MEASURING SELECTION AND CONSTRAINT IN THE EVOLUTION OF GROWTH

We present a quantitative genetic model for the evolution of growth trajectories that makes no assumptions about the shapes of growth trajectories that are possible. Evolution of a population's mean growth trajectory is governed by the selection gradient function and the additive genetic covariance function. The selection gradient function is determined by the impact of changes in size on the birth and death rates at different ages, and can be estimated for natural populations. The additive genetic covariance function can also be estimated empirically, as we demonstrate with four vertebrate populations. Using the genetic data from mice, a computer simulation shows that evolution of a growth trajectory can be constrained by the absence of genetic variation for certain changes in the trajectory's shape. These constraints can be visualized with an analysis of the covariance function. Results from four vertebrate populations show that while each has substantial genetic variation for some evolutionary changes in its growth trajectory, most types of changes have little or no variation available. This suggests that constraints may often play an important role in the evolution of growth.     

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.     

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.     

Opposite responses to selection and where to find them

We generally expect traits to evolve in the same direction as selection. However, many organisms possess traits that appear to be costly for individuals, while plant and animal breeding experiments reveal that selection may lead to no response or even negative responses to selection. We formalize both of these instances as cases of “opposite responses to selection.” Using quantitative genetic models for the response to selection, we outline when opposite responses to selection should be expected. These typically occur when social selection opposes direct selection, when individuals interact with others less related to them than a random member of the population, and if the genetic covariance between direct and indirect effects is negative. We discuss the likelihood of each of these occurring in nature and therefore summarize how frequent opposite responses to selection are likely to be. This links several evolutionary phenomena within a single framework.     

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.     

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.     

Constrained evolution of the sex comb in Drosophila simulans

Male fitness is dependent on sexual traits that influence mate acquisition (precopulatory sexual selection) and paternity (post‐copulatory sexual selection), and although many studies have documented the form of selection in one or the other of these arenas, fewer have done it for both. Nonetheless, it appears that the dominant form of sexual selection is directional, although theoretically, populations should converge on peaks in the fitness surface, where selection is stabilizing. Many factors, however, can prevent populations from reaching adaptive peaks. Genetic constraints can be important if they prevent the development of highest fitness phenotypes, as can the direction of selection if it reverses across episodes of selection. In this study, we examine the evidence that these processes influence the evolution of the multivariate sex comb morphology of male Drosophila simulans. To do this, we conduct a quantitative genetic study together with a multivariate selection analysis to infer how the genetic architecture and selection interact. We find abundant genetic variance and covariance in elements of the sex comb. However, there was little evidence for directional selection in either arena. Significant nonlinear selection was detected prior to copulation when males were mated to nonvirgin females, and post‐copulation during sperm offence (again with males mated to nonvirgins). Thus, contrary to our predictions, the evolution of the D. simulans sex comb is limited neither by genetic constraints nor by antagonistic selection between pre‐ and post‐copulatory arenas, but nonlinear selection on the multivariate phenotype may prevent sex combs from evolving to reach some fitness maximizing optima.     

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.     

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.     

Sexual variation in heritability and genetic correlations of morphological traits in house sparrow (Passer domesticus)

Estimates of genetic components are important for our understanding of how individual characteristics are transferred between generations. We show that the level of heritability varies between 0.12 and 0.68 in six morphological traits in house sparrows (Passer domesticus L.) in northern Norway. Positive and negative genetic correlations were present among traits, suggesting evolutionary constraints on the evolution of some of these characters. A sexual difference in the amount of heritable genetic variation was found in tarsus length, wing length, bill depth and body condition index, with generally higher heritability in females. In addition, the structure of the genetic variance-covariance matrix for the traits differed between the sexes. Genetic correlations between males and females for the morphological traits were however large and not significantly different from one, indicating that sex-specific responses to selection will be influenced by intersexual differences in selection differentials. Despite this, some traits had heritability above 0.1 in females, even after conditioning on the additive genetic covariance between sexes and the additive genetic variances in males. Moreover, a meta-analysis indicated that higher heritability in females than in males may be common in birds. Thus, this indicates sexual differences in the genetic architecture of birds. Consequently, as in house sparrows, the evolutionary responses to selection will often be larger in females than males. Hence, our results suggest that sex-specific additive genetic variances and covariances, although ignored in most studies, should be included when making predictions of evolutionary changes from standard quantitative genetic models.