MIPoD: a hypothesis-testing framework for microevolutionary inference from patterns of divergence

Despite the many triumphs of comparative biology during the past few decades, the field has remained strangely divorced from evolutionary genetics. In particular, comparative methods have failed to incorporate multivariate process models of microevolution that include genetic constraint in the form of the G matrix. Here we explore the insights that might be gained by such an analysis. A neutral model of evolution by genetic drift that depends on effective population size and the G matrix predicts a probability distribution for divergence of population trait means on a phylogeny. Use of a maximum likelihood (ML) framework then allows us to compare independent direct estimates of G with the ML estimates based on the observed pattern of trait divergence among taxa. We assess the departure from neutrality, and thus the role of different types of selection and other forces, in a stepwise hypothesis-testing procedure based on parameters for the size, shape, and orientation of G. We illustrate our approach with a test case of data on vertebral number evolution in garter snakes.     

The constancy of the G matrix through species divergence and the effects of quantitative genetic constraints on phenotypic evolution: a case study in crickets

Long-term phenotypic evolution can be modeled using the response-to-selection equation of quantitative genetics, which incorporates information about genetic constraints (the G matrix). However, little is known about the evolution of G and about its long-term importance in constraining phenotypic evolution. We first investigated the degree of conservation of the G matrix across three species of crickets and qualitatively compared the pattern of variation of G to the phylogeny of the group. Second, we investigated the effect of G on phenotypic evolution by comparing the direction of greatest quantitative genetic variation within species (g(max)) to the direction of phenotypic divergence between species (Delta(z)). Each species, Gryllus veletis, G. firmus, and G. pennsylvanicus, was reared in the laboratory using a full-sib breeding design to extract quantitative genetic information. Five morphological traits related to size were measured. G matrices were compared using three statistical approaches: the T method, the Flury hierarchy, and the MANOVA method. Results revealed that the differences between matrices were small and mostly caused by differences in the magnitude of the genetic variation, not by differences in principal component structure. This suggested that the G matrix structure of this group of species was preserved, despite significant phenotypic divergence across species. The small observed differences in G matrices across species were qualitatively consistent with genetic distances, whereas ecological information did not provide a good prediction of G matrix variation. The comparison of g(max) and Delta(z) revealed that the angle between these two vectors was small in two of three species comparisons, whereas the larger angle corresponding to the third species comparison was caused in large part by one of the five traits. This suggests that multivariate phenotypic divergence occurred mostly in a direction predicted by the direction of greatest genetic variation, although it was not possible to demonstrate the causal relationship from G to Delta(z). Overall, this study provided some support for the validity of the predictive power of quantitative genetics over evolutionary time scales.     

Genetic covariances promote climatic adaptation in Australian Drosophila*

Evolutionary potential for adaptation hinges upon the orientation of genetic variation for traits under selection, captured by the additive genetic variance-covariance matrix (G), as well as the evolutionary stability of G. Yet studies that assess both the stability of G and its alignment with selection are extraordinarily rare. We evaluated the stability of G in three Drosophila melanogaster populations that have adapted to local climatic conditions along a latitudinal cline. We estimated population- and sex-specific G matrices for wing size and three climatic stress-resistance traits that diverge adaptively along the cline. To determine how G affects evolutionary potential within these populations, we used simulations to quantify how well G aligns with the direction of trait divergence along the cline (as a proxy for the direction of local selection) and how genetic covariances between traits and sexes influence this alignment. We found that G was stable across the cline, showing no significant divergence overall, or in sex-specific subcomponents, among populations. G also aligned well with the direction of clinal divergence, with genetic covariances strongly elevating evolutionary potential for adaptation to climatic extremes. These results suggest that genetic covariances between both traits and sexes should significantly boost evolutionary responses to environmental change.     

Phylogenetic analysis of correlation structure in stalk-eyed flies (Diasemopsis,Diopsidae)

Morphological divergence among species may be constrained by the pattern of genetic variances and covariances among traits within species. Assessing the existence of such a relationship in nature requires information on the stability of intraspecific correlation and covariance structure and the correspondence of this structure to the pattern of evolutionary divergence within a lineage. Here, we investigate these issues for nine morphological traits and 15 species of stalk-eyed flies in the genus Diasemopsis. Within-species matrices for these traits were generated from phenotypic data for all the Diasemopsis species and from genetic data for a single Diasemopsis species, D. dubia. The among-species pattern of divergence was assessed by calculating the evolutionary correlations for all pairwise combinations of the morphological traits along the phylogeny of these species. Comparisons of intraspecific matrices reveal significant similarity among all species in the phenotypic correlations matrices but not the covariance matrices. In addition, the differences in correlation structure that do exist among species are not related to their phylogenetic placement or change in the means of the traits. Comparisons of the phenotypic and phylogenetic matrices suggest a strong relationship between the pattern of evolutionary change among species and both the intraspecific correlation structure and the stability of this structure among species. The phenotypic and the phylogenetic matrices are significantly similar, and pairs of traits whose intraspecific correlations are more stable across taxa exhibit stronger coevolution on the phylogeny. These results suggest either the existence of strong constraints on the pattern of evolutionary change or a consistent pattern of correlated selection shaping both the phenotypic and phylogenetic matrices. The genetic correlation structure for D. dubia, however, does not correspond with patterns found in the phenotypic and phylogenetic data. Possible reasons for this disagreement are discussed.     

Genetics of body shape and armour variation in threespine sticklebacks

Patterns of genetic variation and covariation can influence the rate and direction of phenotypic evolution. We explored the possibility that the parallel morphological evolution seen in threespine stickleback (Gasterosteus aculeatus) populations colonizing freshwater environments is facilitated by patterns of genetic variation and covariation in the ancestral (marine) population. We estimated the genetic (G) and phenotypic (P) covariance matrices and directions of maximum additive genetic (g(max) ) and phenotypic (p(max) ) covariances of body shape and armour traits. Our results suggest a role for the ancestral G in explaining parallel morphological evolution in freshwater populations. We also found evidence of genetic constraints owing to the lack of variance in the ancestral G. Furthermore, strong genetic covariances and correlations among traits revealed that selective factors responsible for threespine stickleback body shape and armour divergence may be difficult to disentangle. The directions of g(max) and p(max) were correlated, but the correlations were not high enough to imply that phenotypic patterns of trait variation and covariation within populations are very informative of underlying genetic patterns.     

An analysis of G matrix variation in two closely related cricket species,Gryllus firmus and G. pennsylvanicus

An important issue in evolutionary biology is understanding the pattern of G matrix variation in natural populations. We estimated four G matrices based on the morphological traits of two cricket species, Gryllus firmus and G. pennsylvanicus, each reared in two environments. We used three matrix comparison approaches, including the Flury hierarchy, to improve our ability to perceive all aspects of matrix variation. Our results demonstrate that different methods perceive different aspects of the matrices, which suggests that, until more is known about these methods, future studies should use several different statistical approaches. We also found that the differences in G matrices within a species can be larger than the differences between species. We conclude that the expression of the genetic architecture can vary with the environment and that future studies should compare G matrices across several environments. We also conclude that G matrices can be conserved at the level of closely related species.     

Characterizing the evolution of genetic variance using genetic covariance tensors

Determining how genetic variance changes under selection in natural populations has proved to be a very resilient problem in evolutionary genetics. In the same way that understanding the availability of genetic variance within populations requires the simultaneous consideration of genetic variance in sets of functionally related traits, determining how genetic variance changes under selection in natural populations will require ascertaining how genetic variance–covariance (G) matrices evolve. Here, we develop a geometric framework using higher-order tensors, which enables the empirical characterization of how G matrices have diverged among populations. We then show how divergence among populations in genetic covariance structure can then be associated with divergence in selection acting on those traits using key equations from evolutionary theory. Using estimates of G matrices of eight male sexually selected traits from nine geographical populations of Drosophila serrata, we show that much of the divergence in genetic variance occurred in a single trait combination, a conclusion that could not have been reached by examining variation among the individual elements of the nine G matrices. Divergence in G was primarily in the direction of the major axes of genetic variance within populations, suggesting that genetic drift may be a major cause of divergence in genetic variance among these populations.     

TYPE I ERROR RATES FOR TESTING GENETIC DRIFT WITH PHENOTYPIC COVARIANCE MATRICES: A SIMULATION STUDY

Studies of evolutionary divergence using quantitative genetic methods are centered on the additive genetic variance–covariance matrix ( G ) of correlated traits. However, estimating G properly requires large samples and complicated experimental designs. Multivariate tests for neutral evolution commonly replace average G by the pooled phenotypic within‐group variance–covariance matrix ( W ) for evolutionary inferences, but this approach has been criticized due to the lack of exact proportionality between genetic and phenotypic matrices. In this study, we examined the consequence, in terms of type I error rates, of replacing average G by W in a test of neutral evolution that measures the regression slope between among‐population variances and within‐population eigenvalues (the Ackermann and Cheverud [AC] test) using a simulation approach to generate random observations under genetic drift. Our results indicate that the type I error rates for the genetic drift test are acceptable when using W instead of average G when the matrix correlation between the ancestral G and P is higher than 0.6, the average character heritability is above 0.7, and the matrices share principal components. For less‐similar G and P matrices, the type I error rates would still be acceptable if the ratio between the number of generations since divergence and the effective population size (t/N_e) is smaller than 0.01 (large populations that diverged recently). When G is not known in real data, a simulation approach to estimate expected slopes for the AC test under genetic drift is discussed.     

Phenotypic divergence along lines of genetic variance

Natural populations inhabiting the same environment often independently evolve the same phenotype. Is this replicated evolution a result of genetic constraints imposed by patterns of genetic covariation? We looked for associations between directions of morphological divergence and the orientation of the genetic variance-covariance matrix (G) by using an experimental system of morphological evolution in two allopatric nonsister species of rainbow fish. Replicate populations of both Melanotaenia eachamensis and Melanotaenia duboulayi have independently adapted to lake versus stream hydrodynamic environments. The major axis of divergence (z) among all eight study populations was closely associated with the direction of greatest genetic variance (gmax), suggesting directional genetic constraint on evolution. However, the direction of hydrodynamic adaptation was strongly associated with vectors of G describing relatively small proportions of the total genetic variance, and was only weakly associated with gmax. In contrast, divergence between replicate populations within each habitat was approximately proportional to the level of genetic variance, a result consistent with theoretical predictions for neutral phenotypic divergence. Divergence between the two species was also primarily along major eigenvectors of G. Our results therefore suggest that hydrodynamic adaptation in rainbow fish was not directionally constrained by the dominant eigenvector of G. Without partitioning divergence as a consequence of the adaptation of interest (here, hydrodynamic adaptation) from divergence due to other processes, empirical studies are likely to overestimate the potential for the major eigenvectors of G to directionally constrain adaptive evolution.     

Concordance between stabilizing sexual selection,intraspecific variation,and interspecific divergence in Phymata

Empirical studies show that lineages typically exhibit long periods of evolutionary stasis and that relative levels of within‐species trait covariance often correlate with the extent of between‐species trait divergence. These observations have been interpreted by some as evidence of genetic constraints persisting for long periods of time. However, an alternative explanation is that both intra‐ and interspecific variation are shaped by the features of the adaptive landscape (e.g., stabilizing selection). Employing a genus of insects that are diverse with respect to a suite of secondary sex traits, we related data describing nonlinear phenotypic (sexual) selection to intraspecific trait covariances and macroevolutionary divergence. We found support for two key predictions (1) that intraspecific trait covariation would be aligned with stabilizing selection and (2) that there would be restricted macroevolutionary divergence in the direction of stabilizing selection. The observed alignment of all three matrices offers a point of caution in interpreting standing variability as metrics of evolutionary constraint. Our results also illustrate the power of sexual selection for determining variation observed at both short and long timescales and account for the apparently slow evolution of some secondary sex characters in this lineage.     

Convergent evolution of phenotypic integration and its alignment with morphological diversification in Caribbean Anolis ecomorphs

The adaptive landscape and the G-matrix are keys concepts for understanding how quantitative characters evolve during adaptive radiation. In particular, whether the adaptive landscape can drive convergence of phenotypic integration (i.e., the pattern of phenotypic variation and covariation summarized in the P-matrix) is not well studied. We estimated and compared P for 19 morphological traits in eight species of Caribbean Anolis lizards, finding that similarity in P among species was not correlated with phylogenetic distance. However, greater similarity in P among ecologically similar Anolis species (i.e., the trunk-ground ecomorph) suggests the role of convergent natural selection. Despite this convergence and relatively deep phylogenetic divergence, a large portion of eigenstructure of P is retained among our eight focal species. We also analyzed P as an approximation of G to test for correspondence with the pattern of phenotypic divergence in 21 Caribbean Anolis species. These patterns of covariation were coincident, suggesting that either genetic constraint has influenced the pattern of among-species divergence or, alternatively, that the adaptive landscape has influenced both G and the pattern of phenotypic divergence among species. We provide evidence for convergent evolution of phenotypic integration for one class of Anolis ecomorph, revealing yet another important dimension of evolutionary convergence in this group.     

Effects of migration on the genetic covariance matrix

In 1996, Schluter showed that the direction of morphological divergence of closely related species is biased toward the line of least genetic resistance, represented by g_max , the leading eigenvector of the matrix of genetic variance–covariance (the G -matrix). G is used to predict the direction of evolutionary change in natural populations. However, this usage requires that G is sufficiently constant over time to have enough predictive significance. Here, we explore the alternative explanation that G can evolve due to gene flow to conform to the direction of divergence between incipient species. We use computer simulations in a mainland–island migration model with stabilizing selection on two quantitative traits. We show that a high level of gene flow from a mainland population is required to significantly affect the orientation of the G -matrix in an island population. The changes caused by the introgression of the mainland alleles into the island population affect all aspects of the shape of G (size, eccentricity, and orientation) and lead to the alignment of g_max with the line of divergence between the two populations' phenotypic optima. Those changes decrease with increased correlation in mutational effects and with a correlated selection. Our results suggest that high migration rates, such as those often seen at the intraspecific level, will substantially affect the shape and orientation of G , whereas low migration (e.g., at the interspecific level) is unlikely to substantially affect the evolution of G .     

THE EVOLUTIONARY STABILITY OF CROSS‐SEX,CROSS‐TRAIT GENETIC COVARIANCES

Although knowledge of the selective agents behind the evolution of sexual dimorphism has advanced considerably in recent years, we still lack a clear understanding of the evolutionary durability of cross‐sex genetic covariances that often constrain its evolution. We tested the relative stability of cross‐sex genetic covariances for a suite of homologous contact pheromones of the fruit fly Drosophila serrata, along a latitudinal gradient where these traits have diverged in mean. Using a Bayesian framework, which allowed us to account for uncertainty in all parameter estimates, we compared divergence in the total amount and orientation of genetic variance across populations, finding divergence in orientation but not total variance. We then statistically compared orientation divergence of within‐sex ( G ) to cross‐sex ( B ) covariance matrices. In line with a previous theoretical prediction, we find that the cross‐sex covariance matrix, B , is more variable than either within‐sex G matrix. Decomposition of B matrices into their symmetrical and nonsymmetrical components revealed that instability is linked to the degree of asymmetry. We also find that the degree of asymmetry correlates with latitude suggesting a role for spatially varying natural selection in shaping genetic constraints on the evolution of sexual dimorphism.     

High evolutionary constraints limited adaptive responses to past climate changes in toad skulls

Interactions among traits that build a complex structure may be represented as genetic covariation and correlation. Genetic correlations may act as constraints, deflecting the evolutionary response from the direction of natural selection. We investigated the relative importance of drift, selection, and constraints in driving skull divergence in a group of related toad species. The distributional range of these species encompasses very distinct habitats with important climatic differences and the species are primarily distinguished by differences in their skulls. Some parts of the toad skull, such as the snout, may have functional relevance in reproductive ecology, detecting water cues. Thus, we hypothesized that the species skull divergence was driven by natural selection associated with climatic variation. However, given that all species present high correlations among skull traits, our second prediction was of high constraints deflecting the response to selection. We first extracted the main morphological direction that is expected to be subjected to selection by using within- and between-species covariance matrices. We then used evolutionary regressions to investigate whether divergence along this direction is explained by climatic variation between species. We also used quantitative genetics models to test for a role of random drift versus natural selection in skull divergence and to reconstruct selection gradients along species phylogeny. Climatic variables explained high proportions of between-species variation in the most selected axis. However, most evolutionary responses were not in the direction of selection, but aligned with the direction of allometric size, the dimension of highest phenotypic variance in the ancestral population. We conclude that toad species have responded to selection related to climate in their skulls, yet high evolutionary constraints dominated species divergence and may limit species responses to future climate change.     

Similarity in G matrix structure among natural populations of Arabidopsis lyrata

Understanding the stability of the G matrix in natural populations is fundamental for predicting evolutionary trajectories; yet, the extent of its spatial variation and how this impacts responses to selection remain open questions. With a nested paternal half‐sib crossing design and plants grown in a field experiment, we examined differences in the genetic architecture of flowering time, floral display, and plant size among four Scandinavian populations of Arabidopsis lyrata. Using a multivariate Bayesian framework, we compared the size, shape, and orientation of G matrices and assessed their potential to facilitate or constrain trait evolution. Flowering time, floral display and rosette size varied among populations and significant additive genetic variation within populations indicated potential to evolve in response to selection. Yet, some characters, including flowering start and number of flowers, may not evolve independently because of genetic correlations. Using a multivariate framework, we found few differences in the genetic architecture of traits among populations. G matrices varied mostly in size rather than shape or orientation. Differences in multivariate responses to selection predicted from differences in G were small, suggesting overall matrix similarity and shared constraints to trait evolution among populations.     

Population differentiation in G matrix structure due to natural selection in Rana temporaria

The additive genetic variance-covariance matrix (G) is a concept central to discussions about evolutionary change over time in a suite of traits. However, at the moment we do not know how fast G itself changes as a consequence of selection or how sensitive it is to environmental influences. We investigated possible evolutionary divergence and environmental influences on G using data from a factorial common-garden experiment where common frog (Rana temporaria) tadpoles from two divergent populations were exposed to three different environmental treatments. G-matrices were estimated using an animal model approach applied to data from a NCII breeding design. Matrix comparisons using both Flury and multivariate analysis of variance methods revealed significant differences in G matrices both between populations and between treatments within populations, the former being generally larger than the latter. Comparison of levels of population differentiation in trait means using Q(ST) indices with that observed in microsatellite markers (F(ST)) revealed that the former values generally exceeded the neutral expectation set by F(ST). Hence, the results suggest that intraspecific divergence in G matrix structure has occurred mainly due to natural selection.     

Morphological differentiation in Carduelis finches: Adaptive vs. constraint models

In this study we show that morphological diversification in the avian genus Carduelis (Carduelinae) has to a large extent been conservative. Using multivariate methods, we found only minor deviations from the common (ancestral) body-plan. In particular, variation in bill morphology was found to be more conservative than variation in other parts of the body. We argue that constraint models of population differentiation can successfully account for the variation in bill morphology in this genus, but are less successful in accounting for variation in other traits. This can be interpreted as a result of long-term overall stabilizing selection for a certain bill morphology which is related to the way the birds open seeds. A trait combination that is adaptive on the evolutionary time scale may thus act as a constraint on changes in bill morphology on the microevolutionary scale. We conclude that the most parsimonious explanation for low divergence in bill morphology in this genus is that all species have retained the ancestral bill morphology. This may mean that each species chooses its environment rather than being moulded by it. This argument seems to apply to bill morphology, but other traits studied in this genus appear to have evolved in a less constrained fashion. A new index of morphometric integration is introduced to describe covariance structures.     

HOW MUCH OF THE VARIATION IN ADAPTIVE DIVERGENCE CAN BE EXPLAINED BY GENE FLOW? AN EVALUATION USING LAKE‐STREAM STICKLEBACK PAIRS

Abstract How much of the variation in adaptive divergence can be explained by gene flow? The answer to this question should objectively reveal whether gene flow generally places a substantial constraint on evolutionary diversification. We studied multiple independent lake‐stream population pairs of threespine stickleback (Gasterosteus acu‐leatus). For each pair, we quantified adaptive divergence based on morphological traits that have a genetic basis and are subject to divergent selection. We then estimated gene flow based on variation at five unlinked microsatellite loci. We found a consistent and significant pattern for morphological divergence to be positively correlated with genetic divergence and negatively correlated with gene flow. Statistical significance and the amount of variation explained varied within and among traits: 36.1–74.1% for body depth and 11.8–51.7% for gill raker number. Variation within each trait was the result of differences among methods for estimating genetic divergence and gene flow. Variation among traits likely reflects different strengths of divergent selection. We conclude that gene flow has a substantial effect on adaptive divergence in nature but that the magnitude of this effect varies among traits. An alternative explanation is that cause and effect are reversed: adaptive divergence is instead constraining gene flow. This effect seems relatively unimportant for our system because genetic divergence and gene flow were not correlated with ecologically relevant habitat features of lakes (surface area) or streams (width, depth, flow, canopy openness).     

The evolution of sexual dimorphism in the house finch. I. Population divergence in morphological covariance structure

Abstract Patterns of genetic variation and covariation strongly affect the rate and direction of evolutionary change by limiting the amount and form of genetic variation available to natural selection. We studied evolution of morphological variance-covariance structure among seven populations of house finches (Carpodacus mexicanus) with a known phylogenetic history. We examined the relationship between within- and among-population covariance structure and, in particular, tested the concordance between hierarchical changes in morphological variance-covariance structure and phylogenetic history of this species. We found that among-population morphological divergence in either males or females did not follow the within-population covariance patterns. Hierarchical patterns of similarity in morphological covariance matrices were not congruent with a priori defined historical pattern of population divergence. Both of these results point to the lack of proportionality in morphological covariance structure of finch populations, suggesting that random drift alone is unlikely to account for observed divergence. Furthermore, drift alone cannot explain the sex differences in within- and among-population covariance patterns or sex-specific patterns of evolution of covariance structure. Our results suggest that extensive among-population variation in sexual dimorphism in morphological covariance structure was produced by population differences in local selection pressures acting on each sex.     

Testing the genetic constraint hypothesis in a phylogenetic context: a simulation study

Quantitative genetic theory predicts that when populations diverge by drift the interspecific divergence (D matrix), calculated from species means, will be proportional to the average value of the additive genetic variance-covariance matrix, or G matrix. Most empirical studies in which this hypothesis has been investigated have ignored phylogenetic nonindependence among included taxa. Baker and Wilkinson (2003; also Revell et al. 2007) used a test for constraint in which the D matrix is calculated from phylogenetically independent contrasts (Felsenstein 1985) instead of directly from the species means. I use computer simulations to show that, on average, when the process of evolution is genetic drift, the divergence matrix calculated from independent contrasts (D(IC)) is more highly correlated with G than is the divergence matrix calculated ignoring phylogenetic nonindependence (D). This effect is more pronounced when speciation is initially slow but increases over time than when speciation decreases over time. Finally, when evolution is primarily by drift but phenotype space is bounded (as if by functional constraint) the average correlation is decreased between both G and D or D(IC), however the correlation between G and D(IC) is much larger than between G and D. Although limited in scope, to my knowledge this is the first study to use individual-based quantitative genetic simulations in a phylogenetic context.