Inferring the distribution of mutational effects on fitness in Drosophila

The properties of the distribution of deleterious mutational effects on fitness (DDME) are of fundamental importance for evolutionary genetics. Since it is extremely difficult to determine the nature of this distribution, several methods using various assumptions about the DDME have been developed, for the purpose of parameter estimation. We apply a newly developed method to DNA sequence polymorphism data from two Drosophila species and compare estimates of the parameters of the distribution of the heterozygous fitness effects of amino acid mutations for several different distribution functions. The results exclude normal and gamma distributions, since these predict too few effectively lethal mutations and power-law distributions as a result of predicting too many lethals. Only the lognormal distribution appears to fit both the diversity data and the frequency of lethals. This DDME arises naturally in complex systems when independent factors contribute multiplicatively to an increase in fitness-reducing damage. Several important parameters, such as the fraction of effectively neutral non-synonymous mutations and the harmonic mean of non-neutral selection coefficients, are robust to the form of the DDME. Our results suggest that the majority of non-synonymous mutations in Drosophila are under effective purifying selection.     

A method for inferring the rate of occurrence and fitness effects of advantageous mutations

The distribution of fitness effects (DFE) of new mutations is of fundamental importance in evolutionary genetics. Recently, methods have been developed for inferring the DFE that use information from the allele frequency distributions of putatively neutral and selected nucleotide polymorphic variants in a population sample. Here, we extend an existing maximum-likelihood method that estimates the DFE under the assumption that mutational effects are unconditionally deleterious, by including a fraction of positively selected mutations. We allow one or more classes of positive selection coefficients in the model and estimate both the fraction of mutations that are advantageous and the strength of selection acting on them. We show by simulations that the method is capable of recovering the parameters of the DFE under a range of conditions. We apply the method to two data sets on multiple protein-coding genes from African populations of Drosophila melanogaster. We use a probabilistic reconstruction of the ancestral states of the polymorphic sites to distinguish between derived and ancestral states at polymorphic nucleotide sites. In both data sets, we see a significant improvement in the fit when a category of positively selected amino acid mutations is included, but no further improvement if additional categories are added. We estimate that between 1% and 2% of new nonsynonymous mutations in D. melanogaster are positively selected, with a scaled selection coefficient representing the product of the effective population size, N(e), and the strength of selection on heterozygous carriers of ～2.5.     

Determinants of synonymous and nonsynonymous variability in three species of Drosophila

We estimated the intensity of selection on preferred codons in Drosophila pseudoobscura and D. miranda at X-linked and autosomal loci, using a published data set on sequence variability at 67 loci, by means of an improved method that takes account of demographic effects. We found evidence for stronger selection at X-linked loci, consistent with their higher levels of codon usage bias. The estimates of the strength of selection and mutational bias in favor of unpreferred codons were similar to those found in other species, after taking into account the fact that D. pseudoobscura showed evidence for a recent expansion in population size. We examined correlates of synonymous and nonsynonymous diversity in these species and found no evidence for effects of recurrent selective sweeps on nonsynonymous mutations, which is probably because this set of genes have much higher than average levels of selective constraints. There was evidence for correlated effects of levels of selective constraints on protein sequences and on codon usage, as expected under models of selection for translational accuracy. Our analysis of a published data set on D. melanogaster provided evidence for the effects of selective sweeps of nonsynonymous mutations on linked synonymous diversity, but only in the subset of loci that experienced the highest rates of nonsynonymous substitutions (about one-quarter of the total) and not at more slowly evolving loci. Our correlational analysis of this data set suggested that both selective constraints on protein sequences and recurrent selective sweeps affect the overall level of codon usage.     

Background selection in single genes may explain patterns of codon bias

Background selection involves the reduction in effective population size caused by the removal of recurrent deleterious mutations from a population. Previous work has examined this process for large genomic regions. Here we focus on the level of a single gene or small group of genes and investigate how the effects of background selection caused by nonsynonymous mutations are influenced by the lengths of coding sequences, the number and length of introns, intergenic distances, neighboring genes, mutation rate, and recombination rate. We generate our predictions from estimates of the distribution of the fitness effects of nonsynonymous mutations, obtained from DNA sequence diversity data in Drosophila. Results for genes in regions with typical frequencies of crossing over in Drosophila melanogaster suggest that background selection may influence the effective population sizes of different regions of the same gene, consistent with observed differences in codon usage bias along genes. It may also help to cause the observed effects of gene length and introns on codon usage. Gene conversion plays a crucial role in determining the sizes of these effects. The model overpredicts the effects of background selection with large groups of nonrecombining genes, because it ignores Hill-Robertson interference among the mutations involved.     

The distribution of fitness effects of new deleterious amino acid mutations in humans

The distribution of fitness effects of new mutations is a fundamental parameter in genetics. Here we present a new method by which the distribution can be estimated. The method is fairly robust to changes in population size and admixture, and it can be corrected for any residual effects if a model of the demography is available. We apply the method to extensively sampled single-nucleotide polymorphism data from humans and estimate the distribution of fitness effects for amino acid changing mutations. We show that a gamma distribution with a shape parameter of 0.23 provides a good fit to the data and we estimate that >50% of mutations are likely to have mild effects, such that they reduce fitness by between one one-thousandth and one-tenth. We also infer that <15% of new mutations are likely to have strongly deleterious effects. We estimate that on average a nonsynonymous mutation reduces fitness by a few percent and that the average strength of selection acting against a nonsynonymous polymorphism is approximately 9 x 10(-5). We argue that the relaxation of natural selection due to modern medicine and reduced variance in family size is not likely to lead to a rapid decline in genetic quality, but that it will be very difficult to locate most of the genes involved in complex genetic diseases.     

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.     

Multilocus analyses reveal little evidence for lineage‐wide adaptive evolution within major clades of soft pines (Pinus subgenus Strobus)

Estimates from molecular data for the fraction of new nonsynonymous mutations that are adaptive vary strongly across plant species. Much of this variation is due to differences in life history strategies as they influence the effective population size (N_e). Ample variation for these estimates, however, remains even when comparisons are made across species with similar values of N_e. An open question thus remains as to why the large disparity for estimates of adaptive evolution exists among plant species. Here, we have estimated the distribution of deleterious fitness effects (DFE) and the fraction of adaptive nonsynonymous substitutions (α) for 11 species of soft pines (subgenus Strobus) using DNA sequence data from 167 orthologous nuclear gene fragments. Most newly arising nonsynonymous mutations were inferred to be so strongly deleterious that they would rarely become fixed. Little evidence for long‐term adaptive evolution was detected, as all 11 estimates for α were not significantly different from zero. Nucleotide diversity at synonymous sites, moreover, was strongly correlated with attributes of the DFE across species, thus illustrating a strong consistency with the expectations from the Nearly Neutral Theory of molecular evolution. Application of these patterns to genome‐wide expectations for these species, however, was difficult as the loci chosen for the analysis were a biased set of conserved loci, which greatly influenced the estimates of the DFE and α. This implies that genome‐wide parameter estimates will need truly genome‐wide data, so that many of the existing patterns documented previously for forest trees (e.g. little evidence for signature of selection) may need revision.     

Comparing analysis methods for mutation-accumulation data: a simulation study

We simulated single-generation data for a fitness trait in mutation-accumulation (MA) experiments, and we compared three methods of analysis. Bateman-Mukai (BM) and maximum likelihood (ML) need information on both the MA lines and control lines, while minimum distance (MD) can be applied with or without the control. Both MD and ML assume gamma-distributed mutational effects. ML estimates of the rate of deleterious mutation had larger mean square error (MSE) than MD or BM had due to large outliers. MD estimates obtained by ignoring the mean decline observed from comparison to a control are often better than those obtained using that information. When effects are simulated using the gamma distribution, reducing the precision with which the trait is assayed increases the probability of obtaining no ML or MD estimates but causes no appreciable increase of the MSE. When the residual errors for the means of the simulated lines are sampled from the empirical distribution in a MA experiment, instead of from a normal one, the MSEs of BM, ML, and MD are practically unaffected. When the simulated gamma distribution accounts for a high rate of mild deleterious mutation, BM detects only approximately 30% of the true deleterious mutation rate, while MD or ML detects substantially larger fractions. To test the robustness of the methods, we also added a high rate of common contaminant mutations with constant mild deleterious effect to a low rate of mutations with gamma-distributed deleterious effects and moderate average. In that case, BM detects roughly the same fraction as before, regardless of the precision of the assay, while ML fails to provide estimates. However, MD estimates are obtained by ignoring the control information, detecting approximately 70% of the total mutation rate when the mean of the lines is assayed with good precision, but only 15% for low-precision assays. Contaminant mutations with only tiny deleterious effects could not be detected with acceptable accuracy by any of the above methods.     

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.     

Selection on Accessible Chromatin Regions in Capsella grandiflora

Accurate estimates of genome-wide rates and fitness effects of new mutations are essential for an improved understanding of molecular evolutionary processes. Although eukaryotic genomes generally contain a large noncoding fraction, functional noncoding regions and fitness effects of mutations in such regions are still incompletely characterized. A promising approach to characterize functional noncoding regions relies on identifying accessible chromatin regions (ACRs) tightly associated with regulatory DNA. Here, we applied this approach to identify and estimate selection on ACRs in Capsella grandiflora, a crucifer species ideal for population genomic quantification of selection due to its favorable population demography. We describe a population-wide ACR distribution based on ATAC-seq data for leaf samples of 16 individuals from a natural population. We use population genomic methods to estimate fitness effects and proportions of positively selected fixations (α) in ACRs and find that intergenic ACRs harbor a considerable fraction of weakly deleterious new mutations, as well as a significantly higher proportion of strongly deleterious mutations than comparable inaccessible intergenic regions. ACRs are enriched for expression quantitative trait loci (eQTL) and depleted of transposable element insertions, as expected if intergenic ACRs are under selection because they harbor regulatory regions. By integrating empirical identification of intergenic ACRs with analyses of eQTL and population genomic analyses of selection, we demonstrate that intergenic regulatory regions are an important source of nearly neutral mutations. These results improve our understanding of selection on noncoding regions and the role of nearly neutral mutations for evolutionary processes in outcrossing Brassicaceae species.     

Fitness effects of derived deleterious mutations in four closely related wild tomato species with spatial structure

A key issue in evolutionary biology is an improved understanding of the genetic mechanisms by which species adapt to various environments. Using DNA sequence data, it is possible to quantify the number of adaptive and deleterious mutations, and the distribution of fitness effects of new mutations (its mean and variance) by simultaneously taking into account the demography of a given species. We investigated how selection functions at eight housekeeping genes of four closely related, outcrossing species of wild tomatoes that are native to diverse environments in western South America (Solanum arcanum, S. chilense, S. habrochaites and S. peruvianum). We found little evidence for adaptive mutations but pervasive evidence for strong purifying selection in coding regions of the four species. In contrast, the strength of purifying selection seems to vary among the four species in non-coding (NC) regions (introns). Using F(ST)-based measures of fixation in subdivided populations, we suggest that weak purifying selection has affected the NC regions of S. habrochaites, S. chilense and S. peruvianum. In contrast, NC regions in S. arcanum show a distribution of fitness effects with mutations being either nearly neutral or very strongly deleterious. These results suggest that closely related species with similar genetic backgrounds but experiencing contrasting environments differ in the variance of deleterious fitness effects.     

Inference of site frequency spectra from high-throughput sequence data: quantification of selection on nonsynonymous and synonymous sites in humans

Sequencing errors and random sampling of nucleotide types among sequencing reads at heterozygous sites present challenges for accurate, unbiased inference of single-nucleotide polymorphism genotypes from high-throughput sequence data. Here, we develop a maximum-likelihood approach to estimate the frequency distribution of the number of alleles in a sample of individuals (the site frequency spectrum), using high-throughput sequence data. Our method assumes binomial sampling of nucleotide types in heterozygotes and random sequencing error. By simulations, we show that close to unbiased estimates of the site frequency spectrum can be obtained if the error rate per base read does not exceed the population nucleotide diversity. We also show that these estimates are reasonably robust if errors are nonrandom. We then apply the method to infer site frequency spectra for zerofold degenerate, fourfold degenerate, and intronic sites of protein-coding genes using the low coverage human sequence data produced by the 1000 Genomes Project phase-one pilot. By fitting a model to the inferred site frequency spectra that estimates parameters of the distribution of fitness effects of new mutations, we find evidence for significant natural selection operating on fourfold sites. We also find that a model with variable effects of mutations at synonymous sites fits the data significantly better than a model with equal mutational effects. Under the variable effects model, we infer that 11% of synonymous mutations are subject to strong purifying selection.     

Positive and negative selection on noncoding DNA close to protein-coding genes in wild house mice

During the past two decades, evidence has accumulated of adaptive evolution within protein-coding genes in a variety of species. However, with the exception of Drosophila and humans, little is known about the extent of adaptive evolution in noncoding DNA. Here, we study regions upstream and downstream of protein-coding genes in the house mouse Mus musculus castaneus, a species that has a much larger effective population size (N(e)) than humans. We analyze polymorphism data for 78 genes from 15 wild-caught M. m. castaneus individuals and divergence to a closely related species, Mus famulus. We find high levels of nucleotide diversity and moderate levels of selective constraint in upstream and downstream regions compared with nonsynonymous sites of protein-coding genes. From the polymorphism data, we estimate the distribution of fitness effects (DFE) of new mutations and infer that most new mutations in upstream and downstream regions behave as effectively neutral and that only a small fraction is strongly negatively selected. We also estimate the fraction of substitutions that have been driven to fixation by positive selection (α) and the ratio of adaptive to neutral divergence (ω(α)). We find that α for upstream and downstream regions (～ 10%) is much lower than α for nonsynonymous sites (～ 50%). However, ω(α) estimates are very similar for nonsynonymous sites (～ 10%) and upstream and downstream regions (～ 5%). We conclude that negative selection operating in upstream and downstream regions of M. m. castaneus is weak and that the low values of α for upstream and downstream regions relative to nonsynonymous sites are most likely due to the presence of a higher proportion of neutrally evolving sites and not due to lower absolute rates of adaptive substitution.     

Accumulation of Spontaneous Mutations in the Ciliate Tetrahymena thermophila

Knowledge of the rate and fitness effects of mutations is essential for understanding the process of evolution. Mutations are inherently difficult to study because they are rare and are frequently eliminated by natural selection. In the ciliate Tetrahymena thermophila, mutations can accumulate in the germline genome without being exposed to selection. We have conducted a mutation accumulation (MA) experiment in this species. Assuming that all mutations are deleterious and have the same effect, we estimate that the deleterious mutation rate per haploid germline genome per generation is U = 0.0047 (95% credible interval: 0.0015, 0.0125), and that germline mutations decrease fitness by s = 11% when expressed in a homozygous state (95% CI: 4.4%, 27%). We also estimate that deleterious mutations are partially recessive on average (h = 0.26; 95% CI: –0.022, 0.62) and that the rate of lethal mutations is <10% of the deleterious mutation rate. Comparisons between the observed evolutionary responses in the germline and somatic genomes and the results from individual-based simulations of MA suggest that the two genomes have similar mutational parameters. These are the first estimates of the deleterious mutation rate and fitness effects from the eukaryotic supergroup Chromalveolata and are within the range of those of other eukaryotes.     

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.     

Cumulative effects of spontaneous mutations for fitness in Caenorhabditis: role of genotype, environment and stress

It is often assumed that the mutation rate is an evolutionarily optimized property of a taxon. The relevant mutation rate is for mutations that affect fitness, U, but the strength of selection on the mutation rate depends on the average effect of a mutation. Determination of U is complicated by the possibility that mutational effects depend on the particular environmental context in which the organism exists. It has been suggested that the effects of deleterious mutations are typically magnified in stressful environments, but most studies confound genotype with environment, so it is unclear to what extent environmental specificity of mutations is specific to a particular starting genotype. We report a study designed to separate effects of species, genotype, and environment on the degradation of fitness resulting from new mutations. Mutations accumulated for >200 generations at 20 degrees in two strains of two species of nematodes that differ in thermal sensitivity. Caenorhabditis briggsae and C. elegans have similar demography at 20 degrees, but C. elegans suffers markedly reduced fitness at 25 degrees. We find little evidence that mutational properties differ depending on environmental conditions and mutational correlations between environments are close to those expected if effects were identical in both environments.     

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.     

Estimating the distribution of selection coefficients from phylogenetic data using sitewise mutation-selection models

Estimation of the distribution of selection coefficients of mutations is a long-standing issue in molecular evolution. In addition to population-based methods, the distribution can be estimated from DNA sequence data by phylogenetic-based models. Previous models have generally found unimodal distributions where the probability mass is concentrated between mildly deleterious and nearly neutral mutations. Here we use a sitewise mutation-selection phylogenetic model to estimate the distribution of selection coefficients among novel and fixed mutations (substitutions) in a data set of 244 mammalian mitochondrial genomes and a set of 401 PB2 proteins from influenza. We find a bimodal distribution of selection coefficients for novel mutations in both the mitochondrial data set and for the influenza protein evolving in its natural reservoir, birds. Most of the mutations are strongly deleterious with the rest of the probability mass concentrated around mildly deleterious to neutral mutations. The distribution of the coefficients among substitutions is unimodal and symmetrical around nearly neutral substitutions for both data sets at adaptive equilibrium. About 0.5% of the nonsynonymous mutations and 14% of the nonsynonymous substitutions in the mitochondrial proteins are advantageous, with 0.5% and 24% observed for the influenza protein. Following a host shift of influenza from birds to humans, however, we find among novel mutations in PB2 a trimodal distribution with a small mode of advantageous mutations.     

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.