Estimating selection on nonsynonymous mutations

The distribution of mutational effects on fitness is of fundamental importance for many aspects of evolution. We develop two methods for characterizing the fitness effects of deleterious, nonsynonymous mutations, using polymorphism data from two related species. These methods also provide estimates of the proportion of amino acid substitutions that are selectively favorable, when combined with data on between-species sequence divergence. The methods are applicable to species with different effective population sizes, but that share the same distribution of mutational effects. The first, simpler, method assumes that diversity for all nonneutral mutations is given by the value under mutation-selection balance, while the second method allows for stronger effects of genetic drift and yields estimates of the parameters of the probability distribution of mutational effects. We apply these methods to data on populations of Drosophila miranda and D. pseudoobscura and find evidence for the presence of deleterious nonsynonymous mutations, mostly with small heterozygous selection coefficients (a mean of the order of 10(-5) for segregating variants). A leptokurtic gamma distribution of mutational effects with a shape parameter between 0.1 and 1 can explain observed diversities, in the absence of a separate class of completely neutral nonsynonymous mutations. We also describe a simple approximate method for estimating the harmonic mean selection coefficient from diversity data on a single species.     

Mutation-selection balance accounting for genetic variation for viability in Drosophila melanogaster as deduced from an inbreeding and artificial selection experiment

We carried out an experiment of inbreeding and upward artificial selection for egg-to-adult viability in a recently captured population of Drosophila melanogaster, as well as computer simulations of the experimental design, in order to obtain information on the nature of genetic variation for this important fitness component. The inbreeding depression was linear with a rate of 0.70 +/- 0.11% of the initial mean per 1% increase in inbreeding coefficient, and the realized heritability was 0.06 +/- 0.07. We compared the empirical observations of inbreeding depression and selection response with computer simulations assuming a balance between the occurrence of partially recessive deleterious mutations and their elimination by selection. Our results suggest that a model assuming mutation-selection balance with realistic mutational parameters can explain the genetic variation for viability in the natural population studied. Several mutational models are incompatible with some observations and can be discarded. Mutational models assuming a low rate of mutations of large average effect and highly recessive gene action, and others assuming a high rate of mutations of small average effect and close to additive gene action, are compatible with all the observations.     

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.     

Asexuals, polyploids, evolutionary opportunists...: the population genetics of positive but deteriorating mutations

Some genetic phenomena originate as mutations that are initially advantageous but decline in fitness until they become distinctly deleterious. Here I give the condition for a mutation-selection balance to form and describe some of the properties of the resulting equilibrium population. A characterization is also given of the fixation probabilities for such mutations.     

Estimation of the upper limit of the mutation rate and mean heterozygous effect of deleterious mutations

Deng et al. have recently proposed that estimates of an upper limit to the rate of spontaneous mutations and their average heterozygous effect can be obtained from the mean and variance of a given fitness trait in naturally segregating populations, provided that allele frequencies are maintained at the balance between mutation and selection. Using simulations they show that this estimation method generally has little bias and is very robust to violations of the mutation-selection balance assumption. Here I show that the particular parameters and models used in these simulations generally reduce the amount of bias that can occur with this estimation method. In particular, the assumption of a large mutation rate in the simulations always implies a low bias of estimates. In addition, the specific model of overdominance used to check the violation of the mutation-selection balance assumption is such that there is not a dramatic decline in mean fitness from overdominant mutations, again implying a low bias of estimates. The assumption of lower mutation rates and/or other models of balancing selection may imply considerably larger biases of the estimates, making the reliability of the proposed method highly questionable.     

Simultaneous Estimation of Additive and Mutational Genetic Variance in an Outbred Population of Drosophila serrata

How new mutations contribute to genetic variation is a key question in biology. Although the evolutionary fate of an allele is largely determined by its heterozygous effect, most estimates of mutational variance and mutational effects derive from highly inbred lines, where new mutations are present in homozygous form. In an attempt to overcome this limitation, middle-class neighborhood (MCN) experiments have been used to assess the fitness effect of new mutations in heterozygous form. However, because MCN populations harbor substantial standing genetic variance, estimates of mutational variance have not typically been available from such experiments. Here we employ a modification of the animal model to analyze data from 22 generations of Drosophila serrata bred in an MCN design. Mutational heritability, measured for eight cuticular hydrocarbons, 10 wing-shape traits, and wing size in this outbred genetic background, ranged from 0.0006 to 0.006 (with one exception), a similar range to that reported from studies employing inbred lines. Simultaneously partitioning the additive and mutational variance in the same outbred population allowed us to quantitatively test the ability of mutation-selection balance models to explain the observed levels of additive and mutational genetic variance. The Gaussian allelic approximation and house-of-cards models, which assume real stabilizing selection on single traits, both overestimated the genetic variance maintained at equilibrium, but the house-of-cards model was a closer fit to the data. This analytical approach has the potential to be broadly applied, expanding our understanding of the dynamics of genetic variance in natural populations.     

Effects of spontaneous mutation accumulation on sex ratio traits in a parasitoid wasp

Sex allocation theory has proved extremely successful at predicting when individuals should adjust the sex of their offspring in response to environmental conditions. However, we know rather little about the underlying genetics of sex ratio or how genetic architecture might constrain adaptive sex-ratio behavior. We examined how mutation influenced genetic variation in the sex ratios produced by the parasitoid wasp Nasonia vitripennis. In a mutation accumulation experiment, we determined the mutability of sex ratio, and compared this with the amount of genetic variation observed in natural populations. We found that the mutability (h(2)(m)) ranges from 0.001 to 0.002, similar to estimates for life-history traits in other organisms. These estimates suggest one mutation every 5-60 generations, which shift the sex ratio by approximately 0.01 (proportion males). In this and other studies, the genetic variation in N. vitripennis sex ratio ranged from 0.02 to 0.17 (broad-sense heritability, H(2)). If sex ratio is maintained by mutation-selection balance, a higher genetic variance would be expected given our mutational parameters. Instead, the observed genetic variance perhaps suggests additional selection against sex-ratio mutations with deleterious effects on other fitness traits as well as sex ratio (i.e., pleiotropy), as has been argued to be the case more generally.     

Analysis of the estimators of the average coefficient of dominance of deleterious mutations

We investigate the sources of bias that affect the most commonly used methods of estimation of the average degree of dominance (h) of deleterious mutations, focusing on estimates from segregating populations. The main emphasis is on the effect of the finite size of the populations, but other sources of bias are also considered. Using diffusion approximations to the distribution of gene frequencies in finite populations as well as stochastic simulations, we assess the behavior of the estimators obtained from populations at mutation-selection-drift balance under different mutational scenarios and compare averages of h for newly arisen and segregating mutations. Because of genetic drift, the inferences concerning newly arisen mutations based on the mutation-selection balance theory can have substantial upward bias depending upon the distribution of h. In addition, estimates usually refer to h weighted by the homozygous deleterious effect in different ways, so that inferences are complicated when these two variables are negatively correlated. Due to both sources of bias, the widely used regression of heterozygous on homozygous means underestimates the arithmetic mean of h for segregating mutations, in contrast to their repeatedly assumed equality in the literature. We conclude that none of the estimators from segregating populations provides, under general conditions, a useful tool to ascertain the properties of the degree of dominance, either for segregating or for newly arisen deleterious mutations. Direct estimates of the average h from mutation-accumulation experiments are shown to suffer some bias caused by purging selection but, because they do not require assumptions on the causes maintaining segregating variation, they appear to give a more reliable average dominance for newly arisen mutations.     

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.     

Optimal bacteriophage mutation rates for phage therapy

The mutability of bacteriophages offers a particular advantage in the treatment of bacterial infections not afforded by other antimicrobial therapies. When phage-resistant bacteria emerge, mutation may generate phage capable of exploiting and thus limiting population expansion among these emergent types. However, while mutation potentially generates beneficial variants, it also contributes to a genetic load of deleterious mutations. Here, we model the influence of varying phage mutation rate on the efficacy of phage therapy. All else being equal, phage types with historical mutation rates of approximately 0.1 deleterious mutations per genome per generation offer a reasonable balance between beneficial mutational diversity and deleterious mutational load. We determine that increasing phage inoculum density can undesirably increase the peak density of a mutant bacterial class by limiting the in situ production of mutant phage variants. For phage populations with minimal genetic load, engineering mutation rate increases beyond the mutation-selection balance optimum may provide even greater protection against emergent bacterial types, but only with very weak selective coefficients for de novo deleterious mutations (below approximately 0.01). Increases to the mutation rate beyond the optimal value at mutation-selection balance may therefore prove generally undesirable.     

Quantitative genetics of ovariole number in Drosophila melanogaster. II. Mutational variation and genotype-environment interaction.

The rare alleles model of mutation-selection balance (MSB) hypothesis for the maintenance of genetic variation was evaluated for two quantitative traits, ovariole number and body size. Mutational variances (VM) for these traits, estimated from mutation accumulation lines, were 4.75 and 1.97 x 10(-4) times the environmental variance (VE), respectively. The mutation accumulation lines were studied in three environments to test for genotype x environment interaction (GEI) of new mutations; significant mutational GEI was found for both traits. Mutations for ovariole number have a quadratic relationship with competitive fitness, suggesting stabilizing selection for the trait; there is no significant correlation between mutations for body size and competitive fitness. Under MSB, the ratio of segregating genetic variance, VG, to mutational variance, VM, estimates the inverse of the selection coefficient against a heterozygote for a new mutation. Estimates of VG/VM for ovariole number and body size were both approximately 1.1 x 10(4). Thus, MSB can explain the level of variation, if mutations affecting these traits are under very weak selection, which is inconsistent with the empirical observation of stabilizing selection, or if the estimate of VM is biased downward by two orders of magnitude. GEI is a possible alternative explanation.     

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.     

Mutation-selection balance: ancestry,load, and maximum principle

We analyze the equilibrium behavior of deterministic haploid mutation-selection models. To this end, both the forward and the time-reversed evolution processes are considered. The stationary state of the latter is called the ancestral distribution, which turns out as a key for the study of mutation-selection balance. We find that the ancestral genotype frequencies determine the sensitivity of the equilibrium mean fitness to changes in the corresponding fitness values and discuss implications for the evolution of mutational robustness. We further show that the difference between the ancestral and the population mean fitness, termed mutational loss, provides a measure for the sensitivity of the equilibrium mean fitness to changes in the mutation rate. The interrelation of the loss and the mutation load is discussed. For a class of models in which the number of mutations in an individual is taken as the trait value, and fitness is a function of the trait, we use the ancestor formulation to derive a simple maximum principle, from which the mean and variance of fitness and the trait may be derived; the results are exact for a number of limiting cases, and otherwise yield approximations which are accurate for a wide range of parameters. These results are applied to threshold phenomena caused by the interplay of selection and mutation (known as error thresholds). They lead to a clarification of concepts, as well as criteria for the existence of error thresholds.     

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.     

Haldane's sieve and adaptation from the standing genetic variation

We consider populations that adapt to a sudden environmental change by fixing alleles found at mutation-selection balance. In particular, we calculate probabilities of fixation for previously deleterious alleles, ignoring the input of new mutations. We find that "Haldane's sieve"--the bias against the establishment of recessive beneficial mutations--does not hold under these conditions. Instead probabilities of fixation are generally independent of dominance. We show that this result is robust to patterns of sex expression for both X-linked and autosomal loci. We further show that adaptive evolution is invariably slower at X-linked than autosomal loci when evolution begins from mutation-selection balance. This result differs from that obtained when adaptation uses new mutations, a finding that may have some bearing on recent attempts to distinguish between hitchhiking and background selection by contrasting the molecular population genetics of X-linked vs. autosomal loci. Last, we suggest a test to determine whether adaptation used new mutations or previously deleterious alleles from the standing genetic variation.     

Mutation-selection balance in mixed mating populations

An approximation to the average number of deleterious mutations per gamete, Q, is derived from a model allowing selection on both zygotes and male gametes. Progeny are produced by either outcrossing or self-fertilization with fixed probabilities. The genetic model is a standard in evolutionary biology: mutations occur at unlinked loci, have equivalent effects, and combine multiplicatively to determine fitness. The approximation developed here treats individual mutation counts with a generalized Poisson model conditioned on the distribution of selfing histories in the population. The approximation is accurate across the range of parameter sets considered and provides both analytical insights and greatly increased computational speed. Model predictions are discussed in relation to several outstanding problems, including the estimation of the genomic deleterious mutation rates (U), the generality of "selective interference" among loci, and the consequences of gametic selection for the joint distribution of inbreeding depression and mating system across species. Finally, conflicting results from previous analytical treatments of mutation-selection balance are resolved to assumptions about the life-cycle and the initial fate of mutations.     

Dynamics of inbreeding depression due to deleterious mutations in small populations: mutation parameters and inbreeding rate

A multilocus stochastic model is developed to simulate the dynamics of mutational load in small populations of various sizes. Old mutations sampled from a large ancestral population at mutation-selection balance and new mutations arising each generation are considered jointly, using biologically plausible lethal and deleterious mutation parameters. The results show that inbreeding depression and the number of lethal equivalents due to partially recessive mutations can be partly purged from the population by inbreeding, and that this purging mainly involves lethals or detrimentals of large effect. However, fitness decreases continuously with inbreeding, due to increased fixation and homozygosity of mildly deleterious mutants, resulting in extinctions of very small populations with low reproductive rates. No optimum inbreeding rate or population size exists for purging with respect to fitness (viability) changes, but there is an optimum inbreeding rate at a given final level of inbreeding for reducing inbreeding depression or the number of lethal equivalents. The interaction between selection against partially recessive mutations and genetic drift in small populations also influences the rate of decay of neutral variation. Weak selection against mutants relative to genetic drift results in apparent overdominance and thus an increase in effective size (Ne) at neutral loci, and strong selection relative to drift leads to a decrease in Ne due to the increased variance in family size. The simulation results and their implications are discussed in the context of biological conservation and tests for purging.     

Redistribution of gene frequency and changes of genetic variation following a bottleneck in population size

Although the distribution of frequencies of genes influencing quantitative traits is important to our understanding of their genetic basis and their evolution, direct information from laboratory experiments is very limited. In theory, different models of selection and mutation generate different predictions of frequency distributions. When a large population at mutation-selection balance passes through a rapid bottleneck in size, the frequency distribution of genes is dramatically altered, causing changes in observable quantities such as the mean and variance of quantitative traits. We investigate the gene frequency distribution of a population at mutation-selection balance under a joint-effect model of real stabilizing and pleiotropic selection and its redistribution and thus changes of the genetic properties of metric and fitness traits after the population passes a rapid bottleneck and expands in size. If all genes that affect the trait are neutral with respect to fitness, the additive genetic variance (VA) is always reduced by a bottleneck in population size, regardless of their degree of dominance. For genes that have been under selection, VA increases following a bottleneck if they are (partially) recessive, while the dominance variance increases substantially for any degree of dominance. With typical estimates of mutation parameters, the joint-effect model can explain data from laboratory experiments on the effect of bottlenecking on fitness and morphological traits, providing further support for it as a plausible mechanism for maintenance of quantitative genetic variation.     

Fitness change in relation to mutation number in spontaneous mutation accumulation lines of Chlamydomonas reinhardtii

Although all genetic variation ultimately stems from mutations, their properties are difficult to study directly. Here, we used multiple mutation accumulation (MA) lines derived from five genetic backgrounds of the green algae Chlamydomonas reinhardtii that have been previously subjected to whole genome sequencing to investigate the relationship between the number of spontaneous mutations and change in fitness from a nonevolved ancestor. MA lines were on average less fit than their ancestors and we detected a significantly negative correlation between the change in fitness and the total number of accumulated mutations in the genome. Likewise, the number of mutations located within coding regions significantly and negatively impacted MA line fitness. We used the fitness data to parameterize a maximum likelihood model to estimate discrete categories of mutational effects, and found that models containing one to two mutational effect categories (one neutral and one deleterious category) fitted the data best. However, the best‐fitting mutational effects models were highly dependent on the genetic background of the ancestral strain.     

Probing the evolution of senescence inDrosophila melanogaster withP-element tagging

Natural populations host a wealth of genetic variation in longevity and age-specific schedules of reproduction. This variation provides critical information for inferring the evolutionary origin of senescence. Patterns of mutational effects on age-specific fecundity and survival provide additional insight to distinguish alternative models of senescence. In this study,P-elements bearing thewhite minigene were inserted at random into a common genetic background, generating lines ofD. melanogaster with single, stable transposon inserts. A series of 48 single-P-element lines revealed statistically significant heterogeneity in both longevity and fecundity. Longevity and early fecundity were only weakly positively correlated (r=0.286,P=0.0398). Both the pooled sample and 30 of the individual lines exhibited a leveling of age-specific mortality at advanced ages, in opposition to the classical demographic models. To the extent that these mutational effects are representative of naturally-occurring mutations in heterogeneous populations, this result presents a problem for the evolutionary theory of senescence. Natural selection is inefficient at removing deleterious mutations that are expressed only at late ages, and selection may not differentiate between mutations whose effects on longevity are post-reproductive. A leveling of the mortality rate would also be seen if mutations whose expression is delayed until very late simply do not occur. A simulation of mutation-selection balance among the 48P-element tagged lines shows that the mean longevity declines monotonically with increasing mutation rate, consistent with the mutation-accumulation model.