The evolution of trade-offs under directional and correlational selection

Using quantitative genetic theory, we develop predictions for the evolution of trade-offs in response to directional and correlational selection. We predict that directional selection favoring an increase in one trait in a trade-off will result in change in the intercept but not the slope of the trade-off function, with the mean value of the selected trait increasing and that of the correlated trait decreasing. Natural selection will generally favor an increase in some combination of trait values, which can be represented as directional selection on an index value. Such selection induces both directional and correlational selection on the component traits. Theory predicts that selection on an index value will also change the intercept but not the slope of the trade-off function but because of correlational selection, the direction of change in component traits may be in the same or opposite directions. We test these predictions using artificial selection on the well-established trade-off between fecundity and flight capability in the cricket, Gryllus firmus and compare the empirical results with a priori predictions made using genetic parameters from a separate half-sibling experiment. Our results support the predictions and illustrate the complexity of trade-off evolution when component traits are subject to both directional and correlational selection.     

Correlational selection leads to genetic integration of body size and an attractive plumage trait in dark-eyed juncos

When a trait's effect on fitness depends on its interaction with other traits, the resultant selection is correlational and may lead to the integration of functionally related traits. In relation to sexual selection, when an ornamental trait interacts with phenotypic quality to determine mating success, correlational sexual selection should generate genetic correlations between the ornament and quality, leading to the evolution of honest signals. Despite its potential importance in the evolution of signal honesty, correlational sexual selection has rarely been measured in natural populations. In the dark-eyed junco (Junco hyemalis), males with experimentally elevated values of a plumage trait (whiteness in the tail or "tail white") are more attractive to females and dominant in aggressive encounters over resources. We used restricted maximum-likelihood analysis of a long-term dataset to measure the heritability of tail white and two components of body size (wing length and tail length), as well as genetic correlations between pairs of these traits. We then used multiple regression to assess directional, quadratic, and correlational selection as they acted on tail white and body size via four components of lifetime fitness (juvenile and adult survival, mating success, and fecundity). We found a positive genetic correlation between tail white and body size (as measured by wing length), which indicates past correlational selection. Correlational selection, which was largely due to sexual selection on males, was also found to be currently acting on the same pair of traits. Larger males with whiter tails sired young with more females, most likely due to a combination of female choice, which favors males with whiter tails, and male-male competition, which favors both tail white and larger body size. To our knowledge, this is the first study to show both genetic correlations between sexually selected traits and currently acting correlational sexual selection, and we suggest that correlational sexual selection frequently may be an important mechanism for maintaining the honesty of sexual signals.     

Elimination of a genetic correlation between the sexes via artificial correlational selection

Genetic correlations between the sexes can constrain the evolution of sexual dimorphism and be difficult to alter, because traits common to both sexes share the same genetic underpinnings. We tested whether artificial correlational selection favoring specific combinations of male and female traits within families could change the strength of a very high between-sex genetic correlation for flower size in the dioecious plant Silene latifolia. This novel selection dramatically reduced the correlation in two of three selection lines in fewer than five generations. Subsequent selection only on females in a line characterized by a lower between-sex genetic correlation led to a significantly lower correlated response in males, confirming the potential evolutionary impact of the reduced correlation. Although between-sex genetic correlations can potentially constrain the evolution of sexual dimorphism, our findings reveal that these constraints come not from a simple conflict between an inflexible genetic architecture and a pattern of selection working in opposition to it, but rather a complex relationship between a changeable correlation and a form of selection that promotes it. In other words, the form of selection on males and females that leads to sexual dimorphism may also promote the genetic phenomenon that limits sexual dimorphism.     

CORRELATIONAL SELECTION FOR COLOR PATTERN AND ANTIPREDATOR BEHAVIOR IN THE GARTER SNAKE THAMNOPHIS ORDINOIDES

Correlational selection favors combinations of traits and is a key element of many models of phenotypic and genetic evolution. Multiple regression techniques for measuring selection allow for the direct estimation of correlational selection gradients, yet few studies in natural populations have investigated this process. Color patterns and antipredator behaviors of snakes are thought to function interactively in predator escape and therefore may be subject to correlational selection. To investigate this hypothesis, I studied the survivorship of juvenile garter snakes, Thamnophis ordinoides, as a function of a suite of escape behaviors and color pattern. The only natural selection detected favored opposite combinations of stripedness of the color pattern and the tendency to perform during escape evasive behaviors called reversals. This selection presumably results from optical illusions created by moving patterns and their effects on visually foraging predators. Analysis of the bivariate selection surface shows that pure correlational selection can be thought of as a series of linear selection functions on one trait whose slopes depend on the value of the second trait. Alternatively, viewing the selection surface along its major axes reveals stabilizing and disruptive components of correlational selection. It is further shown that correlational selection alone can promote genetic variance and covariance within a generation. This phenomenon may be partially responsible for the extreme variation in color pattern and the genetic covariance between color pattern and behavior observed in natural populations of T. ordinoides.     

The genetic variance but not the genetic covariance of life‐history traits changes towards the north in a time‐constrained insect

Seasonal time constraints are usually stronger at higher than lower latitudes and can exert strong selection on life‐history traits and the correlations among these traits. To predict the response of life‐history traits to environmental change along a latitudinal gradient, information must be obtained about genetic variance in traits and also genetic correlation between traits, that is the genetic variance‐covariance matrix, G . Here, we estimated G for key life‐history traits in an obligate univoltine damselfly that faces seasonal time constraints. We exposed populations to simulated native temperatures and photoperiods and common garden environmental conditions in a laboratory set‐up. Despite differences in genetic variance in these traits between populations (lower variance at northern latitudes), there was no evidence for latitude‐specific covariance of the life‐history traits. At simulated native conditions, all populations showed strong genetic and phenotypic correlations between traits that shaped growth and development. The variance–covariance matrix changed considerably when populations were exposed to common garden conditions compared with the simulated natural conditions, showing the importance of environmentally induced changes in multivariate genetic structure. Our results highlight the importance of estimating variance–covariance matrixes in environments that mimic selection pressures and not only trait variances or mean trait values in common garden conditions for understanding the trait evolution across populations and environments.     

The G matrix under fluctuating correlational mutation and selection

Theoretical quantitative genetics provides a framework for reconstructing past selection and predicting future patterns of phenotypic differentiation. However, the usefulness of the equations of quantitative genetics for evolutionary inference relies on the evolutionary stability of the additive genetic variance-covariance matrix (G matrix). A fruitful new approach for exploring the evolutionary dynamics of G involves the use of individual-based computer simulations. Previous studies have focused on the evolution of the eigenstructure of G. An alternative approach employed in this paper uses the multivariate response-to-selection equation to evaluate the stability of G. In this approach, I measure similarity by the correlation between response-to-selection vectors due to random selection gradients. I analyze the dynamics of G under several conditions of correlational mutation and selection. As found in a previous study, the eigenstructure of G is stabilized by correlational mutation and selection. However, over broad conditions, instability of G did not result in a decreased consistency of the response to selection. I also analyze the stability of G when the correlation coefficients of correlational mutation and selection and the effective population size change through time. To my knowledge, no prior study has used computer simulations to investigate the stability of G when correlational mutation and selection fluctuate. Under these conditions, the eigenstructure of G is unstable under some simulation conditions. Different results are obtained if G matrix stability is assessed by eigenanalysis or by the response to random selection gradients. In this case, the response to selection is most consistent when certain aspects of the eigenstructure of G are least stable and vice versa.     

Rapid divergence of genetic variance-covariance matrix within a natural population

The matrix of genetic variances and covariances (G matrix) represents the genetic architecture of multiple traits sharing developmental and genetic processes and is central for predicting phenotypic evolution. These predictions require that the G matrix be stable. Yet the timescale and conditions promoting G matrix stability in natural populations remain unclear. We studied stability of the G matrix in a 20-year evolution field experiment, where a population of the cosmopolitan parthenogenetic soil nematode Acrobeloides nanus was subjected to drift and divergent selection (benign and stress environments). Selection regime did not influence the level of absolute genetic constraints: under both regimes, two genetic dimensions for three life-history traits were identified. A substantial response to selection in principal components structure and in general matrix pattern was indicated by three statistical methods. G structure was also influenced by drift, with higher divergence under benign conditions. These results show that the G matrix might evolve rapidly in natural populations. The observed high dynamics of G structure probably represents the general feature of asexual species and limits the predictive power of G in phenotypic evolution analyses.     

VARIATION IN GENETIC ARCHITECTURE OF CALLING SONG AMONG POPULATIONS OF ALLONEMOBIUS SOCIUS,A. FASCIATUS,AND A HYBRID POPULATION: DRIFT OR SELECTION?

Predictions using quantitative genetic models generally assume that the variance-covariance matrices remain constant over time. This assumption is based on the supposition that selection is generally weak and hence variation lost through selection can be replaced by new mutations. Whether this is generally true can only be ascertained from empirical studies. Ideally for such a study we should be able to make a prediction concerning the relative strength of selection versus genetic drift. If the latter force is prevalent then the variance-covariances matrices should be proportional to each other. Previous studies have indicated that females in the two sibling cricket species Allonemobius socius and A. fasciatus do not discriminate between males of the two species by their calling song. Therefore, differences between the calling song of the two males most likely result from drift rather than sexual selection. We test this hypothesis by comparing the genetic architecture of calling song of three populations of A. fasciatus with two populations of A. socius. We found no differences among populations within species, but significant differences in the G (genetic) and P (phenotypic) matrices between species, with the matrices being proportional as predicted under the hypothesis of genetic drift. Because of the proportional change in the (co)variances no differences between species are evident in the heritabilities or genetic correlations. Comparison of the two species with a hybrid population from a zone of overlap showed highly significant nonproportional variation in genetic architecture. This variation is consistent with a general mixture of two separate genomes or selection. Qualitative conclusions reached using the phenotypic matrices are the same as those reached using the genetic matrices supporting the hypothesis that the former may be used as surrogate measures of the latter.     

CONDITION, GENOTYPE-BY-ENVIRONMENT INTERACTION, AND CORRELATIONAL SELECTION IN LIZARD LIFE-HISTORY MORPHS

Abstract We compared reproductive allocation and variation in condition and survivorship of two heritable female throat color morphs (orange and yellow) in a free‐living population of side‐blotched lizards (Uta stansburiana). Using path analysis and structural equation modeling, we investigated how variation in the social environment affected clutch size and egg mass and two condition traits (postlaying mass, immunological condition) and how these traits in turn affected female field survival. In the presence of many neighbors, both morphs increased their clutch sizes, although these effects were only significant in yellow females. In addition, yellow females increased their egg mass in the presence of many orange neighbors. Orange females surrounded by many orange neighbors showed sign of stress in the form of immunosuppression, whereas this effect was less pronounced in yellow females. The morphs also differed in the impact of variation in clutch size and egg mass on both condition traits. Finally, female morphotype and immune responsiveness affected fitness interactively, and hence these two traits showed signs of fitness epistasis: Selection gradients on this trait were opposite in sign in the two morphs. The correlational selection gradient (_{γthroatxantibody response}) between female throat color and antibody responsiveness was ‐0.365. Our data thus reveal important interactive effects such as genotype‐by‐environment interaction toward the social environment and morph‐specific trade‐offs as well as the occurrence of correlational selection. We discuss the use of naturally occurring and conspicuous genetic polymorphisms in field studies of selection and life‐history allocation.     

The B-matrix harbors significant and sex-specific constraints on the evolution of multicharacter sexual dimorphism

The extent to which sexual dimorphism can evolve within a population depends on an interaction between sexually divergent selection and constraints imposed by a genetic architecture that is shared between males and females. The degree of constraint within a population is normally inferred from the intersexual genetic correlation, r(mf) . However, such bivariate correlations ignore the potential constraining effect of genetic covariances between other sexually coexpressed traits. Using the fruit fly Drosophila serrata, a species that exhibits mutual mate preference for blends of homologous contact pheromones, we tested the impact of between-sex between-trait genetic covariances using an extended version of the genetic variance-covariance matrix, G, that includes Lande's (1980) between-sex covariance matrix, B. We find that including B greatly reduces the degree to which male and female traits are predicted to diverge in the face of divergent phenotypic selection. However, the degree to which B alters the response to selection differs between the sexes. The overall rate of male trait evolution is predicted to decline, but its direction remains relatively unchanged, whereas the opposite is found for females. We emphasize the importance of considering the B-matrix in microevolutionary studies of constraint on the evolution of sexual dimorphism.     

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.     

Selection on skewed characters and the paradox of stasis

Observed phenotypic responses to selection in the wild often differ from predictions based on measurements of selection and genetic variance. An overlooked hypothesis to explain this paradox of stasis is that a skewed phenotypic distribution affects natural selection and evolution. We show through mathematical modeling that, when a trait selected for an optimum phenotype has a skewed distribution, directional selection is detected even at evolutionary equilibrium, where it causes no change in the mean phenotype. When environmental effects are skewed, Lande and Arnold's (1983) directional gradient is in the direction opposite to the skew. In contrast, skewed breeding values can displace the mean phenotype from the optimum, causing directional selection in the direction of the skew. These effects can be partitioned out using alternative selection estimates based on average derivatives of individual relative fitness, or additive genetic covariances between relative fitness and trait (Robertson–Price identity). We assess the validity of these predictions using simulations of selection estimation under moderate sample sizes. Ecologically relevant traits may commonly have skewed distributions, as we here exemplify with avian laying date — repeatedly described as more evolutionarily stable than expected — so this skewness should be accounted for when investigating evolutionary dynamics in the wild.     

An evolutionary quantitative genetics model for phenotypic (co)variances under limited dispersal,with an application to socially synergistic traits

Darwinian evolution consists of the gradual transformation of heritable traits due to natural selection and the input of random variation by mutation. Here, we use a quantitative genetics approach to investigate the coevolution of multiple quantitative traits under selection, mutation, and limited dispersal. We track the dynamics of trait means and of variance–covariances between traits that experience frequency‐dependent selection. Assuming a multivariate‐normal trait distribution, we recover classical dynamics of quantitative genetics, as well as stability and evolutionary branching conditions of invasion analyses, except that due to limited dispersal, selection depends on indirect fitness effects and relatedness. In particular, correlational selection that associates different traits within‐individuals depends on the fitness effects of such associations between‐individuals. We find that these kin selection effects can be as relevant as pleiotropy for the evolution of correlation between traits. We illustrate this with an example of the coevolution of two social traits whose association within‐individuals is costly but synergistically beneficial between‐individuals. As dispersal becomes limited and relatedness increases, associations between‐traits between‐individuals become increasingly targeted by correlational selection. Consequently, the trait distribution goes from being bimodal with a negative correlation under panmixia to unimodal with a positive correlation under limited dispersal.     

A tale of two matrices: multivariate approaches in evolutionary biology

Two symmetric matrices underlie our understanding of microevolutionary change. The first is the matrix of nonlinear selection gradients (gamma) which describes the individual fitness surface. The second is the genetic variance-covariance matrix (G) that influences the multivariate response to selection. A common approach to the empirical analysis of these matrices is the element-by-element testing of significance, and subsequent biological interpretation of pattern based on these univariate and bivariate parameters. Here, I show why this approach is likely to misrepresent the genetic basis of quantitative traits, and the selection acting on them in many cases. Diagonalization of square matrices is a fundamental aspect of many of the multivariate statistical techniques used by biologists. Applying this, and other related approaches, to the analysis of the structure of gamma and G matrices, gives greater insight into the form and strength of nonlinear selection, and the availability of genetic variance for multiple traits.     

Statistical Power to Detect Genetic (Co)Variance of Complex Traits Using SNP Data in Unrelated Samples

We have recently developed analysis methods (GREML) to estimate the genetic variance of a complex trait/disease and the genetic correlation between two complex traits/diseases using genome-wide single nucleotide polymorphism (SNP) data in unrelated individuals. Here we use analytical derivations and simulations to quantify the sampling variance of the estimate of the proportion of phenotypic variance captured by all SNPs for quantitative traits and case-control studies. We also derive the approximate sampling variance of the estimate of a genetic correlation in a bivariate analysis, when two complex traits are either measured on the same or different individuals. We show that the sampling variance is inversely proportional to the number of pairwise contrasts in the analysis and to the variance in SNP-derived genetic relationships. For bivariate analysis, the sampling variance of the genetic correlation additionally depends on the harmonic mean of the proportion of variance explained by the SNPs for the two traits and the genetic correlation between the traits, and depends on the phenotypic correlation when the traits are measured on the same individuals. We provide an online tool for calculating the power of detecting genetic (co)variation using genome-wide SNP data. The new theory and online tool will be helpful to plan experimental designs to estimate the missing heritability that has not yet been fully revealed through genome-wide association studies, and to estimate the genetic overlap between complex traits (diseases) in particular when the traits (diseases) are not measured on the same samples.     

GENE FLOW FROM DOMESTICATED SPECIES TO WILD RELATIVES: MIGRATION LOAD IN A MODEL OF MULTIVARIATE SELECTION

Domesticated species frequently spread their genes into populations of wild relatives through interbreeding. The domestication process often involves artificial selection for economically desirable traits. This can lead to an indirect response in unknown correlated traits and a reduction in fitness of domesticated individuals in the wild. Previous models for the effect of gene flow from domesticated species to wild relatives have assumed that evolution occurs in one dimension. Here, I develop a quantitative genetic model for the balance between migration and multivariate stabilizing selection. Different forms of correlational selection consistent with a given observed ratio between average fitness of domesticated and wild individuals offsets the phenotypic means at migration–selection balance away from predictions based on simpler one-dimensional models. For almost all parameter values, correlational selection leads to a reduction in the migration load. For ridge selection, this reduction arises because the distance the immigrants deviates from the local optimum in effect is reduced. For realistic parameter values, however, the effect of correlational selection on the load is small, suggesting that simpler one-dimensional models may still be adequate in terms of predicting mean population fitness and viability.     

THE EVOLUTION OF ALTERNATE MORPHOLOGIES: FITNESS AND WING MORPHOLOGY IN MALE SAND CRICKETS

Many organisms show distinct morphological types. We argue that the evolution of these alternate morphologies depends upon both fitness differences between morphs within each sex and the genetic correlation between sexes. In this paper, we examine the evolution of alternate morphologies using wing dimorphism in insects as a model system. Many insect species are wing dimorphic, one morph having wings and being capable of flight, the other lacking functional wings. While there is a well established trade-off in females between macroptery and reproduction, there are few data on the possible costs in males. We examine trade-offs between macroptery and life-history traits in male sand crickets, Gryllus firmus, and estimate the genetic correlation of wing dimorphism between the sexes. Macropterous males develop faster than micropterous males and are either larger or the same size depending upon rearing conditions. There is no difference in absolute or relative testis size at eclosion or 7 d thereafter. Finally, there is no difference between macropterous and micropterous males in relative success at siring offspring. Thus, with respect to the above traits, there are no costs associated with being winged in male G. firmus. It is possible that there may be a trade-off between calling rate and macroptery. A comparison of the relative frequency of macroptery between males and female across different orders of insects supports this hypothesis. The genetic correlation of wing dimorphism between the sexes is high (r₈ = 0.86), and hence the frequency of macroptery in males may be strongly influenced by selection acting on females.     

Is the Expression of Male Traits in Female Lesser Kestrels Related to Sexual Selection?

Some lesser kestrel females (Falco naumanni) show male plumage traits, i.e. grey rumps and tails. This phenomenon has seldom been analyzed in birds, and two hypotheses have been suggested to explain it. The first proposes that, when sexual selection acts favouring the expression of a trait in males, females could show the analogous character by genetic correlation (indirect sexual selection). Alternatively, the expression of these traits in females could be favoured by intra-sexual competition or even by male mate choice selecting ornamented females (direct sexual selection). We have tested if females with male traits are favoured by direct sexual selection, through a 3-yr observational study of 239 female lesser kestrels. Our results cannot support the predictions, as females with grey plumages do not achieve access to better breeding opportunities or fitness benefits. These traits do not seem to be honest signals of phenotypic quality, since physical condition and survival did not differ between females which showed male traits and those which did not. The expression of male traits in these females increased with their ages, but showing a high individual variability. Finally, since the genetic correlation hypothesis is unlikely in this species because all males have grey rumps and tails, we propose a new age-related hormonal explanation.     

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.