Examination of Sample Size Determination in Integration Studies Based on the Integration Coefficient of Variation (ICV)

Reduced limb integration characterizes primate clades with diverse locomotor adaptations

Hominoids exhibit a strikingly diverse set of locomotor adaptations-including knuckle-walking, brachiation, quadrumanuous suspension, and striding bipedalism-while also possessing morphologies associated with forelimb suspension. It has been suggested that changes in limb element integration facilitated the evolution of diverse locomotor modes by reducing covariation between serial homologs and allowing the evolution of a greater diversity of limb lengths. Here, I compare limb element integration in hominoids with that of other primate taxa, including two that have converged with them in forelimb morphology, Ateles and Pygathrix. Ateles is part of a clade that, such as hominoids, exhibits diverse locomotor adaptations, whereas Pygathrix is an anomaly in a much more homogeneous (in terms of locomotor adaptations) clade. I find that all atelines (and possibly all atelids), not just Ateles, share reduced limb element integration with hominoids. Pygathrix does not, however, instead resembling other members of its own family. Indriids also seem to have higher limb integration than apes, despite using their forelimbs and hindlimbs in divergent ways, although there is more uncertainty in this group due to poor sample size. These results suggest that reduced limb integration is characteristic of certain taxonomic groups with high locomotor diversity rather than taxa with specific, specialized locomotor adaptations. This is consistent with the hypothesis that reduced integration serves to open new areas of morphospace to those clades while suggesting that derived locomotion with divergent demands on limbs is not necessarily associated with reduced limb integration.

Morphology, evolution, and the whole organism imperative: Why evolutionary questions need multi-trait evolutionary quantitative genetics

Since Washburn's New Physical Anthropology, researchers have sought to understand the complexities of morphological evolution among anatomical regions in human and non-human primates. Researchers continue, however, to preferentially use comparative and functional approaches to examine complex traits, but these methods cannot address questions about evolutionary process and often conflate function with fitness. Moreover, researchers also tend to examine anatomical elements in isolation, which implicitly assumes independent evolution among different body regions. In this paper, we argue that questions asked in primate evolution are best examined using multiple anatomical regions subjected to model-bound methods built from an understanding of evolutionary quantitative genetics. A nascent but expanding number of studies over the last two decades use this approach, examining morphological integration, evolvability, and selection modeling. To help readers learn how to use these methods, we review fundamentals of evolutionary processes within a quantitative genetic framework, explore the importance of neutral evolutionary theory, and explain the basics of evolutionary quantitative genetics, namely the calculation of evolutionary potential for multiple traits in response to selection. Leveraging these methods, we demonstrate their use to understand non-independence in possible evolutionary responses across the limbs, limb girdles, and basicranium of humans. Our results show that model-bound quantitative genetic methods can reveal unexpected genetic covariances among traits that create a novel but measurable understanding of evolutionary complexity among multiple traits. We advocate for evolutionary quantitative genetic methods to be a standard whenever appropriate to keep studies of primate morphological evolution relevant for the next seventy years and beyond.

Morphological integration of the hominoid postcranium

Previous research has suggested that magnitudes of integration may be distinct in the postcranium of hominoids when compared to other primate species. To test this hypothesis, we estimated and compared magnitudes of integration of eight postcranial bones from three-dimensional surface scans for 57 Hylobates lar, 58 Gorilla gorilla, 60 Pan troglodytes, 60 Homo sapiens, 60 Chlorocebus pygerythrus, and 60 Macaca fascicularis. We tested the hypotheses that 1) magnitudes of integration would be distinct in the postcranium of hominoids compared to cercopithecoids, with the explicit prediction that magnitudes of integration would be lower in hominoids than in cercopithecoids, and 2) girdle elements (scapula, os coxa) would have lower magnitudes of integration across all taxa. Integration was quantified using the integration coefficient of variation from interlandmark distances reflecting anatomical and developmental modules defined according to a priori criteria. A resampling protocol was employed to generate distributions of integration values that were then compared statistically using Mann-Whitney U tests with Bonferroni adjustment. Support for hypothesis 1 was mixed: with the exception of Gorilla, hominoid taxa were less integrated than the cercopithecoids for all anatomical modules. However, Homo, Gorilla, and, to a lesser extent, Pan showed higher integration than Hylobates and the cercopithecoids for homologous limb elements, with magnitudes of integration for both modules being lowest for Hylobates. These results generally support the hypothesis of distinct patterns of magnitudes of integration in the hominoid postcranium. The high integration of Gorilla may be explained by the effects of overall body size. The results supported the predictions of the second hypothesis. Regardless of taxon, the os coxa and scapula were generally the least integrated skeletal elements, while the femur and radius were the most integrated. The lower integration of the girdle elements suggests that the geometric complexities of particular elements may significantly influence study outcomes.

Morphological integration in the hominid midfoot

The calculation of morphological integration across living apes and humans may provide important insights into the potential influence of integration on evolutionary trajectories in the hominid lineage. Here, we quantify magnitudes of morphological integration among and within elements of the midfoot in great apes and humans to examine the link between locomotor differences and trait covariance. We test the hypothesis that the medial elements of the great ape foot are less morphologically integrated with one another compared to humans based on their abducted halluces, and aim to determine how adaptations for midfoot mobility/stiffness and locomotor specialization influence magnitudes of morphological integration. The study sample is composed of all cuneiforms, the navicular, the cuboid, and metatarsals 1-5 of Homo sapiens (n = 80), Pan troglodytes (n = 63), Gorilla gorilla (n = 39), and Pongo sp. (n = 41). Morphological integration was quantified using the integration coefficient of variation of interlandmark distances organized into sets of a priori-defined modules. Magnitudes of integration across these modules were then compared against sets of random traits from the whole midfoot. Results show that all nonhuman apes have less integrated medial elements, whereas humans have highly integrated medial elements, suggesting a link between hallucal abduction and reduced levels of morphological integration. However, we find considerable variation in magnitudes of morphological integration across metatarsals 2-5, the intermediate and lateral cuneiform, the cuboid, and navicular, emphasizing the influence of functional and nonfunctional factors in magnitudes of integration. Lastly, we find that humans and orangutans show the lowest overall magnitudes of integration in the midfoot, which may be related to their highly specialized functions, and suggest a link between strong diversifying selection and reduced magnitudes of morphological integration.

Statistics of eigenvalue dispersion indices: Quantifying the magnitude of phenotypic integration

Analysis of trait covariation plays a pivotal role in the study of phenotypic evolution. The magnitude of covariation is often quantified with statistics based on dispersion of eigenvalues of a covariance or correlation matrix-eigenvalue dispersion indices. This study clarifies the statistical justifications of these statistics and elaborates on their sampling properties. The relative eigenvalue variance of a covariance matrix is known in the statistical literature a test statistic for sphericity, and thus is an appropriate measure of eccentricity of variation. The same of a correlation matrix is equal to the average squared correlation, which has a straightforward interpretation as a measure of integration. Here, expressions for the mean and variance of these statistics are analytically derived under multivariate normality, clarifying the effects of sample size N, number of variables p, and parameters on sampling bias and error. Simulations confirm that approximations involved are reasonably accurate with a moderate sample size (N ≥ 16-64). Importantly, sampling properties of these indices are not adversely affected by a high p:N ratio, promising their utility in high-dimensional phenotypic analyses. They can furthermore be applied to shape variables and phylogenetically structured data with appropriate modifications.

Examination of magnitudes of integration in the catarrhine vertebral column

The evolution of novel vertebral morphologies observed in humans and other extant hominoids may be related to changes in the magnitudes and/or patterns of covariation among traits. To examine this, we tested magnitudes of integration in the vertebral column of cercopithecoids and hominoids, including humans. Three-dimensional surface scans of 14 vertebral elements from 30 Cercopithecus, 32 Chlorocebus, 39 Macaca, 45 Hylobates, 31 Pan, and 86 Homo specimens were used. A resampling method was used to generate distributions of integration coefficient of variation scores for vertebral elements individually using interlandmark distances. Interspecific comparisons of mean integration coefficient of variation were conducted using Mann-Whitney U tests with Bonferroni adjustment. The results showed that hominoids generally had lower mean integration coefficient of variation than cercopithecoids. In addition, humans showed lower mean integration coefficient of variation than other hominoids in their last thoracic and lumbar vertebrae. Cercopithecoids and Hylobates showed relatively lower mean integration coefficient of variation in cervical vertebrae than in thoracolumbar vertebrae. Pan and Homo showed relatively lower mean integration coefficient of variation in the last thoracic and lumbar vertebrae in the thoracolumbar region, except for the L1 of Pan. The results suggest fewer integration-mediated constraints on the evolution of vertebral morphology in hominoids when compared with cercopithecoids. The weaker magnitudes of integration in lumbar vertebrae in humans when compared with chimpanzees likewise suggest fewer constraints on the evolution of novel lumbar vertebrae morphology in humans.