. The Cope and Lacy (Cope and Lacy [1992] Am. J. Phys. Anthropol. 89:359–378) simulation technique was also employed in the analysis. Based on these analyses, there is no justification for a taxonomic separation between the australopithecine material from Swartkrans and Kromdraai. Therefore, the assertion that the Swartkrans and Kromdraai material represent two distinct species is not indicated by the available dental metric evidence. © 1996 Wiley-Liss, Inc.     

Habiline variation: A new approach using STET

The problem of whether the hominid fossil sample of habiline specimens is comprised of more than one species has received much attention in paleoanthropology. The core of this debate has critical implications about when and how variation can be explained by taxonomy. In this paper, we examine the problem of whether the observed variation in habiline samples reflects species differences. We test the null hypothesis of no difference by examining the degree of variability in habiline sample in comparison with other single-species early hominid fossil samples from Sterkfontein and Swartkrans (Sterkfontein is earlier than the habiline sample, Swartkrans may be within the habiline time span). We developed a new method for this examination, which we call STandard Error Test of the null hypothesis of no difference (STET). Our sampling statistic is based on the standard error of the slope of regressions between pairs of specimens, relating all of the homologous measurements that each pair shares. We show that the null hypothesis for the habiline sample cannot be rejected. The similarities of specimen pairs within the habiline sample are not more than those observed between the specimens in the australopithecine samples we analyzed.     

Variation in the Habiline Crania – Must it be Taxonomic?

The problem of whether the hominid fossil sample of habiline specimens is comprised of more than one species has received much attention in paleoanthropology. The core of this debate has significant implications about when and how variation must be explained by taxonomy. In this paper, we examine the problem of whether the observed variation in habiline sample must be interpreted to reflect species differences. We test the null hypothesis of no difference by examining the degree of variability in habiline sample in comparison with other single-species early hominid fossil samples from Sterkfontein and Swartkrans (Sterkfontein is earlier than the habiline sample; Swartkrans may be within the habiline time span). We use the standard error test for this analysis, a sampling statistic based on the standard error of the slope of regressions between pairs of specimens that relates all of the homologous measurements each pair shares. We show that the null hypothesis for the habiline sample cannot be rejected. The similarities of specimen pairs within the habiline sample are not more than those observed between the specimens in the two australopithecine samples we analyzed.     

Temporal trends and metric variation in the mandibles and dentition of Australopithecus afarensis

The Pliocene hominin samples from Hadar and Laetoli are thought to represent one species, Australopithecus afarensis, that exhibits stasis throughout its temporal range and has high levels of skeletal sexual dimorphism. In this paper, we test the hypothesis of stasis in dental and mandibular dimensions using nonparametric rank correlation methods to detect temporal trends and randomization tests to evaluate their statistical significance. We then use two methods (CV resampling; Fligner-Killeen test) to compare overall levels of variation in the fossil sample to those of extant hominoid species. Together, these analyses allow us to gauge the effects of changes through time on variation in mandibles and teeth of A. afarensis.P(3)mesiodistal length, M(3)size, and canine shape change through time but do not appear unusually variable in the sample as a whole. These temporal trends possibly reflect differences between the Laetoli and Hadar site-samples. For mandibles, a pronounced trend towards greater corpus size occurs late in the temporal sequence and contributes to high levels of variation compared to African apes. These results show that significant directional changes do occur in the A. afarensis mandibles and teeth, and in these elements, at least, the species is not static. Temporal variation is clearly an important component of overall variation in the A. afarensis lineage, even though other factors, such as sexual dimorphism, may also play a part.     

Brief communication: Is variation in the cranial capacity of the Dmanisi sample too high to be from a single species?

This study uses data resampling to test the null hypothesis that the degree of variation in the cranial capacity of the Dmanisi hominid sample is within the range variation of a single species. The statistical significance of the variation in the Dmanisi sample is examined using simulated distributions based on comparative samples of modern humans, chimpanzees, and gorillas. Results show that it is unlikely to find the maximum difference observed in the Dmanisi sample in distributions of female-female pairs from comparative single-species samples. Given that two sexes are represented, the difference in the Dmanisi sample is not enough to reject the null hypothesis of a single species. Results of this study suggest no compelling reason to invoke multiple taxa to explain variation in the cranial capacity of the Dmanisi hominids.     

Patterns of tooth crown size and shape variation in great apes and humans and species recognition in the hominid fossil record

It has been suggested that patterns of craniodental variation in living hominids (Gorilla, Homo, Pan, and Pongo) may be useful for evaluating variation in fossil hominid assemblages. Using this approach, a fossil sample exhibiting a pattern of variation that deviates from one shared among living taxa would be regarded as taxonomically heterogeneous. Here we examine patterns of tooth crown size and shape variation in great apes and humans to determine 1) if these taxa share a pattern of dental variation, and 2) if such a pattern can reliably discriminate between samples that contain single species and those that contain multiple species. We use parametric and nonparametric correlation methods to establish the degree of pattern similarity among taxa, and randomization tests to assess their statistical significance. The results of this study show that extant hominids do not share a pattern of dental size variation, and thus these taxa cannot be used to generate expectations for patterns of size variation in fossil hominid species. The hominines (Gorilla, Homo, and Pan) do share a pattern of shape variation in the mandibular dentition; however, Pongo is distinct, and thus it is unclear which, if either, pattern should be expected in fossil hominids. Moreover, in this case, most combined-species samples exhibit patterns of shape variation that are similar to those for single hominine species samples. Thus, although a common pattern of shape variation is present in the mandibular dentition, it is not useful for recognizing taxonomically mixed paleontological samples.     

Using extant patterns of dental variation to identify species in the primate fossil record: a case study of middle Eocene <Emphasis Type="Italic">Omomys</Emphasis> from the Bridger Basin,southwestern Wyoming

Patterns of extant primate dental variation provide important data for interpreting taxonomic boundaries in fossil forms. Here I use dental data from several well-known living primates (as well as data from selected Eocene forms) to evaluate dental variation in Middle Eocene Omomys, the first North American fossil primate identified by paleontologists. Measurements were collected from a sample of 148 omomyid dental specimens recovered from Bridger B localities in the Bridger Basin, Wyoming. Most of these specimens have not previously been described. Nonmetric traits were also scored for this sample. Lower molar coefficients of variation range from 4.01 for M₂ length (n = 80) to 6.73 for M₃ talonid width (n = 57). All of the nonmetric traits scored exhibit less than 100% presence in the overall sample, including traits previously described as representative of Omomys (e.g., P₄ metaconids present in 91%, n = 55; M² pericones present in 80%, n = 15). Dental traits also vary in a set of spatially restricted localities from the same fossil horizon and in a separate, single fossil locality (DMNH 868, P₄ metaconids present in 67%, n = 6). An increasing frequency in several premolar traits across time in these more restricted samples suggests an anagenetic change in Bridger B Omomys. However, this degree of morphological variability is consistent with that seen in extant primate species from single locations. Metric variation in this sample is comparable to that seen in other Eocene primates, such as new data presented here for the omomyid Arapahovius gazini from the Washakie Basin, southern Wyoming. Omomys metric variation is also comparable to that found in several samples of well-known extant primates from single localities (e.g., ring-tailed lemurs and gray–brown mouse lemurs). These metric data also correspond to the patterns of variability described in previously published studies of Omomys carteri. In sum, a single species interpretation (O. carteri) for this new Bridger B Omomys sample from southern Wyoming is affirmed, and this study illustrates the usefulness of dental data from extant primates for evaluating primate fossil samples.     

Dental metric comparisons of Morotopithecus and Afropithecus: implications for the validity of the genus Morotopithecus

Morotopithecus bishopi and Afropithecus turkanensis are two large-bodied hominoid primates from early Miocene deposits of eastern Africa. Researchers have used both cranial and postcranial characters to distinguish these two species. Unfortunately, of the fossil material attributed to each, only the face, palate, and upper dentition are preserved well enough in both species for direct comparisons. There are currently no known directly comparable postcranial elements. In this study, we reevaluated dental characters argued to distinguish the type specimens of Morotopithecus from Afropithecus: relative size of the upper premolars and M3. Exact randomization methods were used to address two questions. First, is it possible to find the degree of dental-size difference observed between Morotopithecus (UMP 62-11) and Afropithecus (KNM-WK 16999) within extant African hominoids? Second, what is the probability of observing the levels of difference found between the fossils among pairs of extant individuals? Metric differences in relative premolar and M3 size were calculated between all possible pairs within the extant sample and the observed difference of the fossil pair was then compared to the resulting distribution of extant pairs. The observed size differences for all comparisons in the fossil teeth were well within the variation observed in the extant African hominoid samples (p>0.05). In light of these results and other currently available cranial evidence, we suggest that the type specimens of Morotopithecus and Afropithecus are not different enough to support taxonomic distinction.     

Hominoid dental variability and species number at the late Miocene site of Lufeng,China

The large hominoid sample from the late Miocene site of Lufeng, China, has been variously claimed to contain either one or two species, but very few metric data in support of either position have been published. We calculate coefficients of variation for the dental remains both for the two presumed species and for the pooled sample as a whole using the summary statistics published by Wu & Oxnard (Wu & Oxnard: American Journal of Primatology 5:303–344, 1983a, Nature 306:258–260, 1983b). These are compared to the same measures of single-sex and combined-sex samples of extant hominoids. We also present metric characterizations of male and female canines of extant great apes, with which we evaluate the gender composition of the Lufeng canine sample. In a two-species alternative, the two presumed species have measures of variability and canine representation that are more compatible with single-sex samples representing males and females, respectively. The pooled dental sample has measures of variability within the ranges of single species of extant great apes. We conclude there is a single large hominoid species represented at Lufeng that is highly sexually dimorphic. The phylogenetic relationships of this species are briefly considered. It is generally primitive in craniodental morhpology and is unlikely to be a member of the Sivapithecus-Pongo clade.     

Population systematics of chimpanzees using molar morphometrics

When dental morphological variation within extant species is used as a guideline to partition variation within fossil samples into species, the underlying assumption is that fossil species are equivalent to extant species. This is the case despite the fact that dental morphology, which is commonly used to differentiate fossil species, is rarely used to differentiate extant species. Aspects of external morphology, ecology, behavior, breeding patterns, and molecular structure that are used to delineate living species are generally not available for fossils. In this paper, the utility of dental evidence for sorting fossil samples into species is evaluated by testing whether molar occlusal morphology is capable of sorting populations of Pan into the species and subspecies already well-established by nondental evidence. The dentitions of 341 chimpanzee individuals, sampled from regions throughout equatorial Africa, were sorted into 16 populations using rivers to demarcate the boundaries between populations. Digital-imaging software was used to measure 15 traits on the occlusal surface of each upper molar and 19 on each lower molar. After applying size adjustments, size-transformed and untransformed variables were subjected to discriminant analysis, with separate analyses carried out for each molar type. Results indicate that populations of Pan troglodytes and Pan paniscus are well differentiated at all molar positions. Populations of P. t. verus are distinct from other populations of P. troglodytes. Populations of P. t. troglodytes and P. t. schweinfurthii show close dental similarity. A distinct population is recognized at the Nigeria-Cameroon border, indicating the presence of P. t. vellerosus. The concordance between the patterns of diversity recognized by this study and other molecular and nonmolecular studies indicates that paleontological species that are similar to species of Pan in terms of size and patterns of diversification may be differentiated using molar morphology.