The Influence of the Mating System on the Maintenance of Genetic Variability in Polygenic Characters

The traditional models of the effect of assortative mating and inbreeding on the genetic variance of polygenic characters (Fisher 1918; Wright 1921) presume that there is no natural selection or mutation. In a large population, the genetic variance determined by additive genes may then increase by up to a factor of two with local inbreeding, and even more with assortative mating. The classical models are still used to interpret data from natural populations. But contrary to their assumptions, most metrical characters in natural populations are usually thought to be under a type of selection which depletes polygenic variation. Mutation is then necessary to maintain genetic variation. The present models show that with the additional features of mutation and selection, in a large population, the mating system has no influence on the amount of genetic variability maintained by additive genes.     

Genotypic dispersion and covariance between relatives under linkage disequilibrium

A random mating diploid population under linkage disequilibrium is considered. In the case of two diallelic loci, the problem about condition and joint distributions of genotypes of relatives being in arbitrary genetic relations is solved. Formulae of the partitioning of genotypic variance and covariance between relatives with respect to a polygenic character are inferred (in the case of many characters - of genotypic covariance matrix).     

Minor quantitative trait loci underlie floral traits associated with mating system divergence in Mimulus

The genetic basis of species differences provides insight into the mode and tempo of phenotypic divergence. We investigate the genetic basis of floral differences between two closely related plant taxa with highly divergent mating systems, Mimulus guttatus (large-flowered outcrosser) and M. nasutus (small-flowered selfer). We had previously constructed a framework genetic linkage map of the hybrid genome containing 174 markers spanning approximately 1800 cM on 14 linkage groups. In this study, we analyze the genetics of 16 floral, reproductive, and vegetative characters measured in a large segregating M. nasutus x M. guttatus F2 population (N = 526) and in replicates of the parental lines and F1 hybrids. Phenotypic analyses reveal strong genetic correlations among floral traits and epistatic breakdown of male and female fertility traits in the F2 hybrids. We use multitrait composite interval mapping to jointly locate and characterize quantitative trait loci (QTLs) underlying interspecific differences in seven floral traits. We identified 24 floral QTLs, most of which affected multiple traits. The large number of QTLs affecting each trait (mean = 13, range = 11-15) indicates a strikingly polygenic basis for floral divergence in this system. In general, QTL effects are small relative to both interspecific differences and environmental variation within genotypes, ruling out QTLs of major effect as contributors to floral divergence between M. guttatus and M. nasutus. QTLs show no pattern of directional dominance. Floral characters associated with pollinator attraction (corolla width) and self-pollen deposition (stigma-anther distance) share several pleiotropic or linked QTLs, but unshared QTLs may have allowed selfing to evolve independently from flower size. We discuss the polygenic nature of divergence between M. nasutus and M. guttatus in light of theoretical work on the evolution of selfing, genetics of adaptation, and maintenance of variation within populations.     

A method to optimize selection on multiple identified quantitative trait loci

A mathematical approach was developed to model and optimize selection on multiple known quantitative trait loci (QTL) and polygenic estimated breeding values in order to maximize a weighted sum of responses to selection over multiple generations. The model allows for linkage between QTL with multiple alleles and arbitrary genetic effects, including dominance, epistasis, and gametic imprinting. Gametic phase disequilibrium between the QTL and between the QTL and polygenes is modeled but polygenic variance is assumed constant. Breeding programs with discrete generations, differential selection of males and females and random mating of selected parents are modeled. Polygenic EBV obtained from best linear unbiased prediction models can be accommodated. The problem was formulated as a multiple-stage optimal control problem and an iterative approach was developed for its solution. The method can be used to develop and evaluate optimal strategies for selection on multiple QTL for a wide range of situations and genetic models.     

The genetics of adaptation: the roles of pleiotropy, stabilizing selection and drift in shaping the distribution of bidirectional fixed mutational effects

Pleiotropy allows for the deterministic fixation of bidirectional mutations: mutations with effects both in the direction of selection and opposite to selection for the same character. Mutations with deleterious effects on some characters can fix because of beneficial effects on other characters. This study analytically quantifies the expected frequency of mutations that fix with negative and positive effects on a character and the average size of a fixed effect on a character when a mutation pleiotropically affects from very few to many characters. The analysis allows for mutational distributions that vary in shape and provides a framework that would allow for varying the frequency at which mutations arise with deleterious and positive effects on characters. The results show that a large fraction of fixed mutations will have deleterious pleiotropic effects even when mutation affects as little as two characters and only directional selection is occurring, and, not surprisingly, as the degree of pleiotropy increases the frequency of fixed deleterious effects increases. As a point of comparison, we show how stabilizing selection and random genetic drift affect the bidirectional distribution of fixed mutational effects. The results are then applied to QTL studies that seek to find loci that contribute to phenotypic differences between populations or species. It is shown that QTL studies are biased against detecting chromosome regions that have deleterious pleiotropic effects on characters.     

GOOD GENES AND DIRECT SELECTION IN THE EVOLUTION OF MATING PREFERENCES

A model is used to study quantitatively the impact of a good genes process and direct natural selection on the evolution of a mating preference. The expression of a male display trait is proportional to genetic quality, which is determined by the number of deleterious mutations a male carries throughout his genome. Genetic variances and covariances, including the covariance between the preference and male trait that drives the good genes process, are allowed to evolve under an infinitesimal model. Results suggest that the good genes process generates only weak indirect selection on preferences, with an effective selection intensity of a few percent or less. If preferences are subject to direct natural selection of the intensity observed for other characters, the good genes process alone is not expected to exaggerate the male trait by more than a few phenotypic standard deviations, contrary to what is observed in highly sexually selected species. Good genes can, however, cause substantial exaggeration if preference genes are nearly selectively neutral. Alternatively, direct selection on preference genes, acting on mating behavior itself or on the genes' pleiotropic effects, can cause mating preferences and male display traits to be exaggerated by any degree. Direct selection of preference genes may therefore play an important role in species that show extreme sexual selection.     

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.     

Quantitative Trait Loci Differentiating the Outbreeding Mimulus Guttatus from the Inbreeding M. Platycalyx

Theoretical predictions about the evolution of selfing depend on the genetic architecture of loci controlling selfing (monogenic vs. polygenic determination, large vs. small effect of alleles, dominance vs. recessiveness), and studies of such architecture are lacking. We inferred the genetic basis of mating system differences between the outbreeding Mimulus guttatus and the inbreeding M. platycalyx by quantitative trait locus (QTL) mapping using random amplified polymorphic DNA and isozyme markers. One to three QTL were detected for each of five mating system characters, and each QTL explained 7.6-28.6% of the phenotypic variance. Taken together, QTL accounted for up to 38% of the variation in mating system characters, and a large proportion of variation was unaccounted for. Inferred QTL often affected more than one trait, contributing to the genetic correlation between those traits. These results are consistent with the hypothesis that quantitative variation in plant mating system characters is primarily controlled by loci with small effect.     

Behavioral genetics of Drosophila ananassae

Drosophila ananassae has a unique status among Drosophila species because of certain peculiarities in its genetic behavior. The most unusual feature of this species is its relatively high frequency of spontaneous male recombination. The results of studies on non-sexual behavior, such as phototactic responses, eclosion rhythm, and preferences for oviposition and pupation sites, lead us to suggest that this behavior is under polygenic control, with a substantial amount of additive genetic variation. Sexual isolation has been reported in D. ananassae with the degree of such isolation being stronger in isofemale lines than in natural populations. The significant variations seen in the mating propensity of several isofemale strains, inversion karyotypes and wild type strains, the diminishing effects of certain mutations on the sexual activity of males, and the positive responses to selection for high and low mating propensity point to a genetic control of sexual behavior in D. ananassae. Males contribute more to variation and thus are more subject to intrasexual selection than females. There is a positive correlation between sternopleural bristle number, mating propensity and fertility in D. ananassae. This correlation between morphometric traits and mating success suggests that larger flies are more successful in mating than smaller ones. There is also evidence for adaptive plasticity and a trade-off between longevity and productivity in D. ananassae. Rare, specific courtship song parameters that provide males with a mating advantage have also been reported in different geographic strains of D. ananassae. The remating behavior of males and females, sperm displacement, and the bi-directional selection for female remating speed indicate that post-mating behavior in this species may also be under genetic control. The occurrence of size assortative mating further indicates that there is size-dependent sexual selection in D. ananassae.     

SPONTANEOUS MUTATIONS FOR LIFE-HISTORY CHARACTERS IN AN OBLIGATE PARTHENOGEN

By allowing mutations to accumulate spontaneously in different lines derived from a single female of an obligately parthenogenetic Daphnia, it has become possible to estimate the rate at which new genetic variance for life-history characters arises as well as to identify the average pleiotropic effects of mutant polygenes. The estimated polygenic mutation rates are quite compatible with those available for sexual organisms. The results are therefore in conflict with the hypothesis that parthenogens compensate for the loss of recombination by elevating the mutation rate. Based on these results, it is argued that the rate of phenotypic evolution may be enhanced as much as five-fold by sexuality. However, if dominance or epistatic gene interactions are of major importance, or if the sensitivity to environmental effects is reduced or the rate of polygenic mutation enhanced under asexuality, the full advantage of sex will not be attained and may even be reversed. Regardless of these conditions, it is clear that the mutational rate of production of polygenic variation is sufficient to allow significant rates of phenotypic evolution in purely asexual organisms.     

Effects of Pleiotropy on Predictions concerning Mutation-Selection Balance for Polygenic Traits

Previous mathematical analyses of mutation-selection balance for metric traits assume that selection acts on the relevant loci only through the character(s) under study. Thus, they implicitly assume that all of the relevant mutation and selection parameters are estimable. A more realistic analysis must recognize that many of the pleiotropic effects of loci contributing variation to a given character are not known. To explore the consequences of these hidden effects, I analyze models of two pleiotropically connected polygenic traits, denoted P1 and P2. The actual equilibrium genetic variance for P1, based on complete knowledge of all mutation and selection parameters for both P1 and P2, can be compared to a prediction based solely on observations of P1. This extrapolation mimics empirically obtainable predictions because of the inevitability of unknown pleiotropic effects. The mutation parameters relevant to P1 are assumed to be known, but selection intensity is estimated from the within-generation reduction of phenotypic variance for P1. The extrapolated prediction is obtained by substituting these parameters into formulas based on single-character analyses. Approximate analytical and numerical results show that the level of agreement between these univariate extrapolations and the actual equilibrium variance depends critically on both the genetic model assumed and the relative magnitudes of the mutation and selection parameters. Unless per locus mutation rates are extremely high, i.e., generally greater than 10(-4), the widely used gaussian approximation for genetic effects at individual loci is not applicable. Nevertheless, the gaussian approximations predict that the true and extrapolated equilibria are in reasonable agreement, i.e., within a factor of two, over a wide range of parameter values. In contrast, an alternative approximation that applies for moderate and low per locus mutation rates predicts that the extrapolation will generally overestimate the true equilibrium variance unless there is little selection associated with hidden effects. The tendency to overestimate is understandable because selection acts on all of the pleiotropic manifestations of a new mutation, but equilibrium covariances among the characters affected may not reveal all of this selection. This casts doubt on the proposal that much of the additive polygenic variance observed in natural populations can be explained by mutation-selection balance. It also indicates the difficulty of critically evaluating this hypothesis.     

QTL analysis of leaf morphological characters in a Quercus robur full-sib family (Q. robur × Q. robur ssp. slavonica)

The distinction between white oak species (section Quercus sensu stricto ) is largely based on leaf morphological characters. There is, however, considerable within-species variation and no single species-diagnostic character, possibly due to phenotypic plasticity and/or underlying genetic variation. The aim of the present study was to identify quantitative trait loci (QTL) underlying the high within-species variation for leaf morphological characters in an F₁ full-sib family derived from a cross between Q. robur and Q. robur ssp. slavonica . In accordance with an earlier QTL mapping study in an intraspecific Q. robur full-sib family, polygenic inheritance was detected for leaf morphological characters that are used to discriminate between the species Quercus robur and Q. petraea . QTLs were distributed over ten linkage groups, showed a moderate effect in terms of phenotypic variance explained (PVE) in the mapping pedigree (3.6–9.6%), but accounted for a considerable amount of the parental differences. Co-localisation of QTLs on the same linkage group in different genetic backgrounds was found for the number and percentage of intercalary veins (NV, PV) on linkage group 3 and for NV on linkage group 5, revealing a high congruence in the relative QTL positions. The generally low correspondence of the other QTLs in the different mapping pedigrees may be an effect of the genetic background and of the environment. In conclusion, leaf morphological characters were found to be under polygenic control, and a comparison to earlier published results led to the identification of two QTLs that were stable across different genetic backgrounds.     

QTL analysis of leaf morphological characters in a Quercus robur full-sib family (Q. robur x Q. robur ssp. slavonica)

The distinction between white oak species (section Quercus sensu stricto) is largely based on leaf morphological characters. There is, however, considerable within-species variation and no single species-diagnostic character, possibly due to phenotypic plasticity and/or underlying genetic variation. The aim of the present study was to identify quantitative trait loci (QTL) underlying the high within-species variation for leaf morphological characters in an F(1) full-sib family derived from a cross between Q. robur and Q. robur ssp. slavonica. In accordance with an earlier QTL mapping study in an intraspecific Q. robur full-sib family, polygenic inheritance was detected for leaf morphological characters that are used to discriminate between the species Quercus robur and Q. petraea. QTLs were distributed over ten linkage groups, showed a moderate effect in terms of phenotypic variance explained (PVE) in the mapping pedigree (3.6-9.6%), but accounted for a considerable amount of the parental differences. Co-localisation of QTLs on the same linkage group in different genetic backgrounds was found for the number and percentage of intercalary veins (NV, PV) on linkage group 3 and for NV on linkage group 5, revealing a high congruence in the relative QTL positions. The generally low correspondence of the other QTLs in the different mapping pedigrees may be an effect of the genetic background and of the environment. In conclusion, leaf morphological characters were found to be under polygenic control, and a comparison to earlier published results led to the identification of two QTLs that were stable across different genetic backgrounds.     

Consequences of genetic linkage for the maintenance of sexually antagonistic polymorphism in hermaphrodites

When selection differs between males and females, pleiotropic effects among genes expressed by both sexes can result in sexually antagonistic selection (SA), where beneficial alleles for one sex are deleterious for the other. For hermaphrodites, alleles with opposing fitness effects through each sex function represent analogous genetic constraints on fitness. Recent theory based on single‐locus models predicts that the maintenance of SA genetic variation should be greatly reduced in partially selfing populations. However, selfing also reduces the effective rate of recombination, which should facilitate selection on linked allelic combinations and expand opportunities for balancing selection in a multilocus context. Here, I develop a two‐locus model of SA selection for simultaneous hermaphrodites, and explore the joint influence of linkage, self‐fertilization, and dominance on the maintainance of SA polymorphism. I find that the effective reduction in recombination caused by selfing significantly expands the parameter space where SA polymorphism can be maintained relative to single‐locus models. In particular, linkage facilitates the invasion of male‐beneficial alleles, partially compensating for the “female‐bias” in the net direction of selection created by selfing. I discuss the implications of accounting for linkage among SA loci for the maintenance of SA genetic variation and mixed mating systems in hermaphrodites.     

Variation in pleiotropy and the mutational underpinnings of the G-matrix

The pattern and extent of pleiotropic gene action can contribute substantially to the internal structure and shape of the additive genetic variance-covariance matrix (G)--a key determinant of evolutionary trajectories. We use data from our study (Estes et al. 2004) on the univariate effects of mutation in a mismatch-repair-defective strain, msh-2, of Caenorhabditis elegans to address the impact of increasing levels of selection on the magnitude and pattern of genetic covariance due to new mutations. Mutational covariances between three life-history traits are shown to exhibit a weak pattern of decline with increasing population size (increasing selection), while the orientation of mutational matrices remains reasonably constant. This suggests that mutations with smaller effects on fitness may tend to be slightly more confined in their influence than large-effect mutations (i.e., small-effect mutations reduce the magnitude of covariation between characters), but do not change the direction of this covariation.     

Pleiotropy or linkage? Their relative contributions to the genetic correlation of quantitative traits and detection by multitrait GWA studies

Genetic correlations between traits may cause correlated responses to selection. Previous models described the conditions under which genetic correlations are expected to be maintained. Selection, mutation, and migration are all proposed to affect genetic correlations, regardless of whether the underlying genetic architecture consists of pleiotropic or tightly linked loci affecting the traits. Here, we investigate the conditions under which pleiotropy and linkage have different effects on the genetic correlations between traits by explicitly modeling multiple genetic architectures to look at the effects of selection strength, degree of correlational selection, mutation rate, mutational variance, recombination rate, and migration rate. We show that at mutation-selection(-migration) balance, mutation rates differentially affect the equilibrium levels of genetic correlation when architectures are composed of pairs of physically linked loci compared to architectures of pleiotropic loci. Even when there is perfect linkage (no recombination within pairs of linked loci), a lower genetic correlation is maintained than with pleiotropy, with a lower mutation rate leading to a larger decrease. These results imply that the detection of causal loci in multitrait association studies will be affected by the type of underlying architectures, whereby pleiotropic variants are more likely to be underlying multiple detected associations. We also confirm that tighter linkage between nonpleiotropic causal loci maintains higher genetic correlations at the traits and leads to a greater proportion of false positives in association analyses.     

Spatial patterns of polygenic variation in Impatiens capensis,a species with an environmentally controlled mixed mating system

Impatiens capensis displays a mixed mating system in which individual out-crossing rate is expected to increase with light and resource availability. We investigated the amount and spatial distribution of polygenic variation for 15 morphological traits within and among six natural populations of I. capensis growing in three distinct light habitats (shaded, mixed, full sun). We grew individuals from each population in uniform greenhouse conditions and detected significant genetic variation among families within populations for all the quantitative traits examined. However, only the features related to the vegetative characteristics of seedlings and sexually mature plants show also differentiation at the population level. Surprisingly, even though light availability is likely to be the most important factor affecting the mating system of I. capensis, we find that: (1) trait means of individuals from similar light environments are not more similar than those from different light environments; (2) partitioning of polygenic variance within and among families differs both among populations from the same light habitat and among characters within each population. If natural selection is maintaining such variation, it must operate primarily through heterogeneous selection pressure within, rather than between, populations.     

Domestication reshaped the genetic basis of inbreeding depression in a maize landrace compared to its wild relative,teosinte

Inbreeding depression is the reduction in fitness and vigor resulting from mating of close relatives observed in many plant and animal species. The extent to which the genetic load of mutations contributing to inbreeding depression is due to large-effect mutations versus variants with very small individual effects is unknown and may be affected by population history. We compared the effects of outcrossing and self-fertilization on 18 traits in a landrace population of maize, which underwent a population bottleneck during domestication, and a neighboring population of its wild relative teosinte. Inbreeding depression was greater in maize than teosinte for 15 of 18 traits, congruent with the greater segregating genetic load in the maize population that we predicted from sequence data. Parental breeding values were highly consistent between outcross and selfed offspring, indicating that additive effects determine most of the genetic value even in the presence of strong inbreeding depression. We developed a novel linkage scan to identify quantitative trait loci (QTL) representing large-effect rare variants carried by only a single parent, which were more important in teosinte than maize. Teosinte also carried more putative juvenile-acting lethal variants identified by segregation distortion. These results suggest a mixture of mostly polygenic, small-effect partially recessive effects in linkage disequilibrium underlying inbreeding depression, with an additional contribution from rare larger-effect variants that was more important in teosinte but depleted in maize following the domestication bottleneck. Purging associated with the maize domestication bottleneck may have selected against some large effect variants, but polygenic load is harder to purge and overall segregating mutational burden increased in maize compared to teosinte.     

Evolution of mating preference and sexual dimorphism

A quantitative genetic model of the joint evolution of female mating preferences and sexual dimorphism in homologous characters of the sexes is described for polygamous species with no male parental effort, such that mating preferences are selectively neutral and evolve only by indirect selection on genetically correlated characters. The male character and the homologous female character are each under stabilizing natural selection toward an optimum phenotype. At an evolutionary equilibrium the female character under natural selection is at its optimum, whereas there is a line of possible equilibria between female mating preferences and the male character. The line of equilibria may be stable or unstable, depending on the intensity of natural selection, the type of mating preferences, and the inheritance of the characters. Various mechanisms for maladaptive evolution of mating preferences and sexual dimorphism are discussed.     

GENOTYPE-ENVIRONMENT INTERACTION AND THE EVOLUTION OF PHENOTYPIC PLASTICITY

Studies of spatial variation in the environment have primarily focused on how genetic variation can be maintained. Many one-locus genetic models have addressed this issue, but, for several reasons, these models are not directly applicable to quantitative (polygenic) traits. One reason is that for continuously varying characters, the evolution of the mean phenotype expressed in different environments (the norm of reaction) is also of interest. Our quantitative genetic models describe the evolution of phenotypic response to the environment, also known as phenotypic plasticity (Gause, 1947), and illustrate how the norm of reaction (Schmalhausen, 1949) can be shaped by selection. These models utilize the statistical relationship which exists between genotype-environment interaction and genetic correlation to describe evolution of the mean phenotype under soft and hard selection in coarse-grained environments. Just as genetic correlations among characters within a single environment can constrain the response to simultaneous selection, so can a genetic correlation between states of a character which are expressed in two environments. Unless the genetic correlation across environments is ± 1, polygenic variation is exhausted, or there is a cost to plasticity, panmictic populations under a bivariate fitness function will eventually attain the optimum mean phenotype for a given character in each environment. However, very high positive or negative correlations can substantially slow the rate of evolution and may produce temporary maladaptation in one environment before the optimum joint phenotype is finally attained. Evolutionary trajectories under hard and soft selection can differ: in hard selection, the environments with the highest initial mean fitness contribute most individuals to the mating pool. In both hard and soft selection, evolution toward the optimum in a rare environment is much slower than it is in a common one. A subdivided population model reveals that migration restriction can facilitate local adaptation. However, unless there is no migration or one of the special cases discussed for panmictic populations holds, no geographical variation in the norm of reaction will be maintained at equilibrium. Implications of these results for the interpretation of spatial patterns of phenotypic variation in natural populations are discussed.