Epistasis in polygenic traits and the evolution of genetic architecture under stabilizing selection

We consider the effects of epistasis in a polygenic trait in the balance of mutation and stabilizing selection. The main issues are the genetic variation maintained in equilibrium and the evolution of the mutational effect distribution. The model assumes symmetric mutation and a continuum of alleles at all loci. Epistasis is modeled proportional to pairwise products of the single-locus effects. A general analytical formalism is developed. Assuming linkage equilibrium, we derive results for the equilibrium mutation load and the genetic and mutational variance in the house of cards and the Gaussian approximation. The additive genetic variation maintained in mutation-selection balance is reduced by any pattern of the epistatic interactions. The mutational variance, in contrast, is often increased. Large differences in mutational effects among loci emerge, and a negative correlation among (standard mean) locus mutation effects and mutation rates is predicted. Contrary to the common view since Waddington, we find that stabilizing selection in general does not lead to canalization of the trait. We propose that canalization as a target of selection instead occurs at the genic level. Here, primarily genes with a high mutation rate are buffered, often at the cost of decanalization of other genes. An intuitive interpretation of this view is given in the discussion.     

A POPULATION GENETIC THEORY OF CANALIZATION

Canalization is the suppression of phenotypic variation. Depending on the causes of phenotypic variation, one speaks either of genetic or environmental canalization. Genetic canalization describes insensitivity of a character to mutations, and the insensitivity to environmental factors is called environmental canalization. Genetic canalization is of interest because it influences the availability of heritable phenotypic variation to natural selection, and is thus potentially important in determining the pattern of phenotypic evolution. In this paper a number of population genetic models are considered of a quantitative character under stabilizing selection. The main purpose of this study is to define the population genetic conditions and constraints for the evolution of canalization. Environmental canalization is modeled as genotype specific environmental variance. It is shown that stabilizing selection favors genes that decrease environmental variance of quantitative characters. However, the theoretical limit of zero environmental variance has never been observed. Of the many ways to explain this fact, two are addressed by our model. It is shown that a “canalization limit” is reached if canalizing effects of mutations are correlated with direct effects on the same character. This canalization limit is predicted to be independent of the strength of stabilizing selection, which is inconsistent with recent experimental data (Sterns et al. 1995). The second model assumes that the canalizing genes have deleterious pleiotropic effects. If these deleterious effects are of the same magnitude as all the other mutations affecting fitness very strong stabilizing selection is required to allow the evolution of environmental canalization. Genetic canalization is modeled as an influence on the average effect of mutations at a locus of other genes. It is found that the selection for genetic canalization critically depends on the amount of genetic variation present in the population. The more genetic variation, the stronger the selection for canalizing effects. All factors that increase genetic variation favor the evolution of genetic canalization (large population size, high mutation rate, large number of genes). If genetic variation is maintained by mutation-selection balance, strong stabilizing selection can inhibit the evolution of genetic canalization. Strong stabilizing selection eliminates genetic variation to a level where selection for canalization does not work anymore. It is predicted that the most important characters (in terms of fitness) are not necessarily the most canalized ones, if they are under very strong stabilizing selection (k > 0.2V_e). The rate of decrease of mutational variance V_m is found to be less than 10% of the initial V_m. From this result it is concluded that characters with typical mutational variances of about 10^–3 V_e are in a metastable state where further evolution of genetic canalization is too slow to be of importance at a microevolutionary time scale. The implications for the explanation of macroevolutionary patterns are discussed.     

Comparing Mutational Variabilities

We have reviewed the available data on V(M), the amount of genetic variation in phenotypic traits produced each generation by mutation. We use these data to make several qualitative tests of the mutation-selection balance hypothesis for the maintenance of genetic variance (MSB). To compare V(M) values, we use three dimensionless quantities: mutational heritability, V(M)/V(E); the mutational coefficient of variation, CV(M); and the ratio of the standing genetic variance to V(M), V(G)/V(M). Since genetic coefficients of variation for life history traits are larger than those for morphological traits, we predict that under MSB, life history traits should also have larger CV(M). This is confirmed; life history traits have a median CV(M) value more than six times higher than that for morphological traits. V(G)/V(M) approximates the persistence time of mutations under MSB in an infinite population. In order for MSB to hold, V(G)/V(M) must be small, substantially less than 1000, and life history traits should have smaller values than morphological traits. V(G)/V(M) averages about 50 generations for life history traits and 100 generations for morphological traits. These observations are all consistent with the predictions of a mutation-selection balance model.     

The Nature and Extent of Mutational Pleiotropy in Gene Expression of Male Drosophila serrata

The nature and extent of mutational pleiotropy remain largely unknown, despite the central role that pleiotropy plays in many areas of biology, including human disease, agricultural production, and evolution. Here, we investigate the variation in 11,604 gene expression traits among 41 mutation accumulation (MA) lines of Drosophila serrata. We first confirmed that these expression phenotypes were heritable, detecting genetic variation in 96% of them in an outbred, natural population of D. serrata. Among the MA lines, 3385 (29%) of expression traits were variable, with a mean mutational heritability of 0.0005. In most traits, variation was generated by mutations of relatively small phenotypic effect; putative mutations with effects of greater than one phenotypic standard deviation were observed for only 8% of traits. With most (71%) traits unaffected by any mutation, our data provide no support for universal pleiotropy. We further characterized mutational pleiotropy in the 3385 variable traits, using sets of 5, randomly assigned, traits. Covariance among traits chosen at random with respect to their biological function is expected only if pleiotropy is extensive. Taking an analytical approach in which the variance unique to each trait in the random 5-trait sets was partitioned from variance shared among traits, we detected significant (at 5% false discovery rate) mutational covariance in 21% of sets. This frequency of statistically supported covariance implied that at least some mutations must pleiotropically affect a substantial number of traits (>70; 0.6% of all measured traits).     

The opportunity for canalization and the evolution of genetic networks

There has been a recent revival of interest in how genetic interactions evolve, spurred on by an increase in our knowledge of genetic interactions at the molecular level. Empirical work on genetic networks has revealed a surprising amount of robustness to perturbations, suggesting that robustness is an evolved feature of genetic networks. Here, we derive a general model for the evolution of canalization that can incorporate any form of perturbation. We establish an upper bound to the strength of selection on canalization that is approximately equal to the fitness load in the system. This method makes it possible to compare different forms of perturbation, including genetic, developmental, and environmental effects. In general, load that arises from mutational processes is low because the mutation rate is itself low. Mutation load can create selection for canalization in a small network that can be achieved through dominance evolution or gene duplication, and in each case selection for canalization is weak at best. In larger genetic networks, selection on genetic canalization can be reasonably strong because larger networks have higher mutational load. Because load induced through migration, segregation, developmental noise, and environmental variance is not mutation limited, each can cause strong selection for canalization.     

Epistasis and its relationship to canalization in the RNA virus phi 6

Although deleterious mutations are believed to play a critical role in evolution, assessing their realized effect has been difficult. A key parameter governing the effect of deleterious mutations is the nature of epistasis, the interaction between the mutations. RNA viruses should provide one of the best systems for investigating the nature of epistasis because the high mutation rate allows a thorough investigation of mutational effects and interactions. Nonetheless, previous investigations of RNA viruses by S. Crotty and co-workers and by S. F. Elena have been unable to detect a significant effect of epistasis. Here we provide evidence that positive epistasis is characteristic of deleterious mutations in the RNA bacteriophage phi 6. We estimated the effects of deleterious mutations by performing mutation-accumulation experiments on five viral genotypes of decreasing fitness. We inferred positive epistasis because viral genotypes with low fitness were found to be less sensitive to deleterious mutations. We further examined environmental sensitivity in these genotypes and found that low-fitness genotypes were also less sensitive to environmental perturbations. Our results suggest that even random mutations impact the degree of canalization, the buffering of a phenotype against genetic and environmental perturbations. In addition, our results suggest that genetic and environmental canalization have the same developmental basis and finally that an understanding of the nature of epistasis may first require an understanding of the nature of canalization.     

A test for selection employing quantitative trait locus and mutation accumulation data

Evolutionary biologists attribute much of the phenotypic diversity observed in nature to the action of natural selection. However, for many phenotypic traits, especially quantitative phenotypic traits, it has been challenging to test for the historical action of selection. An important challenge for biologists studying quantitative traits, therefore, is to distinguish between traits that have evolved under the influence of strong selection and those that have evolved neutrally. Most existing tests for selection employ molecular data, but selection also leaves a mark on the genetic architecture underlying a trait. In particular, the distribution of quantitative trait locus (QTL) effect sizes and the distribution of mutational effects together provide information regarding the history of selection. Despite the increasing availability of QTL and mutation accumulation data, such data have not yet been effectively exploited for this purpose. We present a model of the evolution of QTL and employ it to formulate a test for historical selection. To provide a baseline for neutral evolution of the trait, we estimate the distribution of mutational effects from mutation accumulation experiments. We then apply a maximum-likelihood-based method of inference to estimate the range of selection strengths under which such a distribution of mutations could generate the observed QTL. Our test thus represents the first integration of population genetic theory and QTL data to measure the historical influence of selection.     

The Evolution of Canalization and Evolvability in Stable and Fluctuating Environments

Using a multilinear model of epistasis we explore the evolution of canalization (reduced mutational effects) and evolvability (levels of additive genetic variance) under different forms of stabilizing and fluctuating selection. We show that the total selection acting on an allele can be divided into a component deriving from adaptation of the trait mean, a component of canalizing selection favoring alleles that epistatically reduce the effects of other allele substitutions, and a component of conservative selection disfavoring rare alleles. While canalizing selection operates in both stable and fluctuating environments, it may not typically maximize canalization, because it gets less efficient with increasing canalization, and reaches a balance with drift, mutation and indirect selection. Fluctuating selection leads to less canalized equilibria than stabilizing selection of comparable strength, because canalization then becomes influenced by erratic correlated responses to shifting trait adaptation. We conclude that epistatic systems under bounded fluctuating selection will become less canalized than under stabilizing selection and may support moderately increased evolvability if the amplitude of fluctuations is large, but canalization is still stronger and evolvability lower than expected under neutral evolution or under patterns of selection that shift the trait in directions of positive (reinforcing) epistasis.     

Properties of spontaneous mutations affecting quantitative traits

Recent mutation accumulation results from invertebrate species suggest that mild deleterious mutation is far less frequent than previously thought, implying smaller expressed mutational loads. Although the rate (lambda) and effect (s) of very slight deleterious mutation remain unknown, most mutational fitness decline would come from moderately deleterious mutation (s approximately 0.2, lambda approximately 0.03), and this situation would not qualitatively change in harsh environments. Estimates of the average coefficient of dominance (h) of non-severe deleterious mutations are controversial. The typical value of h = 0.4 can be questioned, and a lower estimate (about 0.1) is suggested. Estimated mutational parameters are remarkably alike for morphological and fitness component traits (excluding lethals), indicating low mutation rates and moderate mutational effects, with a distribution generally showing strong negative asymmetry and little leptokurtosis. New mutations showed considerable genotype-environment interaction. However, the mutational variance of fitness-component traits due to non-severe detrimental mutations did not increase with environmental harshness. For morphological traits, a class of predominantly additive mutations with no detectable effect on fitness and relatively small effect on the trait was identified. This should be close to that responsible for standing variation in natural populations.     

Polygenic mutation in Drosophila melanogaster: Mapping spontaneous mutations affecting sensory bristle number

Our ability to predict long-term responses to artificial and natural selection, and understand the mechanisms by which naturally occurring variation for quantitative traits is maintained, depends on detailed knowledge of the properties of spontaneous polygenic mutations, including the quantitative trait loci (QTL) at which mutations occur, mutation rates, and mutational effects. These parameters can be estimated by mapping QTL that cause divergence between mutation-accumulation lines that have been established from an inbred base population and selected for high and low trait values. Here, we have utilized quantitative complementation to deficiencies to map QTL at which spontaneous mutations affecting Drosophila abdominal and sternopleural bristle number have occurred in 11 replicate lines during 206 generations of divergent selection. Estimates of the numbers of mutations were consistent with diploid per-character mutation rates for bristle traits of 0.03. The ratio of the per-character mutation rate to total mutation rate (0.023) implies that >2% of the genome could affect just one bristle trait and that there must be extensive pleiotropy for quantitative phenotypes. The estimated mutational effects were not, however, additive and exhibited dependency on genetic background consistent with diminishing epistasis. However, these inferences must be tempered by the potential for epistatic interactions between spontaneous mutations and QTL affecting bristle number on the deficiency-bearing chromosomes, which could lead to overestimates in numbers of QTL and inaccurate inference of gene action.     

Female mating preferences determine system-level evolution in a gene network model

Environmental patterns of directional, stabilizing and fluctuating selection can influence the evolution of system-level properties like evolvability and mutational robustness. Intersexual selection produces strong phenotypic selection and these dynamics may also affect the response to mutation and the potential for future adaptation. In order to to assess the influence of mating preferences on these evolutionary properties, I modeled a male trait and female preference determined by separate gene regulatory networks. I studied three sexual selection scenarios: sexual conflict, a Gaussian model of the Fisher process described in Lande (in Proc Natl Acad Sci 78(6):3721–3725, 1981) and a good genes model in which the male trait signalled his mutational condition. I measured the effects these mating preferences had on the potential for traits and preferences to evolve towards new states, and mutational robustness of both the phenotype and the individual’s overall viability. All types of sexual selection increased male phenotypic robustness relative to a randomly mating population. The Fisher model also reduced male evolvability and mutational robustness for viability. Under good genes sexual selection, males evolved an increased mutational robustness for viability. Females choosing their mates is a scenario that is sufficient to create selective forces that impact genetic evolution and shape the evolutionary response to mutation and environmental selection. These dynamics will inevitably develop in any population where sexual selection is operating, and affect the potential for future adaptation.     

Mutation-selection balance for environmental variance

The role of mutation-selection balance in maintaining environmental variance (V(E)) of quantitative traits is investigated under the assumption that genotypes differ in the magnitude of phenotypic variance, given genotypic value. Thus, V(E) can be regarded as a quantitative trait. As stabilizing selection on phenotype favors genotypes contributing low V(E), mutations that decrease V(E) are more likely to become fixed than those that increase it, and therefore V(E) should decline. If, however, essentially all mutants increase V(E) and overall selection is sufficiently strong that no mutants become fixed, then V(E) can be maintained. The heritability of the trait is determined by the relative sizes of mutational effects on phenotypic mean and residual variance and is independent of mutation rate and pleiotropic effects. This conclusion is not robust for small populations because some mutants may become fixed, which indicates that other selective forces must be involved, such as an intrinsic cost of homogeneity.     

Behavioral degradation under mutation accumulation in Caenorhabditis elegans

Spontaneous mutations play a fundamental role in the maintenance of genetic variation in natural populations, the nature of inbreeding depression, the evolution of sexual reproduction, and the conservation of endangered species. Using long-term mutation-accumulation lines of the nematode Caenorhabditis elegans, we estimate the rate and magnitude of mutational effects for a suite of behaviors characterizing individual chemosensory responses to a repellant stimulus. In accordance with evidence that the vast majority of mutations are deleterious, we find that behavioral responses degrade over time as a result of spontaneous mutation accumulation. The rate of mutation for behavioral traits is roughly of the same order or slightly smaller than those previously estimated for reproductive traits and the average size of the mutational effects is also comparable. These results have important implications for the maintenance of genetic variation for behavior in natural populations as well as for expectations for behavioral change within endangered species and captive populations.     

EMS-induced polygenic mutation rates for nine quantitative characters in Drosophila melanogaster.

Polygenic mutations were induced by treating Drosophila melanogaster adult males with 2.5 mM EMS. The treated second chromosomes, along with untreated controls, were then made homozygous, and five life history, two behavioral, and two morphological traits were measured. EMS mutagenesis led to reduced performance for life history traits. Changes in means and increments in genetic variance were relatively much higher for life history than for morphological traits, implying large differences in mutational target size. Maximum likelihood was used to estimate mutation rates and parameters of distributions of mutation effects, but parameters were strongly confounded with one another. Several traits showed evidence of leptokurtic distributions of effects and mean effects smaller than a few percent of trait means. Distributions of effects for all traits were strongly asymmetrical, and most mutations were deleterious. Correlations between life history mutation effects were positive. Mutation parameters for one generation of spontaneous mutation were predicted by scaling parameter estimates from the EMS experiment, extrapolated to the whole genome. Predicted mutational coefficients of variation were in good agreement with published estimates. Predicted changes in means were up to 0.14% or 0.6% for life history traits, depending on the model of scaling assumed.     

FITNESS SENSITIVITY AND THE CANALIZATION OF LIFE-HISTORY TRAITS

Canalization is an abstract term that describes unknown developmental mechanisms that reduce phenotypic variation. A trait can be canalized against environmental perturbations (e.g., changes in temperature or nutrient quality), or genetic perturbations (e.g., mutations or recombination); this paper is about genetic canalization. Stabilizing selection should improve the canalization of traits, and the degree of canalization should be positively correlated with the traits' impact on fitness. Experiments testing this idea should measure the canalization of a series of traits whose impact on fitness is known or can be inferred, exclude differences among traits in the number of loci and alleles segregating as an explanation for the pattern of variability found, and distinguish between canalization against genetic and environmental variation. These conditions were met by three experiments within which the variation of fitness components among Drosophila melanogaster lines was measured and among which the genetic contribution to the variation among lines was clearly different. The canalization of the traits increased with their impact on fitness and did not depend on the degree of genetic differences among lines. That the flies used had been transformed by a P-element insert suggests that canalization was also effective against novel genetic variation. The results reported here cannot be explained by the classical hypothesis of reduction in the number of loci segregating for traits with greater impact on fitness and confirm that traits with greater impact on fitness are more strongly canalized. This pattern of canalization reveals an underappreciated role for development in microevolution. There is differential genetic canalization of fitness components in D. melanogaster.     

The mutational structure of metabolism in Caenorhabditis elegans

A properly functioning organism must maintain metabolic homeostasis. Deleterious mutations degrade organismal function, presumably at least in part via effects on metabolic function. Here we present an initial investigation into the mutational structure of the Caenorhabditis elegans metabolome by means of a mutation accumulation experiment. We find that pool sizes of 29 metabolites vary greatly in their vulnerability to mutation, both in terms of the rate of accumulation of genetic variance (the mutational variance, VM) and the rate of change of the trait mean (the mutational bias, ΔM). Strikingly, some metabolites are much more vulnerable to mutation than any other trait previously studied in the same way. Although we cannot statistically assess the strength of mutational correlations between individual metabolites, principal component analysis provides strong evidence that some metabolite pools are genetically correlated, but also that there is substantial scope for independent evolution of different groups of metabolites. Averaged over mutation accumulation lines, PC3 is positively correlated with relative fitness, but a model in which metabolites are uncorrelated with fitness is nearly as good by Akaike's Information Criterion.     

Evidence for canalization of Distal-less function in the leg of Drosophila melanogaster

A considerable body of theory pertaining to the evolution of canalization has emerged recently, yet there have been few empirical investigations of their predictions. To address this, patterns of canalization and trait correlation were investigated under the individual and joint effects of the introgression of a loss-of-function allele of the Distal-less gene and high-temperature stress on a panel of iso-female lines. Variation was examined for number of sex comb teeth and the length of the basi-tarsus on the pro-thoracic leg of male Drosophila melanogaster. I demonstrate that whereas there is evidence for trait canalization, there is no evidence to support the hypothesis of the evolution of genetic canalization as a response to microenvironmental canalization. Furthermore, I demonstrate that although there are genetic correlations between these traits, there is no association between their measures of canalization. I discuss the prospects of the evolutionary lability of the Distal-less gene within the context of changes in genetic variation and covariation.     

The mutation matrix and the evolution of evolvability

Evolvability is a key characteristic of any evolving system, and the concept of evolvability serves as a unifying theme in a wide range of disciplines related to evolutionary theory. The field of quantitative genetics provides a framework for the exploration of evolvability with the promise to produce insights of global importance. With respect to the quantitative genetics of biological systems, the parameters most relevant to evolvability are the G-matrix, which describes the standing additive genetic variances and covariances for a suite of traits, and the M-matrix, which describes the effects of new mutations on genetic variances and covariances. A population's immediate response to selection is governed by the G-matrix. However, evolvability is also concerned with the ability of mutational processes to produce adaptive variants, and consequently the M-matrix is a crucial quantitative genetic parameter. Here, we explore the evolution of evolvability by using analytical theory and simulation-based models to examine the evolution of the mutational correlation, r(mu), the key parameter determining the nature of genetic constraints imposed by M. The model uses a diploid, sexually reproducing population of finite size experiencing stabilizing selection on a two-trait phenotype. We assume that the mutational correlation is a third quantitative trait determined by multiple additive loci. An individual's value of the mutational correlation trait determines the correlation between pleiotropic effects of new alleles when they arise in that individual. Our results show that the mutational correlation, despite the fact that it is not involved directly in the specification of an individual's fitness, does evolve in response to selection on the bivariate phenotype. The mutational variance exhibits a weak tendency to evolve to produce alignment of the M-matrix with the adaptive landscape, but is prone to erratic fluctuations as a consequence of genetic drift. The interpretation of this result is that the evolvability of the population is capable of a response to selection, and whether this response results in an increase or decrease in evolvability depends on the way in which the bivariate phenotypic optimum is expected to move. Interestingly, both analytical and simulation results show that the mutational correlation experiences disruptive selection, with local fitness maxima at -1 and +1. Genetic drift counteracts the tendency for the mutational correlation to persist at these extreme values, however. Our results also show that an evolving M-matrix tends to increase stability of the G-matrix under most circumstances. Previous studies of G-matrix stability, which assume nonevolving M-matrices, consequently may overestimate the level of instability of G relative to what might be expected in natural systems. Overall, our results indicate that evolvability can evolve in natural systems in a way that tends to result in alignment of the G-matrix, the M-matrix, and the adaptive landscape, and that such evolution tends to stabilize the G-matrix over evolutionary time.     

Genes Confer Similar Robustness to Environmental,Stochastic, and Genetic Perturbations in Yeast

Gene inactivation often has little or no apparent consequence for the phenotype of an organism. This property—enetic (or mutational) robustness—is pervasive, and has important implications for disease and evolution, but is not well understood. Dating back to at least Waddington, it has been suggested that mutational robustness may be related to the requirement to withstand environmental or stochastic perturbations. Here I show that global quantitative data from yeast are largely consistent with this idea. Considering the effects of mutations in all nonessential genes shows that genes that confer robustness to environmental or stochastic change also buffer the effects of genetic change, and with similar efficacy. This means that selection during evolution for environmental or stochastic robustness (also referred to as canalization) may frequently have the side effect of increasing genetic robustness. A dynamic environment may therefore promote the evolution of phenotypic complexity. It also means that “hub” genes in genetic interaction (synthetic lethal) networks are generally genes that confer environmental resilience and phenotypic stability.     

How does mutation affect the distribution of phenotypes?

The potential for mutational processes to influence patterns of neutral or adaptive phenotypic evolution is not well understood. If mutations are directionally biased, shifting trait means in a particular direction, or if mutation generates more variance in some directions of multivariate trait space than others, mutation itself might be a source of bias in phenotypic evolution. Here, we use mutagenesis to investigate the affect of mutation on trait mean and (co)variances in zebrafish, Danio rerio. Mutation altered the relationship between age and both prolonged swimming speed and body shape. These observations suggest that mutational effects on ontogeny or aging have the potential to generate variance across the phenome. Mutations had a far greater effect in males than females, although whether this is a reflection of sex‐specific ontogeny or aging remains to be determined. In males, mutations generated positive covariance between swimming speed, size, and body shape suggesting the potential for mutation to affect the evolutionary covariation of these traits. Overall, our observations suggest that mutation does not generate equal variance in all directions of phenotypic space or in each sex, and that pervasive variation in ontogeny or aging within a cohort could affect the variation available to evolution.