The relationship between the pleiotropic phenotypic effects of a mutation fixed by selection

A pleiotropic model of mutation is presented that allows for correlations between the effects of a new mutation and for the distribution of mutational effects to vary from being leptokurtic to normally distributed. Using this model I quantify how selection transforms the correlation between the effects of a new (random) mutation into the correlation between the effects of a mutation that is fixed by selection and contributes to an adaptation. Results suggest that under most conditions the correlation between the effects of a fixed mutation is less than the correlation between the effects of a new mutation. I also generalize previous results that quantified the expected size of a fixed mutation's effect on a character given an observed effect of that mutation on another character. In agreement with previous results, work here suggests that as the observed effect becomes large and beneficial the expected effect on another character approaches the expected effect of a new (random) mutation given the observed effect. Lastly, these theoretical results are related to recent empirical work that found beneficial mutations had a positive correlation in their pleiotropic effects.     

Deleterious Mutations, Apparent Stabilizing Selection and the Maintenance of Quantitative Variation

Apparent stabilizing selection on a quantitative trait that is not causally connected to fitness can result from the pleiotropic effects of unconditionally deleterious mutations, because as N. Barton noted, "...individuals with extreme values of the trait will tend to carry more deleterious alleles...." We use a simple model to investigate the dependence of this apparent selection on the genomic deleterious mutation rate, U; the equilibrium distribution of K, the number of deleterious mutations per genome; and the parameters describing directional selection against deleterious mutations. Unlike previous analyses, we allow for epistatic selection against deleterious alleles. For various selection functions and realistic parameter values, the distribution of K, the distribution of breeding values for a pleiotropically affected trait, and the apparent stabilizing selection function are all nearly Gaussian. The additive genetic variance for the quantitative trait is kQa2, where k is the average number of deleterious mutations per genome, Q is the proportion of deleterious mutations that affect the trait, and a2 is the variance of pleiotropic effects for individual mutations that do affect the trait. In contrast, when the trait is measured in units of its additive standard deviation, the apparent fitness function is essentially independent of Q and a2; and beta, the intensity of selection, measured as the ratio of additive genetic variance to the "variance" of the fitness curve, is very close to s = U/k, the selection coefficient against individual deleterious mutations at equilibrium. Therefore, this model predicts appreciable apparent stabilizing selection if s exceeds about 0.03, which is consistent with various data. However, the model also predicts that beta must equal Vm/VG, the ratio of new additive variance for the trait introduced each generation by mutation to the standing additive variance. Most, although not all, estimates of this ratio imply apparent stabilizing selection weaker than generally observed. A qualitative argument suggests that even when direct selection is responsible for most of the selection observed on a character, it may be essentially irrelevant to the maintenance of variation for the character by mutation-selection balance. Simple experiments can indicate the fraction of observed stabilizing selection attributable to the pleiotropic effects of deleterious mutations.     

Constrained evolution of a quantitative character by pleiotropic mutation

The long-term response to directional selection and its selection limit are derived for a quantitative character that is controlled by pleiotropic mutations with direct deleterious effect on fitness. Directional selection is assumed to be weaker than the selection acting directly on mutations via deleterious effects (purging selection), which renders all mutations to eventual elimination. The analysis embedding this restrictive assumption indicates that the evolutionary response of the character starting from an equilibrium state, in which mutation and purging selection balance but no directional selection is operating, decreases monotonically with time at an exponential rate. And the fading rate of responses is mostly determined by the direct deleterious effect. Contrary to the expectation by the standard selection limit theory based on fixation of extant genetic variation, the present model predicts that the selection limit depends on the intensity of directional selection, the limit being proportional to the ratio of the directional selection intensity to the direct deleterious effect. A slightly larger genetic variance is maintained at the selection limit than would be without directional selection.     

Pleiotropic Models of Quantitative Variation

It is widely held that each gene typically affects many characters, and that each character is affected by many genes. Moreover, strong stabilizing selection cannot act on an indefinitely large number of independent traits. This makes it likely that heritable variation in any one trait is maintained as a side effect of polymorphisms which have nothing to do with selection on that trait. This paper examines the idea that variation is maintained as the pleiotropic side effect of either deleterious mutation, or balancing selection. If mutation is responsible, it must produce alleles which are only mildly deleterious (s approximately 10(-3)), but nevertheless have significant effects on the trait. Balancing selection can readily maintain high heritabilities; however, selection must be spread over many weakly selected polymorphisms if large responses to artificial selection are to be possible. In both classes of pleiotropic model, extreme phenotypes are less fit, giving the appearance of stabilizing selection on the trait. However, it is shown that this effect is weak (of the same order as the selection on each gene): the strong stabilizing selection which is often observed is likely to be caused by correlations with a limited number of directly selected traits. Possible experiments for distinguishing the alternatives are discussed.     

Joint effects of pleiotropic selection and stabilizing selection on the maintenance of quantitative genetic variation at mutation-selection balance

In quantitative genetics, there are two basic "conflicting" observations: abundant polygenic variation and strong stabilizing selection that should rapidly deplete that variation. This conflict, although having attracted much theoretical attention, still stands open. Two classes of model have been proposed: real stabilizing selection directly on the metric trait under study and apparent stabilizing selection caused solely by the deleterious pleiotropic side effects of mutations on fitness. Here these models are combined and the total stabilizing selection observed is assumed to derive simultaneously through these two different mechanisms. Mutations have effects on a metric trait and on fitness, and both effects vary continuously. The genetic variance (V(G)) and the observed strength of total stabilizing selection (V(s,t)) are analyzed with a rare-alleles model. Both kinds of selection reduce V(G) but their roles in depleting it are not independent: The magnitude of pleiotropic selection depends on real stabilizing selection and such dependence is subject to the shape of the distributions of mutational effects. The genetic variation maintained thus depends on the kurtosis as well as the variance of mutational effects: All else being equal, V(G) increases with increasing leptokurtosis of mutational effects on fitness, while for a given distribution of mutational effects on fitness, V(G) decreases with increasing leptokurtosis of mutational effects on the trait. The V(G) and V(s,t) are determined primarily by real stabilizing selection while pleiotropic effects, which can be large, have only a limited impact. This finding provides some promise that a high heritability can be explained under strong total stabilizing selection for what are regarded as typical values of mutation and selection parameters.     

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.     

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

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

Sexual selection on spontaneous mutations strengthens the between‐sex genetic correlation for fitness

A proposed benefit to sexual selection is that it promotes purging of deleterious mutations from populations. For this benefit to be realized, sexual selection, which is usually stronger on males, must purge mutations deleterious to both sexes. Here, we experimentally test the hypothesis that sexual selection on males purges deleterious mutations that affect both male and female fitness. We measured male and female fitness in two panels of spontaneous mutation‐accumulation lines of the fly, Drosophila serrata, each established from a common ancestor. One panel of mutation accumulation lines limited both natural and sexual selection (LS lines), whereas the other panel limited natural selection, but allowed sexual selection to operate (SS lines). Although mutation accumulation caused a significant reduction in male and female fitness in both the LS and SS lines, sexual selection had no detectable effect on the extent of the fitness reduction. Similarly, despite evidence of mutational variance for fitness in males and females of both treatments, sexual selection had no significant impact on the amount of mutational genetic variance for fitness. However, sexual selection did reshape the between‐sex correlation for fitness: significantly strengthening it in the SS lines. After 25 generations, the between‐sex correlation for fitness was positive but considerably less than one in the LS lines, suggesting that, although most mutations had sexually concordant fitness effects, sex‐limited, and/or sex‐biased mutations contributed substantially to the mutational variance. In the SS lines this correlation was strong and could not be distinguished from unity. Individual‐based simulations that mimick the experimental setup reveal two conditions that may drive our results: (1) a modest‐to‐large fraction of mutations have sex‐limited (or highly sex‐biased) fitness effects, and (2) the average fitness effect of sex‐limited mutations is larger than the average fitness effect of mutations that affect both sexes similarly.     

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.     

Evolution of sex in RNA viruses

The distribution of deleterious mutations in a population of organisms is determined by the opposing effects of two forces, mutation pressure and selection. If mutation rates are high, the resulting mutation-selection balance can generate a substantial mutational load in the population. Sex can be advantageous to organisms experiencing high mutation rates because it can either buffer the mutation-selection balance from genetic drift, thus preventing any increases in the mutational load (Muller, 1964: Mut. Res. 1, 2), or decrease the mutational load by increasing the efficiency of selection (Crow, 1970: Biomathematics 1, 128). Muller's hypothesis assumes that deleterious mutations act independently, whereas Crow's hypothesis assumes that deleterious mutations interact synergistically, i.e., the acquisition of a deleterious mutation is proportionately more harmful to a genome with many mutations than it is to a genome with a few mutations. RNA viruses provide a test for these two hypotheses because they have extremely high mutation rates and appear to have evolved specific adaptations to reproduce sexually. Population genetic models for RNA viruses show that Muller's and Crow's hypotheses are also possible explanations for why sex is advantageous to these viruses. A re-analysis of published data on RNA viruses that are cultured by undiluted passage suggests that deleterious mutations in such viruses interact synergistically and that sex evolved there as a mechanism to reduce the mutational load.     

MUTATION LOAD AND THE SURVIVAL OF SMALL POPULATIONS

Previous attempts to model the joint action of selection and mutation in finite populations have treated population size as being independent of the mutation load. However, the accumulation of deleterious mutations is expected to cause a gradual reduction in population size. Consequently, in small populations random genetic drift will progressively overpower selection making it easier to fix future mutations. This synergistic interaction, which we refer to as a mutational melt-down, ultimately leads to population extinction. For many conditions, the coefficient of variation of extinction time is less than 0.1, and for species that reproduce by binary fission, the expected extinction time is quite insensitive to population carrying capacity. These results are consistent with observations that many cultures of ciliated protozoans and vertebrate fibroblasts have characteristic extinction times. The model also predicts that clonal lineages are unlikely to survive more than 10⁴ to 10⁵ generations, which is consistent with existing data on parthenogenetic animals. Contrary to the usual view that Muller's ratchet does more damage when selection is weak, we show that the mean extinction time declines as mutations become more deleterious. Although very small sexual populations, such as self-fertilized lines, are subject to mutational meltdowns, recombination effectively eliminates the process when the effective population size exceeds a dozen or so. The concept of the effective mutation load is developed, and several procedures for estimating it are described. It is shown that this load can be reduced substantially when mutational effects are highly variable.     

The rate of spontaneous mutation for life-history traits in Caenorhabditis elegans.

Spontaneous mutations were accumulated in 100 replicate lines of Caenorhabditis elegans over a period of approximately 50 generations. Periodic assays of these lines and comparison to a frozen control suggest that the deleterious mutation rate for typical life-history characters in this species is at least 0.05 per diploid genome per generation, with the average mutational effect on the order of 14% or less in the homozygous state and the average mutational heritability approximately 0.0034. While the average mutation rate per character and the average mutational heritability for this species are somewhat lower than previous estimates for Drosophila, these differences can be reconciled to a large extent when the biological differences between these species are taken into consideration.     

Rate of deleterious mutation and the distribution of its effects on fitness in vesicular stomatitis virus

Despite their importance, the parameters describing the spontaneous deleterious mutation process have not been well described in many organisms. If mutations are important for the evolution of every living organism, their importance becomes critical in the case of RNA-based viruses, in which the frequency of mutation is orders of magnitude larger than in DNA-based organisms. The present work reports minimum estimates of the deleterious mutation rate, as well as the characterization of the distribution of deleterious mutational effects on the total fitness of the vesicular stomatitis virus (VSV). The estimates are based on mutation-accumulation experiments in which selection against deleterious mutations was minimized by recurrently imposing genetic bottlenecks of size one. The estimated deleterious mutation rate was 1.2 mutations per genome and generation, with a mean fitness effect of –0.39% per generation. At the end of the mutation-accumulation experiment, the average reduction in fitness was 38% and the distribution of accumulated deleterious effects was, on average, left-skewed. The magnitude of the skewness depends on the initial fitness of the clone analysed. The implications of our findings for the evolutionary biology of RNA viruses are discussed.     

Strong sexual selection in males against a mutation load that reduces offspring production in seed beetles

Theory predicts that sexual reproduction can increase population viability relative to asexual reproduction by allowing sexual selection in males to remove deleterious mutations from the population without large demographic costs. This requires that selection acts more strongly in males than females and that mutations affecting male reproductive success have pleiotropic effects on population productivity, but empirical support for these assumptions is mixed. We used the seed beetle Callosobruchus maculatus to implement a three‐generation breeding design where we induced mutations via ionizing radiation (IR) in the F₀ generation and measured mutational effects (relative to nonirradiated controls) on an estimate of population productivity in the F₁ and effects on sex‐specific competitive lifetime reproductive success (LRS) in the F₂. Regardless of whether mutations were induced via F₀ males or females, they had strong negative effects on male LRS, but a nonsignificant influence on female LRS, suggesting that selection is more efficient in removing deleterious alleles in males. Moreover, mutations had seemingly shared effects on population productivity and competitive LRS in both sexes. Thus, our results lend support to the hypothesis that strong sexual selection on males can act to remove the mutation load on population viability, thereby offering a benefit to sexual reproduction.     

Genomic Background and Generation Time Influence Deleterious Mutation Rates in Daphnia

Understanding how genetic variation is generated and how selection shapes mutation rates over evolutionary time requires knowledge of the factors influencing mutation and its effects on quantitative traits. We explore the impact of two factors, genomic background and generation time, on deleterious mutation in Daphnia pulicaria, a cyclically parthenogenic aquatic microcrustacean, using parallel mutation-accumulation experiments. The deleterious mutational properties of life-history characters for individuals from two different populations, and for individuals maintained at two different generation times, were quantified and compared. Mutational properties varied between populations, especially for clutch size, suggesting that genomic background influences mutational properties for some characters. Generation time was found to have a greater effect on mutational properties, with higher per-generation deleterious mutation rates in lines with longer generation times. These results suggest that differences in genetic architecture among populations and species may be explained in part by demographic features that significantly influence generation time and therefore the rate of mutation.     

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.     

Modeling the evolution of genetic architecture: A continuum of alleles model with pairwise AxA epistasis

A continuum of alleles model with pair-wise AxA epistasis is proposed and its transmission genetic, and variational properties are analysed. The basic idea is that genes control the values of underlying variables, which affect the genotypic value of phenotypic characters proportional to a "scaling factor". Epistasis is the influence of one gene on the average effect of another gene. In this model, epistasis is introduced as a mutational effect of one gene on the scaling factors of another gene. In accordance with empirical results, the model assumes that the average direct effect of mutations is zero, as is the average epistatic effect. The model predicts that, on average, a mutation at one locus increases the expected mutational variance of mutations at another interacting locus. The increase in mutational variance is predicted to be equal to the variance of the pair-wise epistatic effects. This result is consistent with the observation that mutant phenotypes tend to be more variable than the wildtype phenotype. Another generic result of this model is that the frequency of canalizing mutations can at most be equal to the frequency of de-canalizing mutations. Furthermore, it is predicted that the mutational variance of a character increases at least linearly with the size of the character; hence this model is scale variant. In the case of two characters it is shown that the dimensionality of the locus-specific mutational effect distribution is invariant, i.e. the rank of the mutational covariance matrix M is invariant. While in additive models the mutational covariance matrix is always and entirely invariant, the invariance in the case of epistatic models is unexpected. Epistatic interactions can change the magnitude of the mutational (co)variances at a locus and can thus influence the structure of the mutational covariance matrix. However, in the present model the dimensionality of the mutational effect distribution remains the same. A consequence of this result is that, in this model, the genetic architecture of a set of characters is always evolvable i.e. no hard constraints can evolve.     

Apparent directional selection by biased pleiotropic mutation

Pleiotropic effects of deleterious mutations are considered to be among the factors responsible for genetic constraints on evolution by long-term directional selection acting on a quantitative trait. If pleiotropic phenotypic effects are biased in a particular direction, mutations generate apparent directional selection, which refers to the covariance between fitness and the trait owing to a linear association between the number of mutations possessed by individuals and the genotypic values of the trait. The present analysis has shown how the equilibrium mean value of the trait is determined by a balance between directional selection and biased pleiotropic mutations. Assuming that genes act additively both on the trait and on fitness, the total variance-standardized directional selection gradient was decomposed into apparent and true components. Experimental data on mutation bias from the bristle traits of Drosophila and life history traits of Daphnia suggest that apparent selection explains a small but significant fraction of directional selection pressure that is observed in nature; the data suggest that changes induced in a trait by biased pleiotropic mutation (i.e., by apparent directional selection) are easily compensated for by (true) directional selection.     

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.     

The effect of antagonistic pleiotropy on the estimation of the average coefficient of dominance of deleterious mutations

We investigate the impact of antagonistic pleiotropy on the most widely used methods of estimation of the average coefficient of dominance of deleterious mutations from segregating populations. A proportion of the deleterious mutations affecting a given studied fitness component are assumed to have an advantageous effect on another one, generating overdominance on global fitness. Using diffusion approximations and transition matrix methods, we obtain the distribution of gene frequencies for nonpleiotropic and pleiotropic mutations in populations at the mutation-selection-drift balance. From these distributions we build homozygous and heterozygous chromosomes and assess the behavior of the estimators of dominance. A very small number of deleterious mutations with antagonistic pleiotropy produces substantial increases on the estimate of the average degree of dominance of mutations affecting the fitness component under study. For example, estimates are increased three- to fivefold when 2% of segregating loci are over-dominant for fitness. In contrast, strengthening pleiotropy, where pleiotropic effects are assumed to be also deleterious, has little effect on the estimates of the average degree of dominance, supporting previous results. The antagonistic pleiotropy model considered, applied under mutational parameters described in the literature, produces patterns for the distribution of chromosomal viabilities, levels of genetic variance, and homozygous mutation load generally consistent with those observed empirically for viability in Drosophila melanogaster.