The evolution of genetic architecture under frequency-dependent disruptive selection

We propose a model to analyze a quantitative trait under frequency-dependent disruptive selection. Selection on the trait is a combination of stabilizing selection and intraspecific competition, where competition is maximal between individuals with equal phenotypes. In addition, there is a density-dependent component induced by population regulation. The trait is determined additively by a number of biallelic loci, which can have different effects on the trait value. In contrast to most previous models, we assume that the allelic effects at the loci can evolve due to epistatic interactions with the genetic background. Using a modifier approach, we derive analytical results under the assumption of weak selection and constant population size, and we investigate the full model by numerical simulations. We find that frequency-dependent disruptive selection favors the evolution of a highly asymmetric genetic architecture, where most of the genetic variation is concentrated on a small number of loci. We show that the evolution of genetic architecture can be understood in terms of the ecological niches created by competition. The phenotypic distribution of a population with an adapted genetic architecture closely matches this niche structure. Thus, evolution of the genetic architecture seems to be a plausible way for populations to adapt to regimes of frequency-dependent disruptive selection. As such, it should be seen as a potential evolutionary pathway to discrete polymorphisms and as a potential alternative to other evolutionary responses, such as the evolution of sexual dimorphism or assortative mating.     

The change in quantitative genetic variation with inbreeding

Inbreeding is known to reduce heterozygosity of neutral genetic markers, but its impact on quantitative genetic variation is debated. Theory predicts a linear decline in additive genetic variance (V(A)) with increasing inbreeding coefficient (F) when loci underlying the trait act additively, but a nonlinear hump-shaped relationship when dominance and epistasis are important. Predictions for heritability (h2) are similar, although the exact shape depends on the value of h2 in the absence of inbreeding. We located 22 published studies in which the level of genetic variation in experimentally inbred populations (measured by V(A) or h2) was compared with that in outbred control populations. For life-history traits, the data strongly supported a nonlinear change in genetic variation with increasing F. V(A) and h2 were, respectively, 244% and 50% higher at F = 0.4 than in outbred populations, and dominance plus epistatic variance together exceeded additive variance by a factor of four. For nonfitness traits the decline was linear and estimates of nonadditive variance were small. These results confirm that population bottlenecks frequently increase V(A) in some traits, and imply that life-history traits are underlain by substantial dominance or epistasis. However, the importance of drift-induced genetic variation in conservation or evolutionary biology is questionable, in part because inbreeding depression usually accompanies inbreeding.     

The effect of a population bottleneck on the evolution of genetic variance/covariance structure

It is well known that standard population genetic theory predicts decreased additive genetic variance (V(a) ) following a population bottleneck and that theoretical models including interallelic and intergenic interactions indicate such loss may be avoided. However, few empirical data from multicellular model systems are available, especially regarding variance/covariance (V/CV) relationships. Here, we compare the V/CV structure of seventeen traits related to body size and composition between control (60 mating pairs/generation) and bottlenecked (2 mating pairs/generation; average F = 0.39) strains of mice. Although results for individual traits vary considerably, multivariate analysis indicates that V(a) in the bottlenecked populations is greater than expected. Traits with patterns and amounts of epistasis predictive of enhanced V(a) also show the largest deviations from additive expectations. Finally, the correlation structure of weekly weights is not significantly different between control and experimental lines but correlations between necropsy traits do differ, especially those involving the heart, kidney and tail length.     

Effects of genetic drift on variance components under a general model of epistasis

We analyze the changes in the mean and variance components of a quantitative trait caused by changes in allele frequencies, concentrating on the effects of genetic drift. We use a general representation of epistasis and dominance that allows an arbitrary relation between genotype and phenotype for any number of diallelic loci. We assume initial and final Hardy-Weinberg and linkage equilibrium in our analyses of drift-induced changes. Random drift generates transient linkage disequilibria that cause correlations between allele frequency fluctuations at different loci. However, we show that these have negligible effects, at least for interactions among small numbers of loci. Our analyses are based on diffusion approximations that summarize the effects of drift in terms of F, the inbreeding coefficient, interpreted as the expected proportional decrease in heterozygosity at each locus. For haploids, the variance of the trait mean after a population bottleneck is var(delta(z)) = sigma(n)k=1 FkV(A(k)), where n is the number of loci contributing to the trait variance, V(A(1)) = V(A) is the additive genetic variance, and V(A(k)) is the kth-order additive epistatic variance. The expected additive genetic variance after the bottleneck, denoted (V*(A)), is closely related to var(delta(z)); (V*(A)) = (1 - F) sigma(n)k=1 kFk-1V(A(k)). Thus, epistasis inflates the expected additive variance above V(A)(1 - F), the expectation under additivity. For haploids (and diploids without dominance), the expected value of every variance component is inflated by the existence of higher order interactions (e.g., third-order epistasis inflates (V*(AA. This is not true in general with diploidy, because dominance alone can reduce (V*(A)) below V(A)(1 - F) (e.g., when dominant alleles are rare). Without dominance, diploidy produces simple expressions: var(delta(z)) = sigma(n)k=1 (2F)kV(A(k)) and (V(A)) = (1 - F) sigma(n)k=1 k(2F)k-1V(A(k)). With dominance (and even without epistasis), var(delta(z)) and (V*(A)) no longer depend solely on the variance components in the base population. For small F, the expected additive variance simplifies to (V*(A)) approximately equal to (1 - F)V(A) + 4FV(AA) + 2FV(D) + 2FC(AD), where C(AD) is a sum of two terms describing covariances between additive effects and dominance and additive X dominance interactions. Whether population bottlenecks lead to expected increases in additive variance depends primarily on the ratio of nonadditive to additive genetic variance in the base population, but dominance precludes simple predictions based solely on variance components. We illustrate these results using a model in which genotypic values are drawn at random, allowing extreme and erratic epistatic interactions. Although our analyses clarify the conditions under which drift is expected to increase V(A), we question the evolutionary importance of such increases.     

Evolution of genetic architecture under directional selection

We investigate the multilinear epistatic model under mutation-limited directional selection. We confirm previous results that only directional epistasis, in which genes on average reinforce or diminish each other's effects, contribute to the initial evolution of mutational effects. Thus, either canalization or decanalization can occur under directional selection, depending on whether positive or negative epistasis is prevalent. We then focus on the evolution of the epistatic coefficients themselves. In the absence of higher-order epistasis, positive pairwise epistasis will tend to weaken relative to additive effects, while negative pairwise epistasis will tend to become strengthened. Positive third-order epistasis will counteract these effects, while negative third-order epistasis will reinforce them. More generally, gene interactions of all orders have an inherent tendency for negative changes under directional selection, which can only be modified by higher-order directional epistasis. We identify three types of nonadditive quasi-equilibrium architectures that, although not strictly stable, can be maintained for an extended time: (1) nondirectional epistatic architectures; (2) canalized architectures with strong epistasis; and (3) near-additive architectures in which additive effects keep increasing relative to epistasis.     

The evolution of genetic canalization under fluctuating selection

Abstract.— If the direction of selection changes from generation to generation, the ability to respond to selection is maladaptive: the response to selection in one generation leads to reduced fitness in the next. Because the response is determined by the amount of genetic variance expressed at the phenotypic level, rapidly fluctuating selection should favor modifier genes that reduce the phenotypic effect of alleles segregating at structural loci underlying the trait. Such reduction in phenotypic expression of genetic variation has been named "genetic canalization." I support this argument with a series of two- and multilocus models with alternating linear selection and Gaussian selection with fluctuating optimum. A canalizing modifier gene affects the fitness of its carriers in three ways: (1) it reduces the phenotypic consequences of genetic response to previous selection; (2) it reduces the genetic response to selection, which is manifested as linkage disequilibrium between the modifier and structural loci; and (3) it reduces the phenotypic variance. The first two effects reduce fitness under directional selection sustained for several generations, but improve fitness when the direction of selection has just been reversed. The net effect tends to favor a canalizing modifier under rapidly fluctuating selection regimes (period of eight generations or less). The third effect improves fitness of the modifier allele if the fitness function is convex and reduces it if the function is concave. Under fluctuating Gaussian selection, the population is more likely to experience the concave portion of the fitness function when selection is stronger. Therefore, only weak to moderately strong fluctuating Gaussian selection favors genetic canalization. This paper considerably broadens the conditions that favor genetic canalization, which so far has only been postulated to evolve under long-term stabilizing selection.     

Variation in genetic architecture of olfactory behaviour among wild-derived populations of Drosophila melanogaster

Odour-guided behaviour is a quantitative trait determined by many genes that are sensitive to gene-environment interactions. Different natural populations are likely to experience different selection pressures on the genetic underpinnings of chemosensory behaviour. However, few studies have reported comparisons of the quantitative genetic basis of olfactory behaviour in geographically distinct populations. We generated isofemale lines of Drosophila melanogaster from six populations in Argentina and measured larval and adult responses to benzaldehyde. There was significant variation within populations for both larval and adult olfactory behaviour and a significant genotype x sex interaction (GSI) for adult olfactory behaviour. However, there is substantial variation in the contribution of GSI to the total phenotypic variance among populations. Estimates of evolvability are orders of magnitude higher for larvae than for adults. Our results suggest that the potential for evolutionary adaptation to the chemosensory environment is greater at the larval feeding stage than at the adult reproductive stage.     

The genetic architecture of adaptation under migration-selection balance

Many ecologically important traits have a complex genetic basis, with the potential for mutations at many different genes to shape the phenotype. Even so, studies of local adaptation in heterogeneous environments sometimes find that just a few quantitative trait loci (QTL) of large effect can explain a large percentage of observed differences between phenotypically divergent populations. As high levels of gene flow can swamp divergence at weakly selected alleles, migration-selection-drift balance may play an important role in shaping the genetic architecture of local adaptation. Here, we use analytical approximations and individual-based simulations to explore how genetic architecture evolves when two populations connected by migration experience stabilizing selection toward different optima. In contrast to the exponential distribution of allele effect sizes expected under adaptation without migration (Orr 1998), we find that adaptation with migration tends to result in concentrated genetic architectures with fewer, larger, and more tightly linked divergent alleles. Even if many small alleles contribute to adaptation at the outset, they tend to be replaced by a few large alleles under prolonged bouts of stabilizing selection with migration. All else being equal, we also find that stronger selection can maintain linked clusters of locally adapted alleles over much greater map distances than weaker selection. The common empirical finding of QTL of large effect is shown to be expected with migration in a heterogeneous landscape, and these QTL may often be composed of several tightly linked alleles of smaller effect.     

Genetic basis of adaptive evolution of a polyphenism by genetic accommodation

Polyphenisms are evolved adaptations in which a genome produces discrete alternative phenotypes in different environments. In this study, the genetic basis of the evolution of a polyphenism by genetic accommodation was investigated. A polyphenic strain and a monophenic strain of Manduca sexta (L.) were crossed and the F(1) offspring and backcross progeny were analysed. The larval colour polyphenism was found to be regulated by one sex-linked gene of major effect and many smaller effect modifier genes. The finding shows that the mechanism of genetic accommodation relies on genetic changes that are consistent with the current view of the genetic basis of adaptive evolution.     

What can genetic variation tell us about the evolution of senescence?

Quantitative genetic approaches have been developed that allow researchers to determine which of two mechanisms, mutation accumulation (MA) or antagonistic pleiotropy (AP), best explain observed variation in patterns of senescence using classical quantitative genetic techniques. These include the creation of mutation accumulation lines, artificial selection experiments and the partitioning of genetic variances across age classes. This last strategy has received the lion''s share of empirical attention. Models predict that inbreeding depression (ID), dominance variance and the variance among inbred line means will all increase with age under MA but not under those forms of AP that generate marginal overdominance. Here, we show that these measures are not, in fact, diagnostic of MA versus AP. In particular, the assumptions about the value of genetic parameters in existing AP models may be rather narrow, and often violated in reality. We argue that whenever ageing-related AP loci contribute to segregating genetic variation, polymorphism at these loci will be enhanced by genetic effects that will also cause ID and dominance variance to increase with age, effects also expected under the MA model of senescence. We suggest that the tests that seek to identify the relative contributions of AP and MA to the evolution of ageing by partitioning genetic variance components are likely to be too conservative to be of general value.     

The evolution of genetic architectures underlying quantitative traits

In the classic view introduced by R. A. Fisher, a quantitative trait is encoded by many loci with small, additive effects. Recent advances in quantitative trait loci mapping have begun to elucidate the genetic architectures underlying vast numbers of phenotypes across diverse taxa, producing observations that sometimes contrast with Fisher''s blueprint. Despite these considerable empirical efforts to map the genetic determinants of traits, it remains poorly understood how the genetic architecture of a trait should evolve, or how it depends on the selection pressures on the trait. Here, we develop a simple, population-genetic model for the evolution of genetic architectures. Our model predicts that traits under moderate selection should be encoded by many loci with highly variable effects, whereas traits under either weak or strong selection should be encoded by relatively few loci. We compare these theoretical predictions with qualitative trends in the genetics of human traits, and with systematic data on the genetics of gene expression levels in yeast. Our analysis provides an evolutionary explanation for broad empirical patterns in the genetic basis for traits, and it introduces a single framework that unifies the diversity of observed genetic architectures, ranging from Mendelian to Fisherian.     

The evolution of phenotypes and genetic parameters under preferential mating

This article extends and adds more realism to Lande's analytical model for evolution under mate choice by using individual‐based simulations in which females sample a finite number of males and the genetic architecture of the preference and preferred trait evolves. The simulations show that the equilibrium heritabilities of the preference and preferred trait and the genetic correlation between them (r_G), depend critically on aspects of the mating system (the preference function, mode of mate choice, choosiness, and number of potential mates sampled), the presence or absence of natural selection on the preferred trait, and the initial genetic parameters. Under some parameter combinations, preferential mating increased the heritability of the preferred trait, providing a possible resolution for the lek paradox. The Kirkpatrick–Barton approximation for r_G proved to be biased downward, but the realized genetic correlations were also low, generally <0.2. Such low values of r_G indicate that coevolution of the preference and preferred trait is likely to be very slow and subject to significant stochastic variation. Lande's model accurately predicted the incidence of runaway selection in the simulations, except where preferences were relative and the preferred trait was subject to natural selection. In these cases, runaways were over‐ or underestimated, depending on the number of males sampled. We conclude that rapid coevolution of preferences and preferred traits is unlikely in natural populations, but that the parameter combinations most conducive to it are most likely to occur in lekking species.     

Rapid evolutionary escape by large populations from local fitness peaks is likely in nature

Fitness interactions between loci in the genome, or epistasis, can result in mutations that are individually deleterious but jointly beneficial. Such epistasis gives rise to multiple peaks on the genotypic fitness landscape. The problem of evolutionary escape from such local peaks has been a central problem of evolutionary genetics for at least 75 years. Much attention has focused on models of small populations, in which the sequential fixation of valley genotypes carrying individually deleterious mutations operates most quickly owing to genetic drift. However, valley genotypes can also be subject to mutation while transiently segregating, giving rise to copies of the high fitness escape genotype carrying the jointly beneficial mutations. In the absence of genetic recombination, these mutations may then fix simultaneously. The time for this process declines sharply with increasing population size, and it eventually comes to dominate evolutionary behavior. Here we develop an analytic expression for N(crit), the critical population size that defines the boundary between these regimes, which shows that both are likely to operate in nature. Frequent recombination may disrupt high-fitness escape genotypes produced in populations larger than N(crit) before they reach fixation, defining a third regime whose rate again slows with increasing population size. We develop a novel expression for this critical recombination rate, which shows that in large populations the simultaneous fixation of mutations that are beneficial only jointly is unlikely to be disrupted by genetic recombination if their map distance is on the order of the size of single genes. Thus, counterintuitively, mass selection alone offers a biologically realistic resolution to the problem of evolutionary escape from local fitness peaks in natural populations.     

The additive genetic variance after bottlenecks is affected by the number of loci involved in epistatic interactions

Abstract We investigated the role of the number of loci coding for a neutral trait on the release of additive variance for this trait after population bottlenecks. Different bottleneck sizes and durations were tested for various matrices of genotypic values, with initial conditions covering the allele frequency space. We used three different types of matrices. First, we extended Cheverud and Routman's model by defining matrices of "pure" epistasis for three and four independent loci; second, we used genotypic values drawn randomly from uniform, normal, and exponential distributions; and third we used two models of simple metabolic pathways leading to physiological epistasis. For all these matrices of genotypic values except the dominant metabolic pathway, we find that, as the number of loci increases from two to three and four, an increase in the release of additive variance is occurring. The amount of additive variance released for a given set of genotypic values is a function of the inbreeding coefficient, independently of the size and duration of the bottleneck. The level of inbreeding necessary to achieve maximum release in additive variance increases with the number of loci. We find that additive-by-additive epistasis is the type of epistasis most easily converted into additive variance. For a wide range of models, our results show that epistasis, rather than dominance, plays a significant role in the increase of additive variance following bottlenecks.     

The probability of parallel genetic evolution from standing genetic variation

Parallel evolution is often assumed to result from repeated adaptation to novel, yet ecologically similar, environments. Here, we develop and analyse a mathematical model that predicts the probability of parallel genetic evolution from standing genetic variation as a function of the strength of phenotypic selection and constraints imposed by genetic architecture. Our results show that the probability of parallel genetic evolution increases with the strength of natural selection and effective population size and is particularly likely to occur for genes with large phenotypic effects. Building on these results, we develop a Bayesian framework for estimating the strength of parallel phenotypic selection from genetic data. Using extensive individual‐based simulations, we show that our estimator is robust across a wide range of genetic and evolutionary scenarios and provides a useful tool for rigorously testing the hypothesis that parallel genetic evolution is the result of adaptive evolution. An important result that emerges from our analyses is that existing studies of parallel genetic evolution frequently rely on data that is insufficient for distinguishing between adaptive evolution and neutral evolution driven by random genetic drift. Overcoming this challenge will require sampling more populations and the inclusion of larger numbers of loci.     

Quantitative genetic analysis of larval life history traits in two alpine populations of Rana temporaria

We estimated genetic and maternal variance components of larval life history characters in alpine populations of Rana temporaria (the common frog) using a full-sib/half-sib breeding design. We studied trait plasticity by raising tadpoles at 14 or 20°C in the laboratory. Larval period and metamorphic mass were greater at 14°C. Larval period did not differ between populations, but high elevation metamorphs were larger than low elevation metamorphs. Significant additive variation for larval period was detected in the low altitude population. No significant additive variation was detected for mass at metamorphosis (MM), which instead displayed significant maternal effects. Plasticity in metamorphic mass of froglets was greater in the high altitude population. The plastic response of larval period to temperature did not differ between the populations. Evolution of metamorphic mass is likely constrained by lack of additive genetic variation. In contrast, significant heritability for larval period suggests this trait may evolve in response to environmental change. These results differ from other studies on R. temporaria, suggesting that populations of this broadly distributed species present substantial geographic variation in the genetic architecture and plasticity of tadpole life history traits.     

The genetic architecture of vitiligo

Vitiligo is an autoimmune disease in which destruction of skin melanocytes results in patches of white skin and hair. Genome‐wide linkage studies and genome‐wide association studies in European ancestry cases identified over 50 vitiligo susceptibility loci, defining a model of melanocyte‐directed autoimmunity. Vitiligo heritability is exceedingly high, ~2/3 coming from common and ~1/3 from rare genomic variants; ~20% of vitiligo risk is environmental. Vitiligo genetic risk is polygenic, with greater additive risk in multiplex vitiligo families than simplex cases. Vitiligo age‐of‐onset is bimodal, also involving a major genetic component; a MHC enhancer haplotype confers extreme risk for vitiligo (OR 8.1) and early disease onset, increasing expression of HLA‐DQB1 mRNA and HLA‐DQ protein and thus perhaps facilitating presentation of triggering antigens. Vitiligo triggering also involves a major environmental component; dramatic delay in vitiligo age‐of‐onset, especially from 1973 to 2004, suggests that exposure or response to a key vitiligo environmental trigger diminished during this period. Together, these findings provide deep understanding of vitiligo pathogenesis and genetic architecture, suggesting that vitiligo represents a tractable model for investigating complex disease genetic architecture and predictive aspects of personalized medicine.     

The heritability of inducible defenses in tadpoles

The evolution of plastic traits requires phenotypic trade-offs and heritable traits, yet the latter requirement has received little attention, especially for predator-induced traits. Using a half-sib design, I examined the narrow-sense heritability of predator-induced behaviour, morphology, and life history in larval wood frogs (Rana sylvatica). Many of the traits had significant additive genetic variation in predator (caged Anax longipes) and no-predator environments. Whereas most traits had moderate to high heritability across environments, tail depth exhibited high heritability with predators but low heritability without predators. In addition, several traits had significant heritability for plasticity, suggesting a potential for selection to act on plasticity per se. Genetic correlations confirmed known phenotypic relationships across environments and identified novel relationships within each environment. This appears to be the first investigation of narrow-sense heritabilities for predator-induced traits and confirms that inducible traits previously shown to be under selection also have a genetic basis and should be capable of exhibiting evolutionary responses.     

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.