What affects the predictability of evolutionary constraints using a G‐matrix? The relative effects of modular pleiotropy and mutational correlation

Phenotypic traits do not always respond to selection independently from each other and often show correlated responses to selection. The structure of a genotype‐phenotype map (GP map) determines trait covariation, which involves variation in the degree and strength of the pleiotropic effects of the underlying genes. It is still unclear, and debated, how much of that structure can be deduced from variational properties of quantitative traits that are inferred from their genetic (co) variance matrix ( G ‐matrix). Here we aim to clarify how the extent of pleiotropy and the correlation among the pleiotropic effects of mutations differentially affect the structure of a G ‐matrix and our ability to detect genetic constraints from its eigen decomposition. We show that the eigenvectors of a G ‐matrix can be predictive of evolutionary constraints when they map to underlying pleiotropic modules with correlated mutational effects. Without mutational correlation, evolutionary constraints caused by the fitness costs associated with increased pleiotropy are harder to infer from evolutionary metrics based on a G ‐matrix's geometric properties because uncorrelated pleiotropic effects do not affect traits' genetic correlations. Correlational selection induces much weaker modular partitioning of traits' genetic correlations in absence then in presence of underlying modular pleiotropy.     

Integration and Evolvability in Primate Hands and Feet

Morphological integration theory predicts that sets of phenotypic traits that covary strongly due to developmental and/or functional connections between them eventually co-evolve because of a coordinated response to selection, and accordingly become less independently evolvable. This process is not irreversible, however, and phenotypic traits can become less integrated, and hence more independently evolvable, in the context of selection for divergent functions and morphologies. This study examines the reciprocal relationship between shared function, integration and evolvability by comparing integration patterns among serially homologous skeletal elements in the hands and feet of a functionally diverse sample of catarrhine primates. Two hypotheses are tested: (1) species in which the autopods are functionally more similar (e.g. quadrupedal monkeys) have more strongly integrated autopods than species in which the autopods are functionally divergent (e.g. gibbons, humans) and (2) the latter have autopods that are more evolvable, collectively and independently. Morphometric data from selected hand and foot digital rays were used to derive phenotypic variance/covariance matrices. The strength of integration among autopods was quantified using eigenanalysis and a measure of trait variational autonomy. Evolvability was estimated by subjecting phenotypic variance/covariance matrices to simulated random selection gradients, and comparing evolutionary responses among species. Results indicate that integration decreases as hands and feet become functionally divergent, and that the strongly integrated hand and foot skeletons of quadrupedal monkeys respond to selection in a highly collinear manner, even when simulated selective pressures acting on each autopod are in opposite directions in phenotypic space. Results confirm that the evolvability of morphological traits depends largely on how strongly they covary with other traits, but also with body size. The role of pleiotropy as a developmental mechanism underlying integration and evolvability is also discussed.     

The Evolution of Modularity in the Mammalian Skull II: Evolutionary Consequences

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.     

Measuring Evolutionary Constraints Through the Dimensionality of the Phenotype: Adjusted Bootstrap Method to Estimate Rank of Phenotypic Covariance Matrices

The potential and direction of phenotypic evolution is constrained by the distribution of genetic variation for the traits as described by the phenotypic (P) and genetic covariance matrices (G). The rank of the covariance matrix reflects the number of independent variational dimensions of the phenotype. Covariance matrices with less than full rank indicate lack of variation in some directions of the phenotype space and thus are an indication of absolute evolutionary constraints. Because selection acts upon phenotypic variation, the rank of P represents the upper limit of the dimensionality in G, relevant for selection response. The limitations of current methods to estimate matrix rank motivated us to analyze and adjust a bootstrap method and evaluate its performance by simulation. The results show that the modified bootstrap method (ABRE) gives reliable and rather conservative rank estimates when the sample size is sufficient for the number of variables studied (the sample size is at least five-fold the number of variables). Applying the method to various datasets suggests high phenotypic dimensionality in all cases. The analysis thus provides no evidence for absolute evolutionary constraints. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Morphological evolution through integration: a quantitative study of cranial integration in Homo, Pan, Gorilla and Pongo

Morphological integration refers to coordinated variation among traits that are closely related in development and/or function. Patterns of integration can offer important insight into the structural relationship between phenotypic units, providing a framework to address questions about phenotypic evolvability and constraints. Integrative features of the primate cranium have recently become a popular subject of study. However, an important question that still remains under-investigated is: what is the pattern of cranial shape integration among closely related hominoids? To address this question, we conducted a Procrustes-based geometric morphometrics study to quantify and analyze shape covariation patterns between different cranial regions in Homo, Pan, Gorilla and Pongo. A total of fifty-six 3D landmarks were collected on 407 adult individuals. We then sub-divided the landmarks corresponding to cranial units as outlined in the ‘functional matrix hypothesis.’ Sub-dividing the cranium in this manner allowed us to explore patterns of covariation between the face, basicranium and cranial vault, using the two-block partial least squares approach. Our results suggest that integrated shape changes in the hominoid cranium are complex, but that the overall pattern of integration is similar among human and non-human apes. Thus, despite having very distinct morphologies the way in which the face, basicranium and cranial vault covary is shared among these taxa. These results imply that the pattern of cranial integration among hominoids is conserved.     

Modularity and intra-floral integration in metameric organisms: plants are more than the sum of their parts

Within-individual variation in virtually every conceivable morphological and functional feature of reiterated structures is a pervasive feature of plant phenotypes. In particular, architectural effects, regular, repeatable patterns of intra-individual variation in form and function that are associated with position are nearly ubiquitous. Yet, flowers also are predicted to be highly integrated. For animal-pollinated plants, the coordination of multiple organs within each flower is required to achieve the complex functions of pollinator attraction and orientation, pollen donation and pollen receipt. To the extent that pollinators may select for multiple independent functions, phenotypic integration within flowers may also be modular. That is, subsets of floral structures may be integrated but vary independently of other subsets of structures that are themselves integrated. How can phenotypic integration and modularity be understood within the context of architectural effects? This essay reviews recent research on patterns of floral integration and modularity and explores the potential for spatial and temporal changes in the selective environment of individual flowers to result in positional variation in patterns of morphological integration.     

Why the short face? Developmental disintegration of the neurocranium drives convergent evolution in neotropical electric fishes

Convergent evolution is widely viewed as strong evidence for the influence of natural selection on the origin of phenotypic design. However, the emerging evo‐devo synthesis has highlighted other processes that may bias and direct phenotypic evolution in the presence of environmental and genetic variation. Developmental biases on the production of phenotypic variation may channel the evolution of convergent forms by limiting the range of phenotypes produced during ontogeny. Here, we study the evolution and convergence of brachycephalic and dolichocephalic skull shapes among 133 species of Neotropical electric fishes (Gymnotiformes: Teleostei) and identify potential developmental biases on phenotypic evolution. We plot the ontogenetic trajectories of neurocranial phenotypes in 17 species and document developmental modularity between the face and braincase regions of the skull. We recover a significant relationship between developmental covariation and relative skull length and a significant relationship between developmental covariation and ontogenetic disparity. We demonstrate that modularity and integration bias the production of phenotypes along the brachycephalic and dolichocephalic skull axis and contribute to multiple, independent evolutionary transformations to highly brachycephalic and dolichocephalic skull morphologies.     

Typology now: homology and developmental constraints explain evolvability

By linking the concepts of homology and morphological organization to evolvability, this paper attempts to (1) bridge the gap between developmental and phylogenetic approaches to homology and to (2) show that developmental constraints and natural selection are compatible and in fact complementary. I conceive of a homologue as a unit of morphological evolvability, i.e., as a part of an organism that can exhibit heritable phenotypic variation independently of the organism’s other homologues. An account of homology therefore consists in explaining how an organism’s developmental constitution results in different homologues/characters as units that can evolve independently of each other. The explanans of an account of homology is developmental, yet the very explanandum is an evolutionary phenomenon: evolvability in a character-by-character fashion, which manifests itself in phylogenetic patterns as recognized by phylogenetic approaches to homology. While developmental constraints and selection have often been viewed as antagonistic forces, I argue that both are complementary as they concern different parts of the evolutionary process. Developmental constraints, conceived of as the presence of the same set of homologues across phenotypic change, pertain to how heritable variation can be generated in the first place (evolvability), while natural selection operates subsequently on the produced variation.

Complex adaptation and system structure

The structural organization of biological systems is one of nature’s most fascinating aspects, but its origin and functional role is not yet fully understood. For instance, basic adaptational mechanisms like genetic mutation and Hebbian adaptation seem to be generic and invariant across many species and are, on their own, fairly well investigated and understood. However, it is the organism’s structure – the representations these mechanisms act upon – that bears the complex functional effects of these mechanisms. While typical technical approaches to system design require detailed problem models and suffer from the need to explicitly take care of all possible cases, the organization of biological systems seems to induce inherent adaptability, flexibility and robustness. In this discussion paper we address the concept of structured variability, particularly the role of system structure as implementing a certain representation on which basic variational mechanisms act on. The functional adaptability (or search distribution) depends crucially on this representation.