THE ACTION OF STABILIZING SELECTION,MUTATION, AND DRIFT ON EPISTATIC QUANTITATIVE TRAITS

For a quantitative trait under stabilizing selection, the effect of epistasis on its genetic architecture and on the changes of genetic variance caused by bottlenecking were investigated using theory and simulation. Assuming empirical estimates of the rate and effects of mutations and the intensity of selection, we assessed the impact of two‐locus epistasis (synergistic/antagonistic) among linked or unlinked loci on the distribution of effects and frequencies of segregating loci in populations at the mutation‐selection‐drift balance. Strong pervasive epistasis did not modify substantially the genetic properties of the trait and, therefore, the most likely explanation for the low amount of variation usually accounted by the loci detected in genome‐wide association analyses is that many causal loci will pass undetected. We investigated the impact of epistasis on the changes in genetic variance components when large populations were subjected to successive bottlenecks of different sizes, considering the action of genetic drift, operating singly (D), or jointly with mutation (MD) and selection (MSD). An initial increase of the different components of the genetic variance, as well as a dramatic acceleration of the between‐line divergence, were always associated with synergistic epistasis but were strongly constrained by selection.     

Genetic models to estimate additive and non-additive effects of marker-associated QTL using multiple regression techniques

Summary The development of molecular markers has recently raised expectations for their application in selection programs. However, some questions related to quantitative trait loci (QTL) identification are still unanswered. The objectives of this paper are (1) to develop statistical genetic models for detecting and locating on the genome multi-QTL with additive, dominance and epistatic effects using multiple linear regression analysis in the backcross and F_n generations from the cross of two inbred lines; and (2) to discuss the bias caused by linked and unlinked QTL on the genetic estimates. Non-linear models were developed for different backcross and F_n generations when both epistasis and no epistasis were assumed. Generation analysis of marked progenies is suggested as a way of increasing the number of observations for the estimates without additional cost for molecular scoring. Some groups of progenies can be created in different generations from the same scored individuals. The non-linear models were transformed into approximate multivariate linear models to which combined stepwise and standard regression analysis could be applied. Expressions for the biases of the marker classes from linked QTL were obtained when no epistasis was assumed. When epistasis was assumed, these expressions increased in complexity, and the biases were caused by both linked and unlinked QTL.     

Epistasis Is a Major Determinant of the Additive Genetic Variance in Mimulus guttatus

The influence of genetic interactions (epistasis) on the genetic variance of quantitative traits is a major unresolved problem relevant to medical, agricultural, and evolutionary genetics. The additive genetic component is typically a high proportion of the total genetic variance in quantitative traits, despite that underlying genes must interact to determine phenotype. This study estimates direct and interaction effects for 11 pairs of Quantitative Trait Loci (QTLs) affecting floral traits within a single population of Mimulus guttatus. With estimates of all 9 genotypes for each QTL pair, we are able to map from QTL effects to variance components as a function of population allele frequencies, and thus predict changes in variance components as allele frequencies change. This mapping requires an analytical framework that properly accounts for bias introduced by estimation errors. We find that even with abundant interactions between QTLs, most of the genetic variance is likely to be additive. However, the strong dependency of allelic average effects on genetic background implies that epistasis is a major determinant of the additive genetic variance, and thus, the population’s ability to respond to selection.     

The role of epistatic gene interactions in the response to selection and the evolution of evolvability

It has been argued that the architecture of the genotype-phenotype map determines evolvability, but few studies have attempted to quantify these effects. In this article we use the multilinear epistatic model to study the effects of different forms of epistasis on the response to directional selection. We derive an analytical prediction for the change in the additive genetic variance, and use individual-based simulations to understand the dynamics of evolvability and the evolution of genetic architecture. This shows that the major determinant for the evolution of the additive variance, and thus the evolvability, is directional epistasis. Positive directional epistasis leads to an acceleration of evolvability, while negative directional epistasis leads to canalization. In contrast, pure non-directional epistasis has little effect on the response to selection. One consequence of this is that the classical epistatic variance components, which do not distinguish directional and non-directional effects, are useless as predictors of evolutionary dynamics. The build-up of linkage disequilibrium also has negligible effects. We argue that directional epistasis is likely to have major effects on evolutionary dynamics and should be the focus of empirical studies of epistasis.     

Epistasis and Its Contribution to Genetic Variance Components

We present a new parameterization of physiological epistasis that allows the measurement of epistasis separate from its effects on the interaction (epistatic) genetic variance component. Epistasis is the deviation of two-locus genotypic values from the sum of the contributing single-locus genotypic values. This parameterization leads to statistical tests for epistasis given estimates of two-locus genotypic values such as can be obtained from quantitative trait locus studies. The contributions of epistasis to the additive, dominance and interaction genetic variances are specified. Epistasis can make substantial contributions to each of these variance components. This parameterization of epistasis allows general consideration of the role of epistasis in evolution by defining its contribution to the additive genetic variance.     

Epistasis: Obstacle or Advantage for Mapping Complex Traits?

Identification of genetic loci in complex traits has focused largely on one-dimensional genome scans to search for associations between single markers and the phenotype. There is mounting evidence that locus interactions, or epistasis, are a crucial component of the genetic architecture of biologically relevant traits. However, epistasis is often viewed as a nuisance factor that reduces power for locus detection. Counter to expectations, recent work shows that fitting full models, instead of testing marker main effect and interaction components separately, in exhaustive multi-locus genome scans can have higher power to detect loci when epistasis is present than single-locus scans, and improvement that comes despite a much larger multiple testing alpha-adjustment in such searches. We demonstrate, both theoretically and via simulation, that the expected power to detect loci when fitting full models is often larger when these loci act epistatically than when they act additively. Additionally, we show that the power for single locus detection may be improved in cases of epistasis compared to the additive model. Our exploration of a two step model selection procedure shows that identifying the true model is difficult. However, this difficulty is certainly not exacerbated by the presence of epistasis, on the contrary, in some cases the presence of epistasis can aid in model selection. The impact of allele frequencies on both power and model selection is dramatic.     

The genetic architecture of male colour differences between a sympatric Lake Malawi cichlid species pair

The genetic basis of traits involved in reproductive isolation is a key parameter in models of sympatric speciation by sexual selection, a potential mechanism driving the explosive radiation of East African cichlids. Analysis of hybrid crosses between two sympatric Lake Malawi cichlid species, representing the extremes of the extant colour distribution, generated Castle-Wright estimates of four to seven loci controlling colour differences. Segregation patterns deviated from a purely additive model with a significant contribution from dominance, and possibly also epistasis. Evidence was found for a strong influence of autosomal loci. As departures from simple additive variation could effect the operation of models of sympatric speciation, dominance and epistasis should not be neglected.     

The Evolution of Epistasis and the Advantage of Recombination in Populations of Bacteriophage T4

Experiments reported here test two hypotheses about the evolution of recombination: first, the Fisher-Muller concept that sexual organisms respond to selection more rapidly than do asexual ones, and second, that epistasis is more likely to evolve in the absence of recombination. Populations of bacteriophage T4 were selected by the drug proflavine in discrete generations and the change in mean population fitness was monitored. Three separate selection series yielded results supporting the Fisher-Muller hypothesis. The amount of epistasis evolved was measured by partitioning the T4 map into regions and comparing the sum of the proflavine resistances of each region with the resistance of the whole. Significantly more interactions were found in phage isolated from the populations with lower total recombination than in those from populations with higher recombination. The degree to which these experiments fit preconceived notions about natural selection suggests that microorganisms may be advantageously used in other population genetics experiments.     

Polygenic Mutation in Drosophila Melanogaster: Non-Linear Divergence among Unselected Strains

A highly inbred strain of Drosophila melanogaster was subdivided into 20 replicate sublines that were maintained independently with 10 pairs of randomly sampled parents per generation for 180 generations. The variance between lines in abdominal and sternopleural bristle number increased little after 100 generations, in contrast to the neutral expectation of a linear increase; and the covariances of line means between different generations declined with increasing number of generations apart, in contrast to the neutral expectation of constant covariance. Thus, under a neutral model, the estimates of mutational variance were lower than for previous estimates from the first 100 generations of subline divergence. An autoregressive model was fitted to the variance of line means that indicated strong natural selection. There is no single unequivocal explanation for the results. Possible and nonexclusive alternatives include stabilizing selection on bristle number and deleterious effects on fitness of bristle mutations. The inferred strengths of selection on both traits are too high for stabilizing selection alone, and the between-line variance did not continue to increase sufficiently for pleiotropy alone to account for the observations. A third potential explanation that does not invoke selection is duplicate epistasis between mutations affecting bristle number.     

Effect on linkage disequilibrium of selection for a quantitative character with epistasis

Summary Selection for a character controlled by additive genes induces linkage disequilibrium which reduces the additive genetic variance usable for further selective gains. Additive x additive epistasis contributes to selection response through development of linkage disequilibrium between interacting loci. To investigate the relative importance of the two effects of linkage disequilibrium, formulae are presented and results are reported of simulations using models involving additive, additive x additive and dominance components. The results suggest that so long as epistatic effects are not large relative to additive effects, and the proportion of pairs of loci which show epistasis is not very high, the predominant effect of linkage disequilibrium will be to reduce the rate of selection response.     

Population differentiation in an annual legume: genetic architecture

Abstract. The presence or absence of epistasis, or gene interaction, is explicitly assumed in many evolutionary models. Although many empirical studies have documented a role of epistasis in population divergence under laboratory conditions, there have been very few attempts at quantifying epistasis in the native environment where natural selection is expected to act. In addition, we have little understanding of the frequency with which epistasis contributes to the evolution of natural populations. In this study we used a quantitative genetic design to quantify the contribution of epistasis to population divergence for fitness components of a native annual legume, Chamaecrista fasciculata . The design incorporated the contrast of performance of F₂ and F₃ segregating progeny of 18 interpopulation crosses with the F₁ and their parents. Crosses were conducted between populations from 100 m to 2000 km apart. All generations were grown for two seasons in the natural environment of one of the parents. The F₁ often outperformed the parents. This F₁ heterosis reveals population structure and suggests that drift is a major contributor to population differentiation. The F₂ generation demonstrated that combining genes from different populations can sometimes have unexpected positive effects. However, the F₃ performance indicated that combining genes from different populations decreased vigor beyond that due to the expected loss of heterozygosity. Combined with previous data, our results suggest that both selection and drift contribute to population differentiation that is based on epistatic genetic divergence. Because only the F₃ consistently expressed hybrid breakdown, we conclude that the epistasis documented in our study reflects interactions among linked loci.     

The evolution of recombination in a heterogeneous environment

Most models describing the evolution of recombination have focused on the case of a single population, implicitly assuming that all individuals are equally likely to mate and that spatial heterogeneity in selection is absent. In these models, the evolution of recombination is driven by linkage disequilibria generated either by epistatic selection or drift. Models based on epistatic selection show that recombination can be favored if epistasis is negative and weak compared to directional selection and if the recombination modifier locus is tightly linked to the selected loci. In this article, we examine the joint effects of spatial heterogeneity in selection and epistasis on the evolution of recombination. In a model with two patches, each subject to different selection regimes, we consider the cases of mutation-selection and migration-selection balance as well as the spread of beneficial alleles. We find that including spatial heterogeneity extends the range of epistasis over which recombination can be favored. Indeed, recombination can be favored without epistasis, with negative and even with positive epistasis depending on environmental circumstances. The selection pressure acting on recombination-modifier loci is often much stronger with spatial heterogeneity, and even loosely linked modifiers and free linkage may evolve. In each case, predicting whether recombination is favored requires knowledge of both the type of environmental heterogeneity and epistasis, as none of these factors alone is sufficient to predict the outcome.     

Long-term selection for a quantitative character in large replicate populations of Drosophila melanogaster

Summary Six replicate lines of Drosophila melanogaster, which had been selected for increased abdominal bristle number for more than 85 generations, were assayed by hierarchical analysis of variance and offspring on parent regression immediately after selection ceased, and by single-generation realised heritability after more than 25 generations of subsequent relaxed selection.Half-sib estimates of heritability in 5 lines were as high as in the base population and much higher than observed genetic gains would suggest, excluding lack of sufficient additive genetic variance as a cause of ineffective selection in these lines. Also, there was considerable diversity among the six lines in composition of phenotypic variability: in addition to differences in the additive genetic component, one or more of the components due to dominance, epistasis, sex-linkage or genotype-environment interaction appeared to be important in different lines.Even after relaxed selection, single-generation realised heritabilities in four lines were as high as in the base population. As a large proportion of total genetic gain must have been made by fixation of favourable alleles, the compensatory increase of genetic variability has been sought in a genetic model involving genes at low initial frequencies, enhancement of gene effects during selection and/or new mutations.     

A unified model for functional and statistical epistasis and its application in quantitative trait Loci analysis

Interaction between genes, or epistasis, is found to be common and it is a key concept for understanding adaptation and evolution of natural populations, response to selection in breeding programs, and determination of complex disease. Currently, two independent classes of models are used to study epistasis. Statistical models focus on maintaining desired statistical properties for detection and estimation of genetic effects and for the decomposition of genetic variance using average effects of allele substitutions in populations as parameters. Functional models focus on the evolutionary consequences of the attributes of the genotype-phenotype map using natural effects of allele substitutions as parameters. Here we provide a new, general and unified model framework: the natural and orthogonal interactions (NOIA) model. NOIA implements tools for transforming genetic effects measured in one population to the ones of other populations (e.g., between two experimental designs for QTL) and parameters of statistical and functional epistasis into each other (thus enabling us to obtain functional estimates of QTL), as demonstrated numerically. We develop graphical interpretations of functional and statistical models as regressions of the genotypic values on the gene content, which illustrates the difference between the models--the constraint on the slope of the functional regression--and when the models are equivalent. Furthermore, we use our theoretical foundations to conceptually clarify functional and statistical epistasis, discuss the advantages of NOIA over previous theory, and stress the importance of linking functional and statistical models.     

Interactions between Pesticide Genes: Model and Experiment

In response to years of intense selection pressure by organophosphate insecticides, several different insecticide resistance mechanisms have evolved in natural populations of the mosquito Culex pipiens. We examined interactions between two of the most important mechanisms using a four-compartment model of insecticide pharmacokinetics. The joint effect of different mechanisms of resistance can be expressed in terms of epistasis at the physiological level in this model. The type of epistasis predicted by the model depends on the particular physiological mechanisms of resistance involved. Resistance due to a reduced penetration of the insecticide combines multiplicatively with other resistance factors, but resistance due to detoxicative processes and to insensitivity of the target site combines additively. How the pattern of epistasis at the physiological level is translated into fitness epistasis in natural populations of this mosquito depends on the intensity and pattern of insecticide selection in the field.     

Genetics of leaf blight resistance in wheat

Summary Studies on the genetics of leaf blight caused byAlternaria triticina using generation mean analysis revealed that additive components played a major role, but that dominance components also contributed significantly in controlling the variability for leaf blight resistance in wheat crosses. Furthermore, the additive x additive type of epistasis was predominant in the first three crosses, whereas in the fourth cross additive x dominance (j) and dominance x dominance (1) components of epistasis were most significant. Because of this it may be desirable to follow a simple recurrent selection scheme for higher tolerance, to isolate resistant plants from the segregating populations derived from crosses of parents of diverse origin following the pedigree method of breeding. CPAN-1887 was very tolerant to leaf blight in the present study and should be utilized in hybridization programs to develop leaf-blight-resistant varieties.     

Predicting the frequencies of transgressive segregants for yield and yield components in wheat

Summary Genetical analysis of the F₂ triple test cross design combined with conventional early generations was used to elucidate the genetical control of yield and yield components in two crosses of winter wheat. From estimates of the additive, {d}, and additive X additive, {i}, components of means, together with the additive genetical variance, D, predicted frequencies of recombinant inbred lines that would transgress the parental range were calculated for each cross. The accuracy of predictions was evaluated by comparing expected frequencies with observed numbers in populations of F₆ lines previously developed by single seed descent.For both crosses and all characters where an adequate genetical model was found to explain the observed variation between the early generations, good agreement between predicted and observed frequencies of transgressive segregants was obtained. Furthermore, for characters exhibiting significant epistasis, allowance for additive X additive {i} epistasis in the prediction equations was sufficient to allow for skewness of the recombinant inbred population.These results demonstrate that cross performance in wheat can be predicted from genetical analysis of early generations, and the value of this approach in breeding new varieties is discussed.     

Nonparametric Method for Genomics-Based Prediction of Performance of Quantitative Traits Involving Epistasis in Plant Breeding

Genomic selection (GS) procedures have proven useful in estimating breeding value and predicting phenotype with genome-wide molecular marker information. However, issues of high dimensionality, multicollinearity, and the inability to deal effectively with epistasis can jeopardize accuracy and predictive ability. We, therefore, propose a new nonparametric method, pRKHS, which combines the features of supervised principal component analysis (SPCA) and reproducing kernel Hilbert spaces (RKHS) regression, with versions for traits with no/low epistasis, pRKHS-NE, to high epistasis, pRKHS-E. Instead of assigning a specific relationship to represent the underlying epistasis, the method maps genotype to phenotype in a nonparametric way, thus requiring fewer genetic assumptions. SPCA decreases the number of markers needed for prediction by filtering out low-signal markers with the optimal marker set determined by cross-validation. Principal components are computed from reduced marker matrix (called supervised principal components, SPC) and included in the smoothing spline ANOVA model as independent variables to fit the data. The new method was evaluated in comparison with current popular methods for practicing GS, specifically RR-BLUP, BayesA, BayesB, as well as a newer method by Crossa et al., RKHS-M, using both simulated and real data. Results demonstrate that pRKHS generally delivers greater predictive ability, particularly when epistasis impacts trait expression. Beyond prediction, the new method also facilitates inferences about the extent to which epistasis influences trait expression.     

Epistasis can accelerate adaptive diversification in haploid asexual populations

A fundamental goal of the biological sciences is to determine processes that facilitate the evolution of diversity. These processes can be separated into ecological, physiological, developmental and genetic. An ecological process that facilitates diversification is frequency-dependent selection caused by competition. Models of frequency-dependent adaptive diversification have generally assumed a genetic basis of phenotype that is non-epistatic. Here, we present a model that indicates diversification is accelerated by an epistatic basis of phenotype in combination with a competition model that invokes frequency-dependent selection. Our model makes use of a genealogical model of epistasis and insights into the effects of balancing selection on the genealogical structure of a population to understand how epistasis can facilitate diversification. The finding that epistasis facilitates diversification may be informative with respect to empirical results that indicate an epistatic basis of phenotype in experimental bacterial populations that experienced adaptive diversification.     

Epistasis can increase multivariate trait diversity in haploid non-recombining populations

We evaluate the effect of epistasis on genetically-based multivariate trait variation in haploid non-recombining populations. In a univariate setting, past work has shown that epistasis reduces genetic variance (additive plus epistatic) in a population experiencing stabilizing selection. Here we show that in a multivariate setting, epistasis also reduces total genetic variation across the entire multivariate trait in a population experiencing stabilizing selection. But, we also show that the pattern of variation across the multivariate trait can be more even when epistasis occurs compared to when epistasis is absent, such that some character combinations will have more genetic variance when epistasis occurs compared to when epistasis is absent. In fact, a measure of generalized multivariate trait variation can be increased by epistasis under weak to moderate stabilizing selection conditions, as well as neutral conditions. Likewise, a measure of conditional evolvability can be increased by epistasis under weak to moderate stabilizing selection and neutral conditions. We investigate the nature of epistasis assuming a multivariate-normal model genetic effects and investigate the nature of epistasis underlying the biophysical properties of RNA. Increased multivariate diversity occurs for populations that are infinite in size, as well as populations that are finite in size. Our model of finite populations is explicitly genealogical and we link our findings about the evenness of eigenvalues with epistasis to prior work on the genealogical mapping of epistatic effects.