Stabilizing selection,mutational bias,and the evolution of sex*

Stabilizing selection around a fixed phenotypic optimum is expected to disfavor sexual reproduction, since asexually reproducing organisms can maintain a higher fitness at equilibrium, while sex disrupts combinations of compensatory mutations. This conclusion rests on the assumption that mutational effects on phenotypic traits are unbiased, that is, mutation does not tend to push phenotypes in any particular direction. In this article, we consider a model of stabilizing selection acting on an arbitrary number of polygenic traits coded by bialellic loci, and show that mutational bias may greatly reduce the mean fitness of asexual populations compared with sexual ones in regimes where mutations have weak to moderate fitness effects. Indeed, mutation and drift tend to push the population mean phenotype away from the optimum, this effect being enhanced by the low effective population size of asexual populations. In a second part, we present results from individual‐based simulations showing that positive rates of sex are favored when mutational bias is present, while the population evolves toward complete asexuality in the absence of bias. We also present analytical (QLE) approximations for the selective forces acting on sex in terms of the effect of sex on the mean and variance in fitness among offspring.     

Effects of partial selfing on the equilibrium genetic variance,mutation load,and inbreeding depression under stabilizing selection

The mating system of a species is expected to have important effects on its genetic diversity. In this article, we explore the effects of partial selfing on the equilibrium genetic variance V_g, mutation load L, and inbreeding depression δ under stabilizing selection acting on a arbitrary number n of quantitative traits coded by biallelic loci with additive effects. When the ratio is low (where U is the total haploid mutation rate on selected traits) and effective recombination rates are sufficiently high, genetic associations between loci are negligible and the genetic variance, mutation load, and inbreeding depression are well predicted by approximations based on single‐locus models. For higher values of and/or lower effective recombination, moderate genetic associations generated by epistasis tend to increase V_g, L, and δ, this regime being well predicted by approximations including the effects of pairwise associations between loci. For yet higher values of and/or lower effective recombination, a different regime is reached under which the maintenance of coadapted gene complexes reduces V_g, L, and δ. Simulations indicate that the values of V_g, L, and δ are little affected by assumptions regarding the number of possible alleles per locus.     

THE EVOLUTION OF CANALIZATION AND THE BREAKING OF VON BAER'S LAWS: MODELING THE EVOLUTION OF DEVELOPMENT WITH EPISTASIS

Evolution can change the developmental processes underlying a character without changing the average expression of the character itself. This sort of change must occur in both the evolution of canalization, in which a character becomes increasingly buffered against genetic or developmental variation, and in the phenomenon of closely related species that show similar adult phenotypes but different underlying developmental patterns. To study such phenomena, I develop a model that follows evolution on a surface representing adult phenotype as a function of underlying developmental characters. A contour on such a “phenotype landscape” is a set of states of developmental characters that produce the same adult phenotype. Epistasis induces curvature of this surface, and degree of canalization is represented by the slope along a contour. I first discuss the geometric properties of phenotype landscapes, relating epistasis to canalization. I then impose a fitness function on the phenotype and model evolution of developmental characters as a function of the fitness function and the local geometry of the surface. This model shows how canalization evolves as a population approaches an optimum phenotype. It further shows that under some circumstances, “decanalization” can occur, in which the expression of adult phenotype becomes increasingly sensitive to developmental variation. This process can cause very similar populations to diverge from one another developmentally even when their adult phenotypes experience identical selection regimes.     

PURGING THE GENOME WITH SEXUAL SELECTION: REDUCING MUTATION LOAD THROUGH SELECTION ON MALES

Healthy males are likely to have higher mating success than unhealthy males because of differential expression of condition‐dependent traits such as mate searching intensity, fighting ability, display vigor, and some types of exaggerated morphological characters. We therefore expect that most new mutations that are deleterious for overall fitness may also be deleterious for male mating success. From this perspective, sexual selection is not limited to influencing those genes directly involved in exaggerated morphological traits but rather affects most, if not all, genes in the genome. If true, sexual selection can be an important force acting to reduce the frequency of deleterious mutations and, as a result, mutation load. We review the literature and find various forms of indirect evidence that sexual selection helps to eliminate deleterious mutations. However, direct evidence is scant, and there are almost no data available to address a key issue: is selection in males stronger than selection in females? In addition, the total effect of sexual selection on mutation load is complicated by possible increases in mutation rate that may be attributable to sexual selection. Finally, sexual selection affects population fitness not only through mutation load but also through sexual conflict, making it difficult to empirically measure how sexual selection affects load. Several lines of enquiry are suggested to better fill large gaps in our understanding of sexual selection and its effect on genetic load.     

SELECTION BIASES THE PREVALENCE AND TYPE OF EPISTASIS ALONG ADAPTIVE TRAJECTORIES

The contribution to an organism's phenotype from one genetic locus may depend upon the status of other loci. Such epistatic interactions among loci are now recognized as fundamental to shaping the process of adaptation in evolving populations. Although little is known about the structure of epistasis in most organisms, recent experiments with bacterial populations have concluded that antagonistic interactions abound and tend to deaccelerate the pace of adaptation over time. Here, we use the NK model of fitness landscapes to examine how natural selection biases the mutations that substitute during evolution based on their epistatic interactions. We find that, even when beneficial mutations are rare, these biases are strong and change substantially throughout the course of adaptation. In particular, epistasis is less prevalent than the neutral expectation early in adaptation and much more prevalent later, with a concomitant shift from predominantly antagonistic interactions early in adaptation to synergistic and sign epistasis later in adaptation. We observe the same patterns when reanalyzing data from a recent microbial evolution experiment. These results show that when the order of substitutions is not known, standard methods of analysis may suggest that epistasis retards adaptation when in fact it accelerates it.     

FIXATION OF MUTATORS IN ASEXUAL POPULATIONS: THE ROLE OF GENETIC DRIFT AND EPISTASIS

We study the evolutionary dynamics of an asexual population of nonmutators and mutators on a class of epistatic fitness landscapes. We consider the situation in which all mutations are deleterious and mutators are produced from nonmutators continually at a constant rate. We find that in an infinitely large population, a minimum nonmutator‐to‐mutator conversion rate is required to fix the mutators but an arbitrarily small conversion rate results in the fixation of mutators in a finite population. We calculate analytical expressions for the mutator fraction at mutation‐selection balance and fixation time for mutators in a finite population when the difference between the mutation rate for mutator and nonmutator is smaller (regime I) and larger (regime II) than the selection coefficient. Our main result is that in regime I, the mutator fraction and the fixation time are independent of epistasis but in regime II, mutators are rarer and take longer to fix when the decrease in fitness with the number of deleterious mutations occurs at an accelerating rate (synergistic epistasis) than at a diminishing rate (antagonistic epistasis). Our analytical results are compared with numerics and their implications are discussed.     

MUTATION AND EXTINCTION: THE ROLE OF VARIABLE MUTATIONAL EFFECTS,SYNERGISTIC EPISTASIS,BENEFICIAL MUTATIONS,AND DEGREE OF OUTCROSSING

Recent theoretical studies have illustrated the potential role of spontaneous deleterious mutation as a cause of extinction in small populations. However, these studies have not addressed several genetic issues, which can in principle have a substantial influence on the risk of extinction. These include the presence of synergistic epistasis, which can reduce the rate of mutation accumulation by progressively magnifying the selective effects of mutations, and the occurrence of beneficial mutations, which can offset the effects of previous deleterious mutations. In stochastic simulations of small populations (effective sizes on the order of 100 or less), we show that both synergistic epistasis and the rate of beneficial mutation must be unrealistically high to substantially reduce the risk of extinction due to random fixation of deleterious mutations. However, in analytical calculations based on diffusion theory, we show that in large, outcrossing populations (effective sizes greater than a few hundred), very low levels of beneficial mutation are sufficient to prevent mutational decay. Further simulation results indicate that in populations small enough to be highly vulnerable to mutational decay, variance in deleterious mutational effects reduces the risk of extinction, assuming that the mean deleterious mutational effect is on the order of a few percent or less. We also examine the magnitude of outcrossing that is necessary to liberate a predominantly selfing population from the threat of long-term mutational deterioration. The critical amount of outcrossing appears to be greater than is common in near-obligately selfing plant species, supporting the contention that such species are generally doomed to extinction via random drift of new mutations. Our results support the hypothesis that a long-term effective population size in the neighborhood of a few hundred individuals defines an approximate threshold, below which outcrossing populations are vulnerable to extinction via fixation of deleterious mutations, and above which immunity is acquired.     

Influence of Gene Interaction on Complex Trait Variation with Multilocus Models

Although research effort is being expended into determining the importance of epistasis and epistatic variance for complex traits, there is considerable controversy about their importance. Here we undertake an analysis for quantitative traits utilizing a range of multilocus quantitative genetic models and gene frequency distributions, focusing on the potential magnitude of the epistatic variance. All the epistatic terms involving a particular locus appear in its average effect, with the number of two-locus interaction terms increasing in proportion to the square of the number of loci and that of third order as the cube and so on. Hence multilocus epistasis makes substantial contributions to the additive variance and does not, per se, lead to large increases in the nonadditive part of the genotypic variance. Even though this proportion can be high where epistasis is antagonistic to direct effects, it reduces with multiple loci. As the magnitude of the epistatic variance depends critically on the heterozygosity, for models where frequencies are widely dispersed, such as for selectively neutral mutations, contributions of epistatic variance are always small. Epistasis may be important in understanding the genetic architecture, for example, of function or human disease, but that does not imply that loci exhibiting it will contribute much genetic variance. Overall we conclude that theoretical predictions and experimental observations of low amounts of epistatic variance in outbred populations are concordant. It is not a likely source of missing heritability, for example, or major influence on predictions of rates of evolution.     

EVOLUTION OF TRADE-OFFS BETWEEN SEXUAL AND ASEXUAL PHASES AND THE ROLE OF REPRODUCTIVE PLASTICITY IN THE GENETIC ARCHITECTURE OF APHID LIFE HISTORIES

Life‐history theory postulates that evolution is constrained by trade‐offs (i.e., negative genetic correlations) among traits that contribute to fitness. However, in organisms with complex life cycles, trade‐offs may drastically differ between phases, putatively leading to different evolutionary trajectories. Here, we tested this possibility by examining changes in life‐history traits in an aphid species that alternates asexual and sexual reproduction in its life cycle. The quantitative genetics of reproductive and dispersal traits was studied in 23 lineages (genotypes) of the bird cherry‐oat aphid Rhopalosiphum padi, during both the sexual and asexual phases, which were induced experimentally under specific environmental conditions. We found large and significant heritabilities (broad‐sense) for all traits and several negative genetic correlations between traits (trade‐offs), which are related to reproduction (i.e., numbers of the various sexual or asexual morphs) or dispersal (i.e., numbers of winged or wingless morphs). These results suggest that R. padi exhibits lineage specialization both in reproductive and dispersal strategies. In addition, we found important differences in the structure of genetic variance–covariance matrices ( G ) between phases. These differences were due to two large, negative genetic correlations detected during the asexual phase only: (1) between fecundity and age at maturity and (2) between the production of wingless and winged parthenogenetic females. We propose that this differential expression in genetic architecture results from a reallocation scheme during the asexual phase, when sexual morphs are not produced. We also found significant G × E interaction and nonsignificant genetic correlations across phases, indicating that genotypes could respond independently to selection in each phase. Our results reveal a rather unique situation in which the same population and even the same genotypes express different genetic (co)variation under different environmental conditions, driven by optimal resource allocation criteria.     

DELETERIOUS MUTATION AND THE EVOLUTION OF GENETIC LIFE CYCLES

It is often proposed that the ability of diploids to mask deleterious mutations leads to an evolutionary advantage over haploidy. In this paper, we studied the evolution of the relative duration of haploid and diploid phases using a model of recurrent deleterious mutations across the entire genome. We found that a completely diploid life cycle is favored under biologically reasonable conditions, even when prolonging the diploid phase reduces a population's mean fitness. A haploid cycle is favored when there is complete linkage throughout the genome or when mutations are either highly deleterious or partially dominant. These results hold when loci interact multiplicatively and for synergistic epistasis. The strength of selection generated on the life cycle can be substantial because of the cumulative effect of selection against mutations across many loci. We did not find conditions that support cycles that retain both phases, such as those found in some plants and algae. Thus, selection against deleterious mutations may be an important force in the evolution of life cycles but may not be sufficient to explain all the patterns of life cycles seen in nature.     

EPISTASIS AND THE EVOLUTION OF ADDITIVE GENETIC VARIANCE IN POPULATIONS THAT PASS THROUGH A BOTTLENECK

Traditional models of genetic drift predict a linear decrease in additive genetic variance for populations passing through a bottleneck. This perceived lack of heritable variance limits the scope of founder-effect models of speciation. We produced 55 replicate bottleneck populations maintained at two male-female pairs through four generations of inbreeding (average F = 0.39). These populations were formed from an F₂ intercross of the LG/J and SM/J inbred mouse strains. Two contemporaneous control strains maintained with more than 60 mating pairs per generation were formed from this same source population. The average level of within-strain additive genetic variance for adult body weight was compared between the control and experimental lines. Additive genetic variance for adult body weight within experimental bottleneck strains was significantly higher than expected under an additive genetic model This enhancement of additive genetic variance under inbreeding is likely to be due to epistasis, which retards or reverses the loss of additive genetic variance under inbreeding for adult body weight in this population. Therefore, founder-effect speciation processes may not be constrained by a loss of heritable variance due to population bottlenecks.     

Evolutionary quantitative genetics of nonlinear developmental systems

In quantitative genetics, the effects of developmental relationships among traits on microevolution are generally represented by the contribution of pleiotropy to additive genetic covariances. Pleiotropic additive genetic covariances arise only from the average effects of alleles on multiple traits, and therefore the evolutionary importance of nonlinearities in development is generally neglected in quantitative genetic views on evolution. However, nonlinearities in relationships among traits at the level of whole organisms are undeniably important to biology in general, and therefore critical to understanding evolution. I outline a system for characterizing key quantitative parameters in nonlinear developmental systems, which yields expressions for quantities such as trait means and phenotypic and genetic covariance matrices. I then develop a system for quantitative prediction of evolution in nonlinear developmental systems. I apply the system to generating a new hypothesis for why direct stabilizing selection is rarely observed. Other uses will include separation of purely correlative from direct and indirect causal effects in studying mechanisms of selection, generation of predictions of medium‐term evolutionary trajectories rather than immediate predictions of evolutionary change over single generation time‐steps, and the development of efficient and biologically motivated models for separating additive from epistatic genetic variances and covariances.     

EVOLUTIONARILY STABLE SEX RATIOS AND MUTATION LOAD

Frequency‐dependent selection should drive dioecious populations toward a 1:1 sex ratio, but biased sex ratios are widespread, especially among plants with sex chromosomes. Here, we develop population genetic models to investigate the relationships between evolutionarily stable sex ratios, haploid selection, and deleterious mutation load. We confirm that when haploid selection acts only on the relative fitness of X‐ and Y‐bearing pollen and the sex ratio is controlled by the maternal genotype, seed sex ratios evolve toward 1:1. When we also consider haploid selection acting on deleterious mutations, however, we find that biased sex ratios can be stably maintained, reflecting a balance between the advantages of purging deleterious mutations via haploid selection, and the disadvantages of haploid selection on the sex ratio. Our results provide a plausible evolutionary explanation for biased sex ratios in dioecious plants, given the extensive gene expression that occurs across plant genomes at the haploid stage.     

THE EFFECTS OF SELECTION IN THE GAMETOPHYTE STAGE ON MUTATIONAL LOAD

We have studied a multilocus selection model of a plant population in which mutations to deleterious alleles occur that may affect not only the diploid sporophyte stage, but also the haploid pollen stage before zygote formation. We investigated the reduction in inbreeding depression (as measured in the sporophyte) caused by the lowering of mutant allele frequencies due to selection in the pollen. This is important for a full understanding of the role of inbreeding depression in the maintenance of outcrossing in seed plants. We also studied the theoretically expected relationship between the pollen fitnesses of different pollen donor genotypes and the fitnesses of the diploid progeny that they sire. This relationship can be compared with the results of experiments in which pollen was subjected to selection, and improved progeny quality was observed. We found that on the mutational load model there is, as expected intuitively, a positive covariance between the pollen and zygote fitnesses, but that it is likely to be small. Subjecting pollen to an episode of strong selection is usually expected to increase sporophyte fitness only slightly.     

SLOWLY SWITCHING BETWEEN ENVIRONMENTS FACILITATES REVERSE EVOLUTION IN SMALL POPULATIONS

Natural populations must constantly adapt to ever‐changing environmental conditions. A particularly interesting question is whether such adaptations can be reversed by returning the population to an ancestral environment. Such evolutionary reversals have been observed in both natural and laboratory populations. However, the factors that determine the reversibility of evolution are still under debate. The time scales of environmental change vary over a wide range, but little is known about how the rate of environmental change influences the reversibility of evolution. Here, we demonstrate computationally that slowly switching between environments increases the reversibility of evolution for small populations that are subject to only modest clonal interference. For small populations, slow switching reduces the mean number of mutations acquired in a new environment and also increases the probability of reverse evolution at each of these “genetic distances.” As the population size increases, slow switching no longer reduces the genetic distance, thus decreasing the evolutionary reversibility. We confirm this effect using both a phenomenological model of clonal interference and also a Wright–Fisher stochastic simulation that incorporates genetic diversity. Our results suggest that the rate of environmental change is a key determinant of the reversibility of evolution, and provides testable hypotheses for experimental evolution.     

FISHER'S MODEL AND THE GENOMICS OF ADAPTATION: RESTRICTED PLEIOTROPY,HETEROGENOUS MUTATION,AND PARALLEL EVOLUTION

Genetic theories of adaptation generally overlook the genes in which beneficial substitutions occur, and the likely variation in their mutational effects. We investigate the consequences of heterogeneous mutational effects among loci on the genetics of adaptation. We use a generalization of Fisher's geometrical model, which assumes multivariate Gaussian stabilizing selection on multiple characters. In our model, mutation has a distinct variance–covariance matrix of phenotypic effects for each locus. Consequently, the distribution of selection coefficients s varies across loci. We assume each locus can only affect a limited number of independent linear combinations of phenotypic traits (restricted pleiotropy), which differ among loci, an effect we term “orientation heterogeneity.” Restricted pleiotropy can sharply reduce the overall proportion of beneficial mutations. Orientation heterogeneity has little impact on the shape of the genomic distribution, but can substantially increase the probability of parallel evolution (the repeated fixation of beneficial mutations at the same gene in independent populations), which is highest with low pleiotropy. We also consider variation in the degree of pleiotropy and in the mean s across loci. The latter impacts the genomic distribution of s, but has a much milder effect on parallel evolution. We discuss these results in the light of evolution experiments.     

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.     

SEXUAL CONFLICT AND THE MAINTENANCE OF MULTIVARIATE GENETIC VARIATION

Mate choice should erode additive genetic variation in sexual displays, yet these traits often harbor substantial genetic variation. Nevertheless, recent developments in quantitative genetics have suggested that multivariate genetic variation in the combinations of traits under selection may still be depleted. Accordingly, the erosion and maintenance of variation may only be detectable by studying whole suites of traits. One potential process favoring the maintenance of genetic variance in multiple trait combinations is the modification of sexual selection via sexually antagonistic interactions between males and females. Here we consider how interlocus sexual conflict can shape the genetic architecture of male sexual traits in the cricket, Teleogryllus commodus. In this species, the ability of each sex to manipulate insemination success significantly alters the selection acting on male courtship call properties. Using a quantitative genetic breeding design we estimated the additive genetic variation in these traits and then predicted the change in variation due to previously documented patterns of sexual selection. Our results indicate that female choice should indeed deplete multivariate genetic variance, but that sexual conflict over insemination success may oppose this loss of variance. We suggest that changes in the direction of selection due to sexually antagonistic interactions will be an important and potentially widespread factor in maintaining multivariate genetic variation.     

THE MAINTENANCE OF OBLIGATE SEX IN FINITE,STRUCTURED POPULATIONS SUBJECT TO RECURRENT BENEFICIAL AND DELETERIOUS MUTATION

Although there is no known general explanation as to why sexual populations resist asexual invasion, previous work has shown that sexuals can outcompete asexuals in structured populations. However, it is currently unknown whether costly sex can be maintained with the weak structure that is commonly observed in nature. We investigate the conditions under which obligate sexuals resist asexual invasion in structured populations subject to recurrent mutation. We determine the level of population structure needed to disfavor asexuals, as calculated using the average F_st between all pairs of demes. We show that the critical F_st needed to maintain sex decreases as the population size increases, and approaches modest levels as observed in many natural populations. Sex is maintained with lower F_st if there are both advantageous and deleterious mutation, if mutation rates are sufficiently high, and if deleterious mutants have intermediate selective strengths, which maximizes the effect of Muller’s ratchet. Additionally, the critical F_st needed to maintain sex is lower when there are a large number of subpopulations. Lower F_st values are needed to maintain sex when demes vary substantially in their pairwise distances (e.g., when arrayed along one dimension), although this effect is often modest, especially if some long‐distance dispersal is present.     

GENERALISTS,SPECIALISTS, AND THE EVOLUTION OF PHENOTYPIC PLASTICITY IN SYMPATRIC POPULATIONS OF DISTINCT SPECIES

The evolution of phenotypic plasticity is studied in a model with two reproductively isolated “species” in a coarse-grained environment, consisting of two types of habitats. A quantitative genetic model for selection was constructed, in which habitats differ in the optimal value for a focal trait, and with random dispersal among habitats. The main interest was to study the effects of different selection regimes. Three cases were investigated: (1) without any limits to plasticity; (2) without genetic variation for plasticity; and (3) with a fitness cost for phenotypically plastic reactions. In almost all cases a generalist strategy to exploit both habitats emerged. Without any limits to plasticity, optimal adaptive reactions evolved. Without any genetic variation for plasticity, a compromise strategy with an intermediate, fixed phenotype evolved, whereas in the presence of costs a plastic compromise between the demands of the habitats and the costs associated with plasticity was found. Specialization and phenotypic differentiation was only found when selection within habitats was severe and optimal phenotypes for different habitats were widely different. Under soft selection (local regulation of population numbers in each habitat) the specialists coexisted; under hard selection (global regulation of population numbers) one specialist outcompeted the other. The prevalent evolutionary outcome of compromises rather than specialization implies that costs or constraints are not necessarily detectable as local adaptation in transplantation or translocation experiments.