RESPONSE TO SELECTION IN PARTIALLY SELF-FERTILIZING POPULATIONS. I. SELECTION ON A SINGLE TRAIT

Self-fertilization is a common form of reproduction in plants and it has important implications for quantitative trait evolution. Here, I present a model of selection on quantitative traits that can accommodate any level of self-fertilization. The “structured linear model” (SLM) predicts the evolution of the mean phenotype as a function of three distinct quantities: the mean additive genetic value, the directional dominance, and the mean inbreeding coefficient. Stochastic simulations of truncation selection demonstrate the accuracy of the SLM in predicting changes in the mean and variance of a quantitative trait over the full range of selfing rates. They also illustrate how complex interactions between selection and mating system determine the population distribution of inbreeding coefficients and also the amount of linkage disequilibrium. Changes in the genetic variance due to linkage disequilibria, which are commonly referred to as the “Bulmer effect,” are greatly magnified by selfing. This complicates the relationship between selfing rate and response to selection. Like the random mating theory, the parameters of the SLM can be estimated from phenotypic data.     

The Genetic Covariance between Characters Maintained by Pleiotropic Mutations

A statistical genetic model of a multivariate phenotype is derived to investigate the covariation of pleiotropic mutations with additive effects under the combined action of phenotypic selection, linkage and the mating system. Equilibrium formulas for large, randomly mating populations demonstrate that, when selection on polygenic variation is much smaller than twice the harmonic mean recombination rate between loci with interacting fitnesses, linkage disequilibrium is negligible and pleiotropy is the main cause of genetic correlations between characters. Under these conditions, approximate expressions for the dynamics of the genetic covariances due to pleiotropic mutations are obtained. Patterns of genetic covariance between characters and their evolution are discussed with reference to data on polygenic mutation, chromosomal organization and morphological integration.     

CORRELATED EVOLUTION OF MATING STRATEGY AND INBREEDING DEPRESSION WITHIN AND AMONG POPULATIONS OF THE HERMAPHRODITIC SNAIL PHYSA ACUTA

Inbreeding depression is one of the main forces opposing the evolution of self-fertilization. Of central importance is the hypothesis that inbreeding depression and selfing coevolve antagonistically, generating either low selfing rate and high inbreeding depression or vice versa. However, there is limited evidence for this coevolution within species. We investigated this topic in the hermaphroditic snail Physa acuta . In this species, isolated individuals delay the onset of egg laying compared to individuals having access to mates. Longer delays ("waiting times") indicate more intense selfing avoidance. We measured inbreeding depression and waiting time in a large quantitative-genetic experiment (281 outbred families derived from 26 natural populations). We observed large genetic variance for both traits and a strong positive genetic covariance between them, most of which resided within rather than among populations. It means that, within populations, individuals with higher mutation load avoided selfing more strongly on average. This genetic covariance may result from pleiotropy and/or linkage disequilibrium. Whatever its genetic architecture, the fact it emerges specifically when individuals are deprived of mates suggests it is not fortuitous and rather reflects the action of natural selection. We conclude that a diversity of mating strategies can arise within populations subjected to variation in inbreeding depression.     

QUANTITATIVE GENETIC VARIANCE MAINTAINED BY FLUCTUATING SELECTION WITH OVERLAPPING GENERATIONS: VARIANCE COMPONENTS AND COVARIANCES

The quantitative genetic variance-covariance that can be maintained in a random environment is studied, assuming overlapping generations and Gaussian stabilizing selection with a fluctuating optimum. The phenotype of an individual is assumed to be determined by additive contributions from each locus on paternal and maternal gametes (i.e., no epistasis and no dominance). Recurrent mutation is ignored, but linkage between loci is arbitrary. The genotype distribution in the evolutionarily stable population is generically discrete: only a finite number of polymorphic alleles with distinctly different effects are maintained, even though we allow a continuum of alleles with arbitrary phenotypic contributions to invade. Fluctuating selection maintains nonzero genetic variance in the evolutionarily stable population if the environmental heterogeneity is larger than a certain threshold. Explicit asymptotic expressions for the standing variance-covariance components are derived for the population near the threshold, or for large generational overlap, as a function of environmental variability and genetic parameters (i.e., number of loci, recombination rate, etc.), using the fact that the genotype distribution is discrete. Above the threshold, the population maintains considerable genetic variance in the form of positive linkage disequilibrium and positive gamete covariance (Hardy-Weinberg disequilibrium) as well as allelic variance. The relative proportion of these disequilibrium variances in the total genetic variance increases with the environmental variability.     

"Runaway" social evolution: reinforcing selection for inbreeding and altruism.

Kin selection theory predicts that altruistic behaviors, those that decrease the fitness of the individual performing the behavior but increase the fitness of the recipient, can increase in frequency if the individuals interacting are closely related. Several studies have shown that inbreeding therefore generally increases the effectiveness of kin selection when fitnesses are linear, additive functions of the number of altruists in the family, although with extreme forms of altruism, inbreeding can actually retard the evolution of altruism. These models assume that a constant proportion of the population mates at random and a constant proportion practices some form of inbreeding. In order to investigate the effect of inbreeding on the evolution of altruistic behavior when the mating structure is allowed to evolve, we examined a two-locus model by computer simulation of a diploid case and illustrated the important qualitative features by mathematical analysis of a haploid case. One locus determines an individual's propensity to perform altruistic social behavior and the second locus determines the probability that an individual will mate within its sibship. We assumed positive selection for altruism and no direct selection at the inbreeding locus. We observed that the altruistic allele and the inbreeding allele become positively associated, even when the initial conditions of the model assume independence between these loci. This linkage disequilibrium becomes established, because the altruistic allele increases more rapidly in the inbreeding segment of the population. This association subsequently results in indirect selection on the inbreeding locus. However, the dynamics of this model go beyond a simple "hitch-hiking" effect, because high levels of altruism lead to increased inbreeding, and high degrees of inbreeding accelerate the rate of change of the altruistic allele in the entire population. Thus, the dynamics of this model are similar to those of "runaway" sexual selection, with gene frequency change at the two loci interactively causing rapid evolutionary change.     

SELECTION ON OVERDOMINANT GENES MAINTAINS HETEROZYGOSITY ALONG MULTIPLE CHROMOSOMES IN A CLONAL LINEAGE OF HONEY BEE

Correlations between fitness and genome‐wide heterozygosity (heterozygosity‐fitness correlations, HFCs) have been reported across a wide range of taxa. The genetic basis of these correlations is controversial: do they arise from genome‐wide inbreeding (“general effects”) or the “local effects” of overdominant loci acting in linkage disequilibrium with neutral loci? In an asexual thelytokous lineage of the Cape honey bee (Apis mellifera capensis), the effects of inbreeding have been homogenized across the population, making this an ideal system in which to detect overdominant loci, and to make inferences about the importance of overdominance on HFCs in general. Here we investigate the pattern of zygosity along two chromosomes in 42 workers from the clonal Cape honey bee population. On chromosome III (which contains the sex‐locus, a gene that is homozygous‐lethal) and chromosome IV we show that the pattern of zygosity is characterized by loss of heterozygosity in short regions followed by the telomeric restoration of heterozygosity. We infer that at least four selectively overdominant genes maintain heterozygosity on chromosome III and three on chromosome IV via local effects acting on neutral markers in linkage disequilibrium. We conclude that heterozygote advantage and local effects may be more common and evolutionarily significant than is generally appreciated.     

EVOLUTION IN FLUCTUATING ENVIRONMENTS: DECOMPOSING SELECTION INTO ADDITIVE COMPONENTS OF THE ROBERTSON–PRICE EQUATION

We analyze the stochastic components of the Robertson–Price equation for the evolution of quantitative characters that enables decomposition of the selection differential into components due to demographic and environmental stochasticity. We show how these two types of stochasticity affect the evolution of multivariate quantitative characters by defining demographic and environmental variances as components of individual fitness. The exact covariance formula for selection is decomposed into three components, the deterministic mean value, as well as stochastic demographic and environmental components. We show that demographic and environmental stochasticity generate random genetic drift and fluctuating selection, respectively. This provides a common theoretical framework for linking ecological and evolutionary processes. Demographic stochasticity can cause random variation in selection differentials independent of fluctuating selection caused by environmental variation. We use this model of selection to illustrate that the effect on the expected selection differential of random variation in individual fitness is dependent on population size, and that the strength of fluctuating selection is affected by how environmental variation affects the covariance in Malthusian fitness between individuals with different phenotypes. Thus, our approach enables us to partition out the effects of fluctuating selection from the effects of selection due to random variation in individual fitness caused by demographic stochasticity.     

Causes of covariation of phenotypic traits among populations

Morphological and life-history traits often vary among populations of a species. Traits generally do not vary independently, but show patterns of covariation that can arise from genetic and environmental influences on phenotype. Covariance of traits may arise at an among-population level when genetically influenced traits diverge among populations in a correlated manner. Genetic correlations caused by pleiotropy and/or gene linkage can cause traits to evolve together, but among-population covariance can also arise among traits that are not genetically correlated. For example, “selective covariance” can arise when natural selection directly causes correlated change in a suite of traits. Similarly, mutation, migration, and drift may also sometimes cause correlated genetic changes among populations. Because covariation of traits among populations can arise by several different processes, the evolution of suites of traits must be interpreted with great caution. We discuss the sources of among-population covariance and illustrate one approach to identifying the sources' using data on floral traits of Dalechampia scandens (Euphorbiaceae).     

An exact form of the breeder's equation for the evolution of a quantitative trait under natural selection

Starting with the Price equation, I show that the total evolutionary change in mean phenotype that occurs in the presence of fitness variation can be partitioned exactly into five components representing logically distinct processes. One component is the linear response to selection, as represented by the breeder's equation of quantitative genetics, but with heritability defined as the linear regression coefficient of mean offspring phenotype on parent phenotype. The other components are identified as constitutive transmission bias, two types of induced transmission bias, and a spurious response to selection caused by a covariance between parental fitness and offspring phenotype that cannot be predicted from parental phenotypes. The partitioning can be accomplished in two ways, one with heritability measured before (in the absence of) selection, and the other with heritability measured after (in the presence of) selection. Measuring heritability after selection, though unconventional, yields a representation for the linear response to selection that is most consistent with Darwinian evolution by natural selection because the response to selection is determined by the reproductive features of the selected group, not of the parent population as a whole. The analysis of an explicitly Mendelian model shows that the relative contributions of the five terms to the total evolutionary change depends on the level of organization (gene, individual, or mated pair) at which the parent population is divided into phenotypes, with each frame of reference providing unique insight. It is shown that all five components of phenotypic evolution will generally have nonzero values as a result of various combinations of the normal features of Mendelian populations, including biparental sex, allelic dominance, inbreeding, epistasis, linkage disequilibrium, and environmental covariances between traits. Additive genetic variance can be a poor predictor of the adaptive response to selection in these models. The narrow-sense heritability sigma2A/sigma2P should be viewed as an approximation to the offspring-parent linear regression rather than the other way around.     

Linkage Disequilibrium in Human Ribosomal Genes: Implications for Multigene Family Evolution

Members of the rDNA multigene family within a species do not evolve independently, rather, they evolve together in a concerted fashion. Between species, however, each multigene family does evolve independently indicating that mechanisms exist which will amplify and fix new mutations both within populations and within species. In order to evaluate the possible mechanisms by which mutation, amplification and fixation occur we have determined the level of linkage disequilibrium between two polymorphic sites in human ribosomal genes in five racial groups and among individuals within two of these groups. The marked linkage disequilibrium we observe within individuals suggests that sister chromatid exchanges are much more important than homologous or nonhomologous recombination events in the concerted evolution of the rDNA family and further that recent models of molecular drive may not apply to the evolution of the rDNA multigene family.     

The genetic basis of female mate preferences

We review the evidence for genetic variation in female and male mate preferences. Genetic differences between species and partially isolated races show that preferences can evolve and were genetically variable in the past. Within populations there is good evidence of genetic variation, both of discrete genetic effects (8 cases) and quantitative genetic effects (17 cases), from a diverse range of taxa. We also review evidence for the presence of genetic covariance between mate preferences and sexual traits in the other sex. The 11 studies go a long way to validating the theoretical prediction of positive genetic covariance. The few negative results are best explained by a lack of appropriate experimental design. One unresolved question is whether genetic covariance is due to linkage disequilibrium between unlinked genes or physical linkage. Some evidence points to linkage disequilibrium but this is not yet conclusive.     

Inbreeding of bottlenecked butterfly populations. Estimation using the likelihood of changes in marker allele frequencies

Polymorphic enzyme and minisatellite loci were used to estimate the degree of inbreeding in experimentally bottlenecked populations of the butterfly, Bicyclus anynana (Satyridae), three generations after founding events of 2, 6, 20, or 300 individuals, each bottleneck size being replicated at least four times. Heterozygosity fell more than expected, though not significantly so, but this traditional measure of the degree of inbreeding did not make full use of the information from genetic markers. It proved more informative to estimate directly the probability distribution of a measure of inbreeding, sigma2, the variance in the number of descendants left per gene. In all bottlenecked lines, sigma2 was significantly larger than in control lines (300 founders). We demonstrate that this excess inbreeding was brought about both by an increase in the variance of reproductive success of individuals, but also by another process. We argue that in bottlenecked lines linkage disequilibrium generated by the small number of haplotypes passing through the bottleneck resulted in hitchhiking of particular marker alleles with those haplotypes favored by selection. In control lines, linkage disequilibrium was minimal. Our result, indicating more inbreeding than expected from demographic parameters, contrasts with the findings of previous (Drosophila) experiments in which the decline in observed heterozygosity was slower than expected and attributed to associative overdominance. The different outcomes may both be explained as a consequence of linkage disequilibrium under different regimes of inbreeding. The likelihood-based method to estimate inbreeding should be of wide applicability. It was, for example, able to resolve small differences in sigma2 among replicate lines within bottleneck-size treatments, which could be related to the observed variation in reproductive viability.     

An inbreeding model of associative overdominance during a population bottleneck

Associative overdominance, the fitness difference between heterozygotes and homozygotes at a neutral locus, is classically described using two categories of models: linkage disequilibrium in small populations or identity disequilibrium in infinite, partially selfing populations. In both cases, only equilibrium situations have been considered. In the present study, associative overdominance is related to the distribution of individual inbreeding levels (i.e., genomic autozygosity). Our model integrates the effects of physical linkage and variation in inbreeding history among individual pedigrees. Hence, linkage and identity disequilibrium, traditionally presented as alternatives, are summarized within a single framework. This allows studying nonequilibrium situations in which both occur simultaneously. The model is applied to the case of an infinite population undergoing a sustained population bottleneck. The effects of bottleneck size, mating system, marker gene diversity, deleterious genomic mutation parameters, and physical linkage are evaluated. Bottlenecks transiently generate much larger associative overdominance than observed in equilibrium finite populations and represent a plausible explanation of empirical results obtained, for instance, in marine species. Moreover, the main origin of associative overdominance is random variation in individual inbreeding whereas physical linkage has little effect.     

Ecological speciation

Ecological processes are central to the formation of new species when barriers to gene flow (reproductive isolation) evolve between populations as a result of ecologically‐based divergent selection. Although laboratory and field studies provide evidence that ‘ecological speciation’ can occur, our understanding of the details of the process is incomplete. Here we review ecological speciation by considering its constituent components: an ecological source of divergent selection, a form of reproductive isolation, and a genetic mechanism linking the two. Sources of divergent selection include differences in environment or niche, certain forms of sexual selection, and the ecological interaction of populations. We explore the evidence for the contribution of each to ecological speciation. Forms of reproductive isolation are diverse and we discuss the likelihood that each may be involved in ecological speciation. Divergent selection on genes affecting ecological traits can be transmitted directly (via pleiotropy) or indirectly (via linkage disequilibrium) to genes causing reproductive isolation and we explore the consequences of both. Along with these components, we also discuss the geography and the genetic basis of ecological speciation. Throughout, we provide examples from nature, critically evaluate their quality, and highlight areas where more work is required.     

Linkage disequilibrium in Bougainville Island

Linkage disequilibria are estimated for three 2-locus systems in 18 samples from Bougainville Island, Solomon Islands. The systems are haptoglobin, acid phosphatase and MN blood group. The disequilibria are estimated two ways: by maximum likelihood (ML) and by the covariance between the non-alleles. Though seven of the 52 ML estimates are statistically different than zero, none of the covariance estimates are significant. We conclude that because linkage disequilibrium for loosely linked loci is a small quantity and because the sample sizes for most populations studied by anthropologists are small, linkage disequilibrium will not be a useful parameter for the study of natural selection in these populations.     

Correlated evolution of life-history with size at maturity in Daphnia pulicaria: patterns within and between populations

Explaining the repeated evolution of similar sets of traits under similar environmental conditions is an important issue in evolutionary biology. The extreme alternative classes of explanations for correlated suites of traits are optimal adaptation and genetic constraint resulting from pleiotropy. Adaptive explanations presume that individual traits are free to evolve to their local optima and that convergent evolution represents particularly adaptive combinations of traits. Alternatively, if pleiotropy is strong and difficult to break, strong selection on one or a few particularly important characters would be expected to result in consistent correlated evolution of associated traits. If pleiotropy is common, we predict that the pattern of divergence among populations will consistently reflect the within-population genetic architecture. To test the idea that the multivariate life-history phenotype is largely a byproduct of strong selection on body size, we imposed divergent artificial selection on size at maturity upon two populations of the cladoceran Daphnia pulicaria, chosen on the basis of their extreme divergence in body size. Overall, the trajectory of divergence between the two natural populations did not differ from that predicted by the genetic architecture within each population. However, the pattern of correlated responses suggested the presence of strong pleiotropic constraints only for adult body size and not for other life-history traits. One trait, offspring size, appears to have evolved in a way different from that expected from the within-population genetic architecture and may be under stabilizing selection.     

Genetic evaluation methods for populations with dominance and inbreeding

Summary The effect of inbreeding on mean and genetic covariance matrix for a quantitative trait in a population with additive and dominance effects is shown. This genetic covariance matrix is a function of five relationship matrices and five genetic parameters describing the population. Elements of the relationship matrices are functions of Gillois (1964) identity coefficients for the four genes at a locus in two individuals. The equivalence of the path coefficient method (Jacquard 1966) and the tabular method (Smith and Mäki-Tanila 1990) to compute the covariance matrix of additive and dominance effects in a population with inbreeding is shown. The tabular method is modified to compute relationship matrices rather than the covariance matrix, which is trait dependent. Finally, approximate and exact Best Linear Unbiased Predictions (BLUP) of additive and dominance effects are compared using simulated data with inbreeding but no directional selection. The trait simulated was affected by 64 unlinked biallelic loci with equal effect and complete dominance. Simulated average inbreeding levels ranged from zero in generation one to 0.35 in generation five. The approximate method only accounted for the effect of inbreeding on mean and additive genetic covariance matrix, whereas the exact accounted for all of the changes in mean and genetic covariance matrix due to inbreeding. Approximate BLUP, which is computable for large populations where exact BLUP is not feasible, yielded unbiased predictions of additive and dominance effects in each generation with only slightly reduced accuracies relative to exact BLUP.     

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.     

Divergence and evolution of assortative mating in a polygenic trait model of speciation with gene flow

Assortative mating is an important driver of speciation in populations with gene flow and is predicted to evolve under certain conditions in few‐locus models. However, the evolution of assortment is less understood for mating based on quantitative traits, which are often characterized by high genetic variability and extensive linkage disequilibrium between trait loci. We explore this scenario for a two‐deme model with migration, by considering a single polygenic trait subject to divergent viability selection across demes, as well as assortative mating and sexual selection within demes, and investigate how trait divergence is shaped by various evolutionary forces. Our analysis reveals the existence of sharp thresholds of assortment strength, at which divergence increases dramatically. We also study the evolution of assortment via invasion of modifiers of mate discrimination and show that the ES assortment strength has an intermediate value under a range of migration‐selection parameters, even in diverged populations, due to subtle effects which depend sensitively on the extent of phenotypic variation within these populations. The evolutionary dynamics of the polygenic trait is studied using the hypergeometric and infinitesimal models. We further investigate the sensitivity of our results to the assumptions of the hypergeometric model, using individual‐based simulations.     

Functional pleiotropy and mating system evolution in plants: frequency-independent mating

Mutations that alter the morphology of floral displays (e.g., flower size) or plant development can change multiple functions simultaneously, such as pollen export and selfing rate. Given the effect of these various traits on fitness, pleiotropy may alter the evolution of both mating systems and floral displays, two characters with high diversity among angiosperms. The influence of viability selection on mating system evolution has not been studied theoretically. We model plant mating system evolution when a single locus simultaneously affects the selfing rate, pollen export, and viability. We assume frequency-independent mating, so our model characterizes prior selfing. Pleiotropy between increased viability and selfing rate reduces opportunities for the evolution of pure outcrossing, can favor complete selfing despite high inbreeding depression, and notably, can cause the evolution of mixed mating despite very high inbreeding depression. These results highlight the importance of pleiotropy for mating system evolution and suggest that selection by nonpollinating agents may help explain mixed mating, particularly in species with very high inbreeding depression.