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.     

Sexual Dimorphism Increases Evolvability in a Genetic Regulatory Network

The majority of work on genetic regulatory networks has focused on environmental and mutational robustness, and much less attention has been paid to the conditions under which a network may produce an evolvable phenotype. Sexually dimorphic characters often show rapid rates of change over short evolutionary time scales and while this is thought to be due to the strength of sexual selection acting on the trait, a dimorphic character with an underlying pleiotropic architecture may also influence the evolution of the regulatory network that controls the character and affect evolvability. As evolvability indicates a capacity for phenotypic change and mutational robustness refers to a capacity for phenotypic stasis, increases in evolvability may show a negative relationship with mutational robustness. I tested this with a computational model of a genetic regulatory network and found that, contrary to expectation, sexually dimorphic characters exhibited both higher mutational robustness and higher evolvability. Decomposition of the results revealed that linkage disequilibrium within sex and linkage disequilibrium between sexes, two of the three primary components of additive genetic variance and evolvability in quantitative genetics models, contributed to the differences in evolvability between sexually dimorphic and monomorphic populations. These results indicate that producing two pleiotropically linked characters did not constrain either the production of a robust phenotype or adaptive potential. Instead, the genetic system evolved to maximize both quantities.     

Phenotypic variability can promote the evolution of adaptive plasticity by reducing the stringency of natural selection

Adaptive phenotypic plasticity is a potent but not ubiquitous solution to environmental heterogeneity, driving interest in what factors promote and limit its evolution. Here, a novel computational model representing stochastic information flow in development is used to explore evolution from a constitutive phenotype to an adaptively plastic response. Results show that populations tend to evolve robustness to developmental stochasticity, but that this evolved robustness limits evolvability; specifically, robust genotypes have less ability to evolve adaptive plasticity when presented with a mix of both the ancestral environment and a new environment. Analytic calculations and computational experiments confirm that this constraint occurs when the initial mutational steps towards plasticity are pleiotropic, such that mutant fitnesses decline in the environment to which their parents are well‐adapted. Greater phenotypic variability improves evolvability in the model by lessening this decline as well as by improving the fitness of partial adaptations to the new environment. By making initial plastic mutations more palatable to natural selection, phenotypic variability can increase the evolvability of an innovative, plastic response without improving evolvability to simpler challenges such as a shifted optimum in a single environment. Populations that evolved robustness by negative feedback between the trait and its rate of change show a particularly strong constraining effect on the evolvability of plasticity, revealing another mechanism by which evolutionary history can limit later innovation. These results document a novel mechanism by which weakening selection could actually stimulate the evolution of a major innovation.     

Female mating preferences determine system-level evolution in a gene network model

Environmental patterns of directional, stabilizing and fluctuating selection can influence the evolution of system-level properties like evolvability and mutational robustness. Intersexual selection produces strong phenotypic selection and these dynamics may also affect the response to mutation and the potential for future adaptation. In order to to assess the influence of mating preferences on these evolutionary properties, I modeled a male trait and female preference determined by separate gene regulatory networks. I studied three sexual selection scenarios: sexual conflict, a Gaussian model of the Fisher process described in Lande (in Proc Natl Acad Sci 78(6):3721–3725, 1981) and a good genes model in which the male trait signalled his mutational condition. I measured the effects these mating preferences had on the potential for traits and preferences to evolve towards new states, and mutational robustness of both the phenotype and the individual’s overall viability. All types of sexual selection increased male phenotypic robustness relative to a randomly mating population. The Fisher model also reduced male evolvability and mutational robustness for viability. Under good genes sexual selection, males evolved an increased mutational robustness for viability. Females choosing their mates is a scenario that is sufficient to create selective forces that impact genetic evolution and shape the evolutionary response to mutation and environmental selection. These dynamics will inevitably develop in any population where sexual selection is operating, and affect the potential for future adaptation.     

Understanding the evolution and stability of the G-matrix

The G-matrix summarizes the inheritance of multiple, phenotypic traits. The stability and evolution of this matrix are important issues because they affect our ability to predict how the phenotypic traits evolve by selection and drift. Despite the centrality of these issues, comparative, experimental, and analytical approaches to understanding the stability and evolution of the G-matrix have met with limited success. Nevertheless, empirical studies often find that certain structural features of the matrix are remarkably constant, suggesting that persistent selection regimes or other factors promote stability. On the theoretical side, no one has been able to derive equations that would relate stability of the G-matrix to selection regimes, population size, migration, or to the details of genetic architecture. Recent simulation studies of evolving G-matrices offer solutions to some of these problems, as well as a deeper, synthetic understanding of both the G-matrix and adaptive radiations.     

Revealing hidden evolutionary capacity to cope with global change

The extent to which global change will impact the long‐term persistence of species depends on their evolutionary potential to adapt to future conditions. While the number of studies that estimate the standing levels of adaptive genetic variation in populations under predicted global change scenarios is growing all the time, few studies have considered multiple environments simultaneously and even fewer have considered evolutionary potential in multivariate context. Because conditions will not be constant, adaptation to climate change is fundamentally a multivariate process so viewing genetic variances and covariances over multivariate space will always be more informative than relying on bivariate genetic correlations between traits. A multivariate approach to understanding the evolutionary capacity to cope with global change is necessary to avoid misestimating adaptive genetic variation in the dimensions in which selection will act. We assessed the evolutionary capacity of the larval stage of the marine polychaete Galeolaria caespitosa to adapt to warmer water temperatures. Galeolaria is an important habitat‐forming species in Australia, and its earlier life‐history stages tend to be more susceptible to stress. We used a powerful quantitative genetics design that assessed the impacts of three temperatures on subsequent survival across over 30 000 embryos across 204 unique families. We found adaptive genetic variation in the two cooler temperatures in our study, but none in the warmest temperature. Based on these results, we would have concluded that this species has very little capacity to evolve to the warmest temperature. However, when we explored genetic variation in multivariate space, we found evidence that larval survival has the potential to evolve even in the warmest temperatures via correlated responses to selection across thermal environments. Future studies should take a multivariate approach to estimating evolutionary capacity to cope with global change lest they misestimate a species’ true adaptive potential.     

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.     

GENETIC REGULATORY NETWORK MOTIFS CONSTRAIN ADAPTATION THROUGH CURVATURE IN THE LANDSCAPE OF MUTATIONAL (CO)VARIANCE

Systems biology is accumulating a wealth of understanding about the structure of genetic regulatory networks, leading to a more complete picture of the complex genotype–phenotype relationship. However, models of multivariate phenotypic evolution based on quantitative genetics have largely not incorporated a network‐based view of genetic variation. Here we model a set of two‐node, two‐phenotype genetic network motifs, covering a full range of regulatory interactions. We find that network interactions result in different patterns of mutational (co)variance at the phenotypic level (the M ‐matrix), not only across network motifs but also across phenotypic space within single motifs. This effect is due almost entirely to mutational input of additive genetic (co)variance. Variation in M has the effect of stretching and bending phenotypic space with respect to evolvability, analogous to the curvature of space–time under general relativity, and similar mathematical tools may apply in each case. We explored the consequences of curvature in mutational variation by simulating adaptation under divergent selection with gene flow. Both standing genetic variation (the G ‐matrix) and rate of adaptation are constrained by M , so that G and adaptive trajectories are curved across phenotypic space. Under weak selection the phenotypic mean at migration‐selection balance also depends on M .     

Rapid changes in genetic architecture of behavioural syndromes following colonization of a novel environment

Behavioural syndromes, that is correlated behaviours, may be a result from adaptive correlational selection, but in a new environmental setting, the trait correlation might act as an evolutionary constraint. However, knowledge about the quantitative genetic basis of behavioural syndromes, and the stability and evolvability of genetic correlations under different ecological conditions, is limited. We investigated the quantitative genetic basis of correlated behaviours in the freshwater isopod Asellus aquaticus. In some Swedish lakes, A. aquaticus has recently colonized a novel habitat and diverged into two ecotypes, presumably due to habitat‐specific selection from predation. Using a common garden approach and animal model analyses, we estimated quantitative genetic parameters for behavioural traits and compared the genetic architecture between the ecotypes. We report that the genetic covariance structure of the behavioural traits has been altered in the novel ecotype, demonstrating divergence in behavioural correlations. Thus, our study confirms that genetic correlations behind behaviours can change rapidly in response to novel selective environments.     

Cross‐sex genetic covariances limit the evolvability of wing‐shape within and among species of Drosophila

The independent evolution of males and females is potentially constrained by both sexes inheriting the same alleles from their parents. This genetic constraint can limit the evolvability of complex traits; however, there are few studies of multivariate evolution that incorporate cross‐sex genetic covariances in their predictions. Drosophila wing‐shape has emerged as a model high‐dimensional phenotype; wing‐shape is highly evolvable in contemporary populations, and yet perplexingly stable across phylogenetic timescales. Here, we show that cross‐sex covariances in Drosophila melanogaster, given by the B ‐matrix, may considerably bias wing‐shape evolution. Using random skewers, we show that B would constrain the response to antagonistic selection by 90%, on average, but would double the response to concordant selection. Both cross‐sex within‐trait and cross‐sex cross‐trait covariances determined the predicted response to antagonistic selection, but only cross‐sex within‐trait covariances facilitated the predicted response to concordant selection. Similar patterns were observed in the direction of extant sexual dimorphism in D. melanogaster, and in directions of most and least dimorphic variation across the Drosophila phylogeny. Our results highlight the importance of considering between‐sex genetic covariances when making predictions about evolution on both macro‐ and microevolutionary timescales, and may provide one more explanatory piece in the puzzle of stasis.     

The effect of mutational robustness on the evolvability of multicellular organisms and eukaryotic cells

Canalization involves mutational robustness, the lack of phenotypic change as a result of genetic mutations. Given the large divergence in phenotype across species, understanding the relationship between high robustness and evolvability has been of interest to both theorists and experimentalists. Although canalization was originally proposed in the context of multicellular organisms, the effect of multicellularity and other classes of hierarchical organization on evolvability has not been considered by theoreticians. We address this issue using a Boolean population model with explicit representation of an environment in which individuals with explicit genotype and a hierarchical phenotype representing multicellularity evolve. Robustness is described by a single real number between zero and one which emerges from the genotype–phenotype map. We find that high robustness is favoured in constant environments, and lower robustness is favoured after environmental change. Multicellularity and hierarchical organization severely constrain robustness: peak evolvability occurs at an absolute level of robustness of about 0.99 compared with values of about 0.5 in a classical neutral network model. These constraints result in a sharp peak of evolvability in which the maximum is set by the fact that the fixation of adaptive mutations becomes more improbable as robustness decreases. When robustness is put under genetic control, robustness levels leading to maximum evolvability are selected for, but maximal relative fitness appears to require recombination.     

Antler size in red deer: heritability and selection but no evolution

We present estimates of the selection on and the heritability of a male secondary sexual weapon in a wild population: antler size in red deer. Male red deer with large antlers had increased lifetime breeding success, both before and after correcting for body size, generating a standardized selection gradient of 0.44 (+/- 0.18 SE). Despite substantial age- and environment-related variation, antler size was also heritable (heritability of antler mass = 0.33 +/- 0.12). However the observed selection did not generate an evolutionary response in antler size over the study period of nearly 30 years, and there was no evidence of a positive genetic correlation between antler size and fitness nor of a positive association between breeding values for antler size and fitness. Our results are consistent with the hypothesis that a heritable trait under directional selection will not evolve if associations between the measured trait and fitness are determined by environmental covariances: In red deer males, for example, both antler size and success in the fights for mates may be heavily dependent on an individual's nutritional state.     

Migration-induced phenotypic divergence: the migration-selection balance of correlated traits

Genetically correlated traits are known to respond to indirect selection pressures caused by directional selection on other traits. It is however unclear how local adaptation in populations diverging along some phenotypic traits but not others is affected by the joint action of gene flow and genetic correlations among traits. This simulation study shows that although gene flow is a potent constraining mechanism of population adaptive divergence, it may induce phenotypic divergence in traits under homogeneous selection among habitats if they are genetically correlated with traits under divergent selection. This correlated phenotypic divergence is a nonmonotonous function of migration and increases with mutational correlation among traits. It also increases with the number of divergently selected traits provided their genetic autonomy relative to the uniformly selected trait is reduced by specific patterns of genetic covariances: populations with lower effective trait dimensionality are more likely to generate very large correlated divergence. The correlated divergence is likely to be picked up by Q(ST)-F(ST) analysis of population genetic differentiation and be erroneously ascribed to adaptive divergence under divergent selection. This study emphasizes the necessity to understand the interaction between selection and the genetic basis of adaptation in a multivariate rather than univariate context.     

Ecomorphological specialization leads to loss of evolvability in primate limbs*

Primate limb morphology is often described as either generalized, that is, suited to a range of locomotor and positional behaviors, or specialized for unique locomotor behaviors such as brachiation or bipedalism. The evolution of highly specialized limb morphology may result in loss of evolvability, that is, in a decreased capacity of the locomotor skeleton to evolve in response to selection towards alternative ecomorphological niches. Using evolutionary simulations, I show that the highly specialized limb anatomy of hominoids is associated with a significant loss of evolvability, defined as the number of generations to reach alternative adaptive peaks, and in parallel an increased risk of extinction, particularly in simulated evolution toward generalized quadrupedal limb proportions. Loss of evolvability in apes and humans correlates with three factors: (1) decreased correlation among limb bone lengths (i.e., integration), which slows the rate of change along lines of least evolutionary resistance; (2) limb specialization, which places apes and humans in relatively remote areas of morphospace; and (3) increased skeletal size as a proxy for body size. Thus, locomotor over-specialization can lead to evolutionary dead-ends that significantly increase the probability of hominoid populations going extinct before evolving new adaptive morphologies.     

Evolution of adaptive phenotypic variation patterns by direct selection for evolvability

A basic assumption of the Darwinian theory of evolution is that heritable variation arises randomly. In this context, randomness means that mutations arise irrespective of the current adaptive needs imposed by the environment. It is broadly accepted, however, that phenotypic variation is not uniformly distributed among phenotypic traits, some traits tend to covary, while others vary independently, and again others barely vary at all. Furthermore, it is well established that patterns of trait variation differ among species. Specifically, traits that serve different functions tend to be less correlated, as for instance forelimbs and hind limbs in bats and humans, compared with the limbs of quadrupedal mammals. Recently, a novel class of genetic elements has been identified in mouse gene-mapping studies that modify correlations among quantitative traits. These loci are called relationship loci, or relationship Quantitative Trait Loci (rQTL), and affect trait correlations by changing the expression of the existing genetic variation through gene interaction. Here, we present a population genetic model of how natural selection acts on rQTL. Contrary to the usual neo-Darwinian theory, in this model, new heritable phenotypic variation is produced along the selected dimension in response to directional selection. The results predict that selection on rQTL leads to higher correlations among traits that are simultaneously under directional selection. On the other hand, traits that are not simultaneously under directional selection are predicted to evolve lower correlations. These results and the previously demonstrated existence of rQTL variation, show a mechanism by which natural selection can directly enhance the evolvability of complex organisms along lines of adaptive change.     

Evolution of evolvability in a developmental model

Evolvability, the ability of populations to adapt, can evolve through changes in the mechanisms determining genetic variation and in the processes of development. Here we construct and evolve a simple developmental model in which the pleiotropic effects of genes can evolve. We demonstrate that selection in a changing environment favors a specific pattern of variability, and that this favored pattern maximizes evolvability. Our analysis shows that mutant genotypes with higher evolvability are more likely to increase to fixation. We also show that populations of highly evolvable genotypes are much less likely to be invaded by mutants with lower evolvability, and that this dynamic primarily shapes evolvability. We examine several theoretical objections to the evolution of evolvability in light of this result. We also show that this result is robust to the presence or absence of recombination, and explore how nonrandom environmental change can select for a modular pattern of variability.     

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.     

A Multivariate Analysis of Genetic Constraints to Life History Evolution in a Wild Population of Red Deer

Evolutionary theory predicts that genetic constraints should be widespread, but empirical support for their existence is surprisingly rare. Commonly applied univariate and bivariate approaches to detecting genetic constraints can underestimate their prevalence, with important aspects potentially tractable only within a multivariate framework. However, multivariate genetic analyses of data from natural populations are challenging because of modest sample sizes, incomplete pedigrees, and missing data. Here we present results from a study of a comprehensive set of life history traits (juvenile survival, age at first breeding, annual fecundity, and longevity) for both males and females in a wild, pedigreed, population of red deer (Cervus elaphus). We use factor analytic modeling of the genetic variance–covariance matrix (G) to reduce the dimensionality of the problem and take a multivariate approach to estimating genetic constraints. We consider a range of metrics designed to assess the effect of G on the deflection of a predicted response to selection away from the direction of fastest adaptation and on the evolvability of the traits. We found limited support for genetic constraint through genetic covariances between traits, both within sex and between sexes. We discuss these results with respect to other recent findings and to the problems of estimating these parameters for natural populations.     

Genetic constraints predict evolutionary divergence in Dalechampia blossoms

If genetic constraints are important, then rates and direction of evolution should be related to trait evolvability. Here we use recently developed measures of evolvability to test the genetic constraint hypothesis with quantitative genetic data on floral morphology from the Neotropical vine Dalechampia scandens (Euphorbiaceae). These measures were compared against rates of evolution and patterns of divergence among 24 populations in two species in the D. scandens species complex. We found clear evidence for genetic constraints, particularly among traits that were tightly phenotypically integrated. This relationship between evolvability and evolutionary divergence is puzzling, because the estimated evolvabilities seem too large to constitute real constraints. We suggest that this paradox can be explained by a combination of weak stabilizing selection around moving adaptive optima and small realized evolvabilities relative to the observed additive genetic variance.