Similarity of genetic and phenotypic variation patterns among populations is important for making quantitative inferences about past evolutionary forces acting to differentiate populations and for evaluating the evolution of relationships among traits in response to new functional and developmental relationships. Here, phenotypic co‐variance and correlation structure is compared among Platyrrhine Neotropical primates. Comparisons range from among species within a genus to the superfamily level. Matrix correlation followed by Mantel's test and vector correlation among responses to random natural selection vectors (random skewers) were used to compare correlation and variance/covariance matrices of 39 skull traits. Sampling errors involved in matrix estimates were taken into account in comparisons using matrix repeatability to set upper limits for each pairwise comparison. Results indicate that covariance structure is not strictly constant but that the amount of variance pattern divergence observed among taxa is generally low and not associated with taxonomic distance. Specific instances of divergence are identified. There is no correlation between the amount of divergence in covariance patterns among the 16 genera and their phylogenetic distance derived from a conjoint analysis of four already published nuclear gene datasets. In contrast, there is a significant correlation between phylogenetic distance and morphological distance (Mahalanobis distance among genus centroids). This result indicates that while the phenotypic means were evolving during the last 30 millions years of New World monkey evolution, phenotypic covariance structures of Neotropical primate skulls have remained relatively consistent. Neotropical primates can be divided into four major groups based on their feeding habits (fruit‐leaves, seed‐fruits, insect‐fruits, and gum‐insect‐fruits). Differences in phenotypic covariance structure are correlated with differences in feeding habits, indicating that to some extent changes in interrelationships among skull traits are associated with changes in feeding habits. Finally, common patterns and levels of morphological integration are found among Platyrrhine primates, suggesting that functional/developmental integration could be one major factor keeping covariance structure relatively stable during evolutionary diversification of South American monkeys.

Morphological integration refers to the modular structuring of inter-trait relationships in an organism, which could bias the direction and rate of morphological change, either constraining or facilitating evolution along certain dimensions of the morphospace. Therefore, the description of patterns and magnitudes of morphological integration and the analysis of their evolutionary consequences are central to understand the evolution of complex traits. Here we analyze morphological integration in the skull of several mammalian orders, addressing the following questions: are there common patterns of inter-trait relationships? Are these patterns compatible with hypotheses based on shared development and function? Do morphological integration patterns and magnitudes vary in the same way across groups? We digitized more than 3,500 specimens spanning 15 mammalian orders, estimated the correspondent pooled within-group correlation and variance/covariance matrices for 35 skull traits and compared those matrices among the orders. We also compared observed patterns of integration to theoretical expectations based on common development and function. Our results point to a largely shared pattern of inter-trait correlations, implying that mammalian skull diversity has been produced upon a common covariance structure that remained similar for at least 65 million years. Comparisons with a rodent genetic variance/covariance matrix suggest that this broad similarity extends also to the genetic factors underlying phenotypic variation. In contrast to the relative constancy of inter-trait correlation/covariance patterns, magnitudes varied markedly across groups. Several morphological modules hypothesized from shared development and function were detected in the mammalian taxa studied. Our data provide evidence that mammalian skull evolution can be viewed as a history of inter-module parcellation, with the modules themselves being more clearly marked in those lineages with lower overall magnitude of integration. The implication of these findings is that the main evolutionary trend in the mammalian skull was one of decreasing the constraints to evolution by promoting a more modular architecture.

Changes in patterns and magnitudes of integration may influence the ability of a species to respond to selection. Consequently, modularity has often been linked to the concept of evolvability, but their relationship has rarely been tested empirically. One possible explanation is the lack of analytical tools to compare patterns and magnitudes of integration among diverse groups that explicitly relate these aspects to the quantitative genetics framework. We apply such framework here using the multivariate response to selection equation to simulate the evolutionary behavior of several mammalian orders in terms of their flexibility, evolvability and constraints in the skull. We interpreted these simulation results in light of the integration patterns and magnitudes of the same mammalian groups, described in a companion paper. We found that larger magnitudes of integration were associated with a blur of the modules in the skull and to larger portions of the total variation explained by size variation, which in turn can exert a strong evolutionary constraint, thus decreasing the evolutionary flexibility. Conversely, lower overall magnitudes of integration were associated with distinct modules in the skull, to smaller fraction of the total variation associated with size and, consequently, to weaker constraints and more evolutionary flexibility. Flexibility and constraints are, therefore, two sides of the same coin and we found them to be quite variable among mammals. Neither the overall magnitude of morphological integration, the modularity itself, nor its consequences in terms of constraints and flexibility, were associated with absolute size of the organisms, but were strongly associated with the proportion of the total variation in skull morphology captured by size. Therefore, the history of the mammalian skull is marked by a trade-off between modularity and evolvability. Our data provide evidence that, despite the stasis in integration patterns, the plasticity in the magnitude of integration in the skull had important consequences in terms of evolutionary flexibility of the mammalian lineages.

Similarity of genetic and phenotypic variation patterns among populations is important for making quantitative inferences about past evolutionary forces acting to differentiate populations and for evaluating the evolution of relationships among traits in response to new functional and developmental relationships. Here, phenotypic co variance and correlation structure is compared among Platyrrhine Neotropical primates. Comparisons range from among species within a genus to the superfamily level. Matrix correlation followed by Mantel's test and vector correlation among responses to random natural selection vectors (random skewers) were used to compare correlation and variance/covariance matrices of 39 skull traits. Sampling errors involved in matrix estimates were taken into account in comparisons using matrix repeatability to set upper limits for each pairwise comparison. Results indicate that covariance structure is not strictly constant but that the amount of variance pattern divergence observed among taxa is generally low and not associated with taxonomic distance. Specific instances of divergence are identified. There is no correlation between the amount of divergence in covariance patterns among the 16 genera and their phylogenetic distance derived from a conjoint analysis of four already published nuclear gene datasets. In contrast, there is a significant correlation between phylogenetic distance and morphological distance (Mahalanobis distance among genus centroids). This result indicates that while the phenotypic means were evolving during the last 30 millions years of New World monkey evolution, phenotypic covariance structures of Neotropical primate skulls have remained relatively consistent. Neotropical primates can be divided into four major groups based on their feeding habits (fruit-leaves, seed-fruits, insect-fruits, and gum-insect-fruits). Differences in phenotypic covariance structure are correlated with differences in feeding habits, indicating that to some extent changes in interrelationships among skull traits are associated with changes in feeding habits. Finally, common patterns and levels of morphological integration are found among Platyrrhine primates, suggesting that functional/developmental integration could be one major factor keeping covariance structure relatively stable during evolutionary diversification of South American monkeys.

New World monkeys (NWM) display substantial variation (two orders of magnitude) in body size. Despite this, variation in skull size and associated shape show a conserved allometric relationship, both within and between genera. Maximum likelihood estimates of quantitative ancestral states were used to compare the direction of morphological differentiation with the phenotypic (p(max)) and genetic (g(max)) lines of least evolutionary resistance (LLER). Diversification in NWM skulls occurred principally along the LLER defined by size variation. We also obtained measures of morphological amount and pace of change using our skull data together with published genetic distances to test whether the LLER influenced the amount and pace of diversification. Moreover, data on an ecological factor (diet) was obtained from the literature and used to test the association of this niche-related measure with the morphological diversification. Two strategies were used to test the association of LLER with the morphological and dietary amount and pace of change, one focusing on both contemporary genera and maximum likelihood reconstructed ancestors and the other using only the 16 contemporary genera in a phylogenetic comparative analysis. Our results suggest that the LLER influenced the path, amount, and pace of morphological change. Evolution also occurred away from the LLER in some taxa but this occurred at a slower pace and resulted in a relatively low amount of morphological change. We found that longer branch lengths (time) are associated with larger differences in p(max) orientation. However, on a macroevolutionary scale there is no such trend. Diet is consistently associated with both absolute size differences and morphological integration patterns, and we suggest that this ecological factor might be driving adaptive radiation in NWM. Invasion of diet-based adaptive zones involves changes in absolute size, due to metabolic and foraging constraints, resulting in simple allometric skull diversification along the LLER. While it is clear that evolutionary change occurred along the LLER, it is not clear whether this macroevolutionary pattern results from a conservation of within-population genetic covariance patterns or long-term adaptation along a size dimension or whether both constraints and selection were inextricably involved.

Comparisons of covariance patterns are becoming more common as interest in the evolution of relationships between traits and in the evolutionary phenotypic diversification of clades have grown. We present parallel analyses of covariance matrix similarity for cranial traits in 14 New World Monkey genera using the Random Skewers (RS), T-statistics, and Common Principal Components (CPC) approaches. We find that the CPC approach is very powerful in that with adequate sample sizes, it can be used to detect significant differences in matrix structure, even between matrices that are virtually identical in their evolutionary properties, as indicated by the RS results. We suggest that in many instances the assumption that population covariance matrices are identical be rejected out of hand. The more interesting and relevant question is, How similar are two covariance matrices with respect to their predicted evolutionary responses? This issue is addressed by the random skewers method described here.

Abstract. New World monkeys (NWM) display substantial variation (two orders of magnitude) in body size. Despite this, variation in skull size and associated shape show a conserved allometric relationship, both within and between genera. Maximum likelihood estimates of quantitative ancestral states were used to compare the direction of morphological differentiation with the phenotypic (p max ) and genetic (g max ) lines of least evolutionary resistance (LLER). Diversification in NWM skulls occurred principally along the LLER defined by size variation. We also obtained measures of morphological amount and pace of change using our skull data together with published genetic distances to test whether the LLER influenced the amount and pace of diversification. Moreover, data on an ecological factor (diet) was obtained from the literature and used to test the association of this niche-related measure with the morphological diversification. Two strategies were used to test the association of LLER with the morphological and dietary amount and pace of change, one focusing on both contemporary genera and maximum likelihood reconstructed ancestors and the other using only the 16 contemporary genera in a phylogenetic comparative analysis. Our results suggest that the LLER influenced the path, amount, and pace of morphological change. Evolution also occurred away from the LLER in some taxa but this occurred at a slower pace and resulted in a relatively low amount of morphological change. We found that longer branch lengths (time) are associated with larger differences in p max orientation. However, on a macroevolutionary scale there is no such trend. Diet is consistently associated with both absolute size differences and morphological integration patterns, and we suggest that this ecological factor might be driving adaptive radiation in NWM. Invasion of diet-based adaptive zones involves changes in absolute size, due to metabolic and foraging constraints, resulting in simple allometric skull diversification along the LLER. While it is clear that evolutionary change occurred along the LLER, it is not clear whether this macroevolutionary pattern results from a conservation of within-population genetic covariance patterns or long-term adaptation along a size dimension or whether both constraints and selection were inextricably involved.

The study of the genetic variance/covariance matrix (G-matrix) is a recent and fruitful approach in evolutionary biology, providing a window of investigating for the evolution of complex characters. Although G-matrix studies were originally conducted for microevolutionary timescales, they could be extrapolated to macroevolution as long as the G-matrix remains relatively constant, or proportional, along the period of interest. A promising approach to investigating the constancy of G-matrices is to compare their phenotypic counterparts (P-matrices) in a large group of related species; if significant similarity is found among several taxa, it is very likely that the underlying G-matrices are also equivalent. Here we study the similarity of covariance and correlation structure in a broad sample of Old World monkeys and apes (Catarrhini). We made phylogenetically structured comparisons of correlation and covariance matrices derived from 39 skull traits, ranging from between species to the superfamily level. We also compared the overall magnitude of integration between skull traits (r2) for all Catarrhini genera. Our results show that P-matrices were not strictly constant among catarrhines, but the amount of divergence observed among taxa was generally low. There was significant and positive correlation between the amount of divergence in correlation and covariance patterns among the 30 genera and their phylogenetic distances derived from a recently proposed phylogenetic hypothesis. Our data demonstrate that the P-matrices remained relatively similar along the evolutionary history of catarrhines, and comparisons with the G-matrix available for a New World monkey genus (Saguinus) suggests that the same holds for all anthropoids. The magnitude of integration, in contrast, varied considerably among genera, indicating that evolution of the magnitude, rather than the pattern of inter-trait correlations, might have played an important role in the diversification of the catarrhine skull.