The phenotypic and genetic covariance structure of drosphilid wings

Evolutionary constraint results from the interaction between the distribution of available genetic variation and the position of selective optima. The availability of genetic variance in multitrait systems, as described by the additive genetic variance-covariance matrix (G), has been the subject of recent attempts to assess the prevalence of genetic constraints. However, evolutionary constraints have not yet been considered from the perspective of the phenotypes available to multivariate selection, and whether genetic variance is present in all phenotypes potentially under selection. Determining the rank of the phenotypic variance-covariance matrix (P) to characterize the phenotypes available to selection, and contrasting it with the rank of G, may provide a general approach to determining the prevalence of genetic constraints. In a study of a laboratory population of Drosophila bunnanda from northern Australia we applied factor-analytic modeling to repeated measures of individual wing phenotypes to determine the dimensionality of the phenotypic space described by P. The phenotypic space spanned by the 10 wing traits had 10 statistically supported dimensions. In contrast, factor-analytic modeling of G estimated for the same 10 traits from a paternal half-sibling breeding design suggested G had fewer dimensions than traits. Statistical support was found for only five and two genetic dimensions, describing a total of 99% and 72% of genetic variance in wing morphology in females and males, respectively. The observed mismatch in dimensionality between P and G suggests that although selection might act to shift the intragenerational population mean toward any trait combination, evolution may be restricted to fewer dimensions.     

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.     

The quantitative genetics of floral trait variation in Lobelia: potential constraints on adaptive evolution

Abstract Although pollinator-mediated natural selection has been measured on many floral traits and in many species, the extent to which selection is constrained from producing optimal floral phenotypes is less frequently studied. In particular, negative correlations between flower size and flower number are hypothesized to be a major constraint on the evolution of floral displays, yet few empirical studies have documented such a trade-off. To determine the potential for genetic constraints on the adaptive evolution of floral displays, I estimated the quantitative genetic basis of floral trait variation in two populations of Lobelia siphilitica . Restricted maximum likelihood (REML) analyses of greenhouse-grown half-sib families were used to estimate genetic variances and covariances for flower number and six measures of flower size. There was significant genetic variation for all seven floral traits in both populations. Flower number was negatively genetically correlated with four measures of flower size in one population and three measures in the other. When the genetic variance-covariance matrices were combined with field estimates of phenotypic selection gradients, the predicted multivariate evolutionary response was less than or opposite in sign to the selection gradient for flower number and five of six measures of flower size, suggesting genetic constraints on the evolution of these traits. More generally, my results indicate that the adaptive evolution of floral displays can be constrained by tradeoffs between flower size and number, as has been assumed by many theoretical models of floral evolution.     

Studying phenotypic evolution using multivariate quantitative genetics

Quantitative genetics provides a powerful framework for studying phenotypic evolution and the evolution of adaptive genetic variation. Central to the approach is G, the matrix of additive genetic variances and covariances. G summarizes the genetic basis of the traits and can be used to predict the phenotypic response to multivariate selection or to drift. Recent analytical and computational advances have improved both the power and the accessibility of the necessary multivariate statistics. It is now possible to study the relationships between G and other evolutionary parameters, such as those describing the mutational input, the shape and orientation of the adaptive landscape, and the phenotypic divergence among populations. At the same time, we are moving towards a greater understanding of how the genetic variation summarized by G evolves. Computer simulations of the evolution of G, innovations in matrix comparison methods, and rapid development of powerful molecular genetic tools have all opened the way for dissecting the interaction between allelic variation and evolutionary process. Here I discuss some current uses of G, problems with the application of these approaches, and identify avenues for future research.     

Population divergence along lines of genetic variance and covariance in the invasive plant Lythrum salicaria in eastern North America

Evolution during biological invasion may occur over contemporary timescales, but the rate of evolutionary change may be inhibited by a lack of standing genetic variation for ecologically relevant traits and by fitness trade-offs among them. The extent to which these genetic constraints limit the evolution of local adaptation during biological invasion has rarely been examined. To investigate genetic constraints on life-history traits, we measured standing genetic variance and covariance in 20 populations of the invasive plant purple loosestrife (Lythrum salicaria) sampled along a latitudinal climatic gradient in eastern North America and grown under uniform conditions in a glasshouse. Genetic variances within and among populations were significant for all traits; however, strong intercorrelations among measurements of seedling growth rate, time to reproductive maturity and adult size suggested that fitness trade-offs have constrained population divergence. Evidence to support this hypothesis was obtained from the genetic variance-covariance matrix (G) and the matrix of (co)variance among population means (D), which were 79.8% (95% C.I. 77.7-82.9%) similar. These results suggest that population divergence during invasive spread of L. salicaria in eastern North America has been constrained by strong genetic correlations among life-history traits, despite large amounts of standing genetic variation for individual traits.     

HOMOGENEITY OF THE GENETIC VARIANCE-COVARIANCE MATRIX FOR ANTIPREDATOR TRAITS IN TWO NATURAL POPULATIONS OF THE GARTER SNAKE THAMNOPHIS ORDINOIDES

Quantitative genetic models of evolution rely on the genetic variance-covariance matrix to predict the phenotypic response to selection. Both prospective and retrospective studies of phenotypic evolution across generations rely on assumptions about the constancy of patterns of genetic covariance through time. In the absence of robust theoretical predictions about the stability of genetic covariances, this assumption must be tested with empirical comparisons of genetic parameters among populations and species. Genetic variance-covariance matrices were estimated for a suite of antipredator traits in two populations of the northwestern garter snake, Thamnophis ordinoides. The characters studied include color pattern and antipredator behaviors that interact to facilitate escape from predators. Significant heritabilities for all traits were detected in both populations. Genetic correlations and covariances were found among behaviors in both populations and between color pattern and behavior in one of the populations. Phenotypic means differed among populations, but pairwise comparisons revealed no heterogeneity of genetic parameters between the populations. The structure of the genetic variance-covariance matrix has apparently not changed significantly during the divergence of these two populations.     

Large body size in an island-dwelling bird: a microevolutionary analysis

Island races of passerine birds display repeated evolution towards larger body size compared with their continental ancestors. The Capricorn silvereye (Zosterops lateralis chlorocephalus) has become up to six phenotypic standard deviations bigger in several morphological measures since colonization of an island approximately 4000 years ago. We estimated the genetic variance-covariance (G) matrix using full-sib and 'animal model' analyses, and selection gradients, for six morphological traits under field conditions in three consecutive cohorts of nestlings. Significant levels of genetic variance were found for all traits. Significant directional selection was detected for wing and tail lengths in one year and quadratic selection on culmen depth in another year. Although selection gradients on many traits were negative, the predicted evolutionary response to selection of these traits for all cohorts was uniformly positive. These results indicate that the G matrix and predicted evolutionary responses are consistent with those of a population evolving in the manner observed in the island passerine trend, that is, towards larger body size.     

Independent axes of genetic variation and parallel evolutionary divergence of opercle bone shape in threespine stickleback

Evolution of similar phenotypes in independent populations is often taken as evidence of adaptation to the same fitness optimum. However, the genetic architecture of traits might cause evolution to proceed more often toward particular phenotypes, and less often toward others, independently of the adaptive value of the traits. Freshwater populations of Alaskan threespine stickleback have repeatedly evolved the same distinctive opercle shape after divergence from an oceanic ancestor. Here we demonstrate that this pattern of parallel evolution is widespread, distinguishing oceanic and freshwater populations across the Pacific Coast of North America and Iceland. We test whether this parallel evolution reflects genetic bias by estimating the additive genetic variance-covariance matrix (G) of opercle shape in an Alaskan oceanic (putative ancestral) population. We find significant additive genetic variance for opercle shape and that G has the potential to be biasing, because of the existence of regions of phenotypic space with low additive genetic variation. However, evolution did not occur along major eigenvectors of G, rather it occurred repeatedly in the same directions of high evolvability. We conclude that the parallel opercle evolution is most likely due to selection during adaptation to freshwater habitats, rather than due to biasing effects of opercle genetic architecture.     

Stability of the G-matrix in a population experiencing pleiotropic mutation, stabilizing selection, and genetic drift

Abstract. Quantitative genetics theory provides a framework that predicts the effects of selection on a phenotype consisting of a suite of complex traits. However, the ability of existing theory to reconstruct the history of selection or to predict the future trajectory of evolution depends upon the evolutionary dynamics of the genetic variance-covariance matrix (G-matrix). Thus, the central focus of the emerging field of comparative quantitative genetics is the evolution of the G-matrix. Existing analytical theory reveals little about the dynamics of G, because the problem is too complex to be mathematically tractable. As a first step toward a predictive theory of G-matrix evolution, our goal was to use stochastic computer models to investigate factors that might contribute to the stability of G over evolutionary time. We were concerned with the relatively simple case of two quantitative traits in a population experiencing stabilizing selection, pleiotropic mutation, and random genetic drift. Our results show that G-matrix stability is enhanced by strong correlational selection and large effective population size. In addition, the nature of mutations at pleiotropic loci can dramatically influence stability of G. In particular, when a mutation at a single locus simultaneously changes the value of the two traits (due to pleiotropy) and these effects are correlated, mutation can generate extreme stability of G. Thus, the central message of our study is that the empirical question regarding G-matrix stability is not necessarily a general question of whether G is stable across various taxonomic levels. Rather, we should expect the G-matrix to be extremely stable for some suites of characters and unstable for others over similar spans of evolutionary time.     

Comparing G: multivariate analysis of genetic variation in multiple populations

The additive genetic variance–covariance matrix (G) summarizes the multivariate genetic relationships among a set of traits. The geometry of G describes the distribution of multivariate genetic variance, and generates genetic constraints that bias the direction of evolution. Determining if and how the multivariate genetic variance evolves has been limited by a number of analytical challenges in comparing G-matrices. Current methods for the comparison of G typically share several drawbacks: metrics that lack a direct relationship to evolutionary theory, the inability to be applied in conjunction with complex experimental designs, difficulties with determining statistical confidence in inferred differences and an inherently pair-wise focus. Here, we present a cohesive and general analytical framework for the comparative analysis of G that addresses these issues, and that incorporates and extends current methods with a strong geometrical basis. We describe the application of random skewers, common subspace analysis, the 4th-order genetic covariance tensor and the decomposition of the multivariate breeders equation, all within a Bayesian framework. We illustrate these methods using data from an artificial selection experiment on eight traits in Drosophila serrata, where a multi-generational pedigree was available to estimate G in each of six populations. One method, the tensor, elegantly captures all of the variation in genetic variance among populations, and allows the identification of the trait combinations that differ most in genetic variance. The tensor approach is likely to be the most generally applicable method to the comparison of G-matrices from any sampling or experimental design.     

Quantifying natural seasonal variation in mutation parameters with mutation accumulation lines

Mutations create novel genetic variants, but their contribution to variation in fitness and other phenotypes may depend on environmental conditions. Furthermore, natural environments may be highly heterogeneous. We assessed phenotypes associated with survival and reproductive success in over 30,000 plants representing 100 mutation accumulation lines of Arabidopsis thaliana across four temporal environments at a single field site. In each of the four assays, environmental variance was substantially larger than mutational variance. For some traits, whether mutational variance was significantly varied between seasons. The founder genotype had mean trait values near the mean of the distribution of the mutation accumulation lines in all field experiments. New mutations also contributed more phenotypic variation than would be predicted, given phenotypic and sequence‐level divergence among natural populations of A. thaliana. The combination of large environmental variance with a mean effect of mutation near zero suggests that mutations could contribute substantially to standing genetic variation.     

HIERARCHICAL COMPARISON OF GENETIC VARIANCE-COVARIANCE MATRICES. II COASTAL-INLAND DIVERGENCE IN THE GARTER SNAKE,THAMNOPHIS ELEGANS

The time-scale for the evolution of additive genetic variance-covariance matrices (G-matrices) is a crucial issue in evolutionary biology. If the evolution of G-matrices is slow enough, we can use standard multivariate equations to model drift and selection response on evolutionary time scales. We compared the G-matrices for meristic traits in two populations of gaiter snakes (Thamnophis elegans) with an apparent separation time of 2 million years. Despite considerable divergence in the meristic traits, foraging habits, and diet, these populations show conservation of structure in their G-matrices. Using Flury's hierarchial approach to matrix comparisons, we found that the populations have retained the principal components (eigenvectors) of their G-matrices, but their eigenvalues have diverged. In contrast, we were unable to reject the hypothesis of equal environmental matrices (E-matrices) for these populations. We propose that a conserved pattern of multivariate stabilizing selection may have contributed to conservation of G- and E-matrix structure during the divergence of these populations.     

Fitness effects of mutation: testing genetic redundancy in Arabidopsis thaliana

Screens of organisms with disruptive mutations in a single gene often fail to detect phenotypic consequences for the majority of mutants. One explanation for this phenomenon is that the presence of paralogous loci provides genetic redundancy. However, it is also possible that the assayed traits are affected by few loci, that effects could be subtle or that phenotypic effects are restricted to certain environments. We assayed a set of T‐DNA insertion mutant lines of Arabidopsis thaliana to determine the frequency with which mutation affected fitness‐related phenotypes. We found that between 8% and 42% of the assayed lines had altered fitness from the wild type. Furthermore, many of these lines exhibited fitness greater than the wild type. In a second experiment, we grew a subset of the lines in multiple environments and found whether a T‐DNA insert increased or decreased fitness traits depended on the assay environment. Overall, our evidence contradicts the hypothesis that genetic redundancy is a common phenomenon in A. thaliana for fitness traits. Evidence for redundancy from prior screens of knockout mutants may often be an artefact of the design of the phenotypic assays which have focused on less complex phenotypes than fitness and have used single environments. Finally, our study adds to evidence that beneficial mutations may represent a significant component of the mutational spectrum of A. thaliana.     

VARIATION IN DEVELOPMENTAL CONSTRAINTS IN SIGMODON

Developmental constraints can be interpreted as factors of developmental origin responsible for covariation among measured variables. Several hypotheses have been proposed to link the possession of such constraints to subsequent evolution. Using confirmatory factor analysis, we compare developmental factors across selected taxa of cotton rats, genus Sigmodon. Three factors explain well the covariation among orofacial measurements: (1) responses to body size variation, (1) coordinated growth of traits of the occluding-tooth complex, and (3) responses to musculoskeletal interactions. Sigmodon taxa share these factors, but differ in the variance-covariance matrix of factors, and the unique variances of individual traits. Patterns of covariation among measurements of the neurocranial complex reflect responses to body size variation, and perhaps also responses to fetal brain growth. While there are no significant differences across taxa in factorpattern, variance-covariance matrix of factors, or unique variance of measured neurocranial variables, the neurocranium is only weakly constrained. We doubt that even the relatively stronger developmental constraints on the orofacial complex would prevent evolutionary divergence because differences in the variances and covariances of factors, and in levels of unique variance of individual traits can provide different opportunities for selection to act in different Sigmodon taxa.     

Effects of selection and drift on G matrix evolution in a heterogeneous environment: a multivariate Qst-Fst Test with the freshwater snail Galba truncatula

Unraveling the effect of selection vs. drift on the evolution of quantitative traits is commonly achieved by one of two methods. Either one contrasts population differentiation estimates for genetic markers and quantitative traits (the Q(st)-F(st) contrast) or multivariate methods are used to study the covariance between sets of traits. In particular, many studies have focused on the genetic variance-covariance matrix (the G matrix). However, both drift and selection can cause changes in G. To understand their joint effects, we recently combined the two methods into a single test (accompanying article by Martin et al.), which we apply here to a network of 16 natural populations of the freshwater snail Galba truncatula. Using this new neutrality test, extended to hierarchical population structures, we studied the multivariate equivalent of the Q(st)-F(st) contrast for several life-history traits of G. truncatula. We found strong evidence of selection acting on multivariate phenotypes. Selection was homogeneous among populations within each habitat and heterogeneous between habitats. We found that the G matrices were relatively stable within each habitat, with proportionality between the among-populations (D) and the within-populations (G) covariance matrices. The effect of habitat heterogeneity is to break this proportionality because of selection for habitat-dependent optima. Individual-based simulations mimicking our empirical system confirmed that these patterns are expected under the selective regime inferred. We show that homogenizing selection can mimic some effect of drift on the G matrix (G and D almost proportional), but that incorporating information from molecular markers (multivariate Q(st)-F(st)) allows disentangling the two effects.     

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.     

Density dependence and population differentiation of genetic architecture in Impatiens capensis in natural environments

We identified environment-dependent constraints on the evolution of plasticity to density under natural conditions in two natural populations of Impatiens capensis. We also examined the expression of population divergence in genetic variance-covariance matrices in these natural environments. Inbred lines, originally collected from a sunny site with high seedling densities and a woodland site with low seedling densities, were planted in both original sites at natural high densities and at low density. Morphological and life-history characters were measured. More genetic variation for plastic responses to density was expressed in the sun site than in the woodland site, so the evolutionary potential of plasticity was greater in the sun site. Strong genetic correlations between the same character expressed at different densities and correlations among different characters could constrain the evolution of plasticity in both sites. Genetically based trade-offs in meristem allocation to vegetative growth and reproduction were apparent only in the high-resource environment with no overhead canopy and no intraspecific competition. Therefore, genetic constraints on the evolution of plasticity depended on the site and density in which plants were grown, and correlated responses to selection on plastic characters are also expected to differ between sites and densities. Population differentiation in genetic variance-covariance matrices was detected, but matrix structural differences, as opposed to proportional differences, were detected between populations only in the sun site at natural high density. Thus, population divergence in genetic architecture can occur rapidly and on a fine spatial scale, but the expression of such divergence may depend on the environment.     

OPTIMIZATION MODELS,QUANTITATIVE GENETICS,AND MUTATION

The process of selection on a multivariate set of characters subject to functional constraints is considered from the points of view of both evolutionary optimization theory and quantitative genetics. Special attention is given to life-history characteristics. It is shown that, under suitable conditions (including weak selection), useful approximate formulas for the relations between the functional constraints and the additive genetic variance-covariance matrix can be derived. These can be used to show that the conditions for equilibrium under selection according to the two different approaches are approximately equivalent. Although large negative genetic correlations are to be expected between some pairs of life-history traits in populations at equilibrium under selection, in general some small negative genetic correlations and some positive genetic correlations will also be present. Thus, the observation of a positive genetic correlation between a pair of life-history traits does not necessarily refute the possibility of trade-offs among a multivariate set of traits that contains the pair in question. The relation between the pattern of functional constraints and the genetic correlations is often complex, and little insight into the former can be derived from the latter. The effects of mutations that lower the overall efficiency of resource utilization, thereby creating a positive component to the genetic covariances among life-history traits, are also considered for a specific model. Although such mutations can have a substantial effect on the form of the life history, extreme conditions seem to be needed for them to produce a large effect on the pattern of genetic correlations in a random-mating population. They can, however, cause the appearance of positive correlations following inbreeding, due to the exposure of deleterious recessive or partially recessive mutations. The analysis also suggests that the population means of individual components of a constrained multivariate system may often equilibrate at values that are far from the optima that would be attained if they were selected in isolation from the other members of the system.     

The dimensionality of genetic variation for wing shape in Drosophila melanogaster

Absolute constraints are limitations on genetic variation that preclude evolutionary change in some aspect of the phenotype. Absolute constraints may reflect complete absence of variation, lack of genetic variation that extends the range of phenotypes beyond some limit, or lack of additive genetic variation. This last type of absolute constraint is bidirectional, because the mean cannot evolve to be larger or smaller. Most traits do possess genetic variation, so bidirectional absolute constraints are most likely to be detected in a multivariate context, where they would reflect combinations of traits, or dimensions in phenotype space that cannot evolve. A bidirectional absolute constraint will cause the additive genetic covariance matrix (G) to have a rank less than the number of traits studied. In this study, we estimate the rank of the G-matrix for 20 aspects of wing shape in Drosophila melanogaster. Our best estimates of matrix rank are 20 in both sexes. Lower 95% confidence intervals of rank are 17 for females and 18 for males. We therefore find little evidence of bidirectional absolute constraints. We discuss the importance of this result for resolving the relative roles of selection and drift processes versus constraints in the evolution of wing shape in Drosophila.     

Evolution and stability of the G-matrix on a landscape with a moving optimum

In quantitative genetics, the genetic architecture of traits, described in terms of variances and covariances, plays a major role in determining the trajectory of evolutionary change. Hence, the genetic variance-covariance matrix (G-matrix) is a critical component of modern quantitative genetics theory. Considerable debate has surrounded the issue of G-matrix constancy because unstable G-matrices provide major difficulties for evolutionary inference. Empirical studies and analytical theory have not resolved the debate. Here we present the results of stochastic models of G-matrix evolution in a population responding to an adaptive landscape with an optimum that moves at a constant rate. This study builds on the previous results of stochastic simulations of G-matrix stability under stabilizing selection arising from a stationary optimum. The addition of a moving optimum leads to several important new insights. First, evolution along genetic lines of least resistance increases stability of the orientation of the G-matrix relative to stabilizing selection alone. Evolution across genetic lines of least resistance decreases G-matrix stability. Second, evolution in response to a continuously changing optimum can produce persistent maladaptation for a correlated trait, even if its optimum does not change. Third, the retrospective analysis of selection performs very well when the mean G-matrix (G) is known with certainty, indicating that covariance between G and the directional selection gradient beta is usually small enough in magnitude that it introduces only a small bias in estimates of the net selection gradient. Our results also show, however, that the contemporary G-matrix only serves as a rough guide to G. The most promising approach for the estimation of G is probably through comparative phylogenetic analysis. Overall, our results show that directional selection actually can increase stability of the G-matrix and that retrospective analysis of selection is inherently feasible. One major remaining challenge is to gain a sufficient understanding of the G-matrix to allow the confident estimation of G.