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.     

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.     

Fixation of new alleles and the extinction of small populations: drift load, beneficial alleles, and sexual selection

With a small effective population size, random genetic drift is more important than selection in determining the fate of new alleles. Small populations therefore accumulate deleterious mutations. Left unchecked, the effect of these fixed alleles is to reduce the reproductive capacity of a species, eventually to the point of extinction. New beneficial mutations, if fixed by selection, can restore some of this lost fitness. This paper derives the overall change in fitness due to fixation of new deleterious and beneficial alleles, as a function of the distribution of effects of new mutations and the effective population size. There is a critical effective size below which a population will on average decline in fitness, but above which beneficial mutations allow the population to persist. With reasonable estimates of the relevant parameters, this critical effective size is likely to be a few hundred. Furthermore, sexual selection can act to reduce the fixation probability of deleterious new mutations and increase the probability of fixing new beneficial mutations. Sexual selection can therefore reduce the risk of extinction of small populations.     

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.     

Joint inference of the distribution of fitness effects of deleterious mutations and population demography based on nucleotide polymorphism frequencies

The distribution of fitness effects of new mutations (DFE) is important for addressing several questions in genetics, including the nature of quantitative variation and the evolutionary fate of small populations. Properties of the DFE can be inferred by comparing the distributions of the frequencies of segregating nucleotide polymorphisms at selected and neutral sites in a population sample, but demographic changes alter the spectrum of allele frequencies at both neutral and selected sites, so can bias estimates of the DFE if not accounted for. We have developed a maximum-likelihood approach, based on the expected allele-frequency distribution generated by transition matrix methods, to estimate parameters of the DFE while simultaneously estimating parameters of a demographic model that allows a population size change at some time in the past. We tested the method using simulations and found that it accurately recovers simulated parameter values, even if the simulated demography differs substantially from that assumed in our analysis. We use our method to estimate parameters of the DFE for amino acid-changing mutations in humans and Drosophila melanogaster. For a model of unconditionally deleterious mutations, with effects sampled from a gamma distribution, the mean estimate for the distribution shape parameter is approximately 0.2 for human populations, which implies that the DFE is strongly leptokurtic. For Drosophila populations, we estimate that the shape parameter is approximately 0.35. Differences in the shape of the distribution and the mean selection coefficient between humans and Drosophila result in significantly more strongly deleterious mutations in Drosophila than in humans, and, conversely, nearly neutral mutations are significantly less frequent.     

Age- and sex-distribution of the mutation load

We investigate the age and sex distribution of genetic fitness under mutation–selection balance by means of simple one-locus two-allele models. We find that the extent of age and sex variation in the mutation load is very dependent on the average effect of new mutations. If the average heterozygote selective effect of new mutations is large, then age and sex differences may constitute a significant fraction of the total load, and be significant as compared to standing genetic variation. Whether the mutation load will increase or decrease with age depends on the age- and sex-specific effects of the new mutations, and on the rate of accumulation of mutations in the germ line as individuals age. We argue that the load will most likely increase with age in animals with continuous germ-cell division throughout life, and that this will occur even when mutations have unconditionally deleterious effects. We show that a male-biased mutation rate is likely to result in both a male-biased mutation load and a load that increases with male age. This revised version was published online in July 2006 with corrections to the Cover Date.     

The relation between the neutrality index for mitochondrial genes and the distribution of mutational effects on fitness

We explore factors affecting patterns of polymorphism and divergence (as captured by the neutrality index) at mammalian mitochondrial loci. To do this, we develop a population genetic model that incorporates a fraction of neutral amino acid sites, mutational bias, and a probability distribution of selection coefficients against new nonsynonymous mutations. We confirm, by reanalyzing publicly available datasets, that the mitochondrial cyt-b gene shows a broad range of neutrality indices across mammalian taxa, and explore the biological factors that can explain this observation. We find that observed patterns of differences in the neutrality index, polymorphism, and divergence are not caused by differences in mutational bias. They can, however, be explained by a combination of a small fraction of neutral amino acid sites, weak selection acting on most amino acid mutations, and differences in effective population size among taxa.     

Rates and Genomic Consequences of Spontaneous Mutational Events in Drosophila melanogaster

Because spontaneous mutation is the source of all genetic diversity, measuring mutation rates can reveal how natural selection drives patterns of variation within and between species. We sequenced eight genomes produced by a mutation-accumulation experiment in Drosophila melanogaster. Our analysis reveals that point mutation and small indel rates vary significantly between the two different genetic backgrounds examined. We also find evidence that ∼2% of mutational events affect multiple closely spaced nucleotides. Unlike previous similar experiments, we were able to estimate genome-wide rates of large deletions and tandem duplications. These results suggest that, at least in inbred lines like those examined here, mutational pressures may result in net growth rather than contraction of the Drosophila genome. By comparing our mutation rate estimates to polymorphism data, we are able to estimate the fraction of new mutations that are eliminated by purifying selection. These results suggest that ∼99% of duplications and deletions are deleterious—making them 10 times more likely to be removed by selection than nonsynonymous mutations. Our results illuminate not only the rates of new small- and large-scale mutations, but also the selective forces that they encounter once they arise.     

The distribution of fitness effects among beneficial mutations

We know little about the distribution of fitness effects among new beneficial mutations, a problem that partly reflects the rarity of these changes. Surprisingly, though, population genetic theory allows us to predict what this distribution should look like under fairly general assumptions. Using extreme value theory, I derive this distribution and show that it has two unexpected properties. First, the distribution of beneficial fitness effects at a gene is exponential. Second, the distribution of beneficial effects at a gene has the same mean regardless of the fitness of the present wild-type allele. Adaptation from new mutations is thus characterized by a kind of invariance: natural selection chooses from the same spectrum of beneficial effects at a locus independent of the fitness rank of the present wild type. I show that these findings are reasonably robust to deviations from several assumptions. I further show that one can back calculate the mean size of new beneficial mutations from the observed mean size of fixed beneficial mutations.     

SnIPRE: Selection Inference Using a Poisson Random Effects Model

We present an approach for identifying genes under natural selection using polymorphism and divergence data from synonymous and non-synonymous sites within genes. A generalized linear mixed model is used to model the genome-wide variability among categories of mutations and estimate its functional consequence. We demonstrate how the model''s estimated fixed and random effects can be used to identify genes under selection. The parameter estimates from our generalized linear model can be transformed to yield population genetic parameter estimates for quantities including the average selection coefficient for new mutations at a locus, the synonymous and non-synynomous mutation rates, and species divergence times. Furthermore, our approach incorporates stochastic variation due to the evolutionary process and can be fit using standard statistical software. The model is fit in both the empirical Bayes and Bayesian settings using the lme4 package in R, and Markov chain Monte Carlo methods in WinBUGS. Using simulated data we compare our method to existing approaches for detecting genes under selection: the McDonald-Kreitman test, and two versions of the Poisson random field based method MKprf. Overall, we find our method universally outperforms existing methods for detecting genes subject to selection using polymorphism and divergence data.     

Mutational bias for body size in rhabditid nematodes

Mutational bias is a potentially important agent of evolution, but it is difficult to disentangle the effects of mutation from those of natural selection. Mutation-accumulation experiments, in which mutations are allowed to accumulate at very small population size, thus minimizing the efficiency of natural selection, are the best way to separate the effects of mutation from those of selection. Body size varies greatly among species of nematode in the family rhabditidae; mutational biases are both a potential cause and a consequence of that variation. We report data on the cumulative effects of mutations that affect body size in three species of rhabditid nematode that vary fivefold in adult size. Results are very consistent with previous studies of mutations underlying fitness in the same strains: two strains of Caenorhabditis briggsae decline in body size about twice as fast as two strains of C. elegans, with a concomitant higher point estimate of the genomic mutation rate; the confamilial Oscheius myriophila is intermediate. There is an overall mutational bias, such that mutations reduce size on average, but the bias appears consistent between species. The genetic correlation between mutations that affect size and those underlying fitness is large and positive, on average.     

Models of Frequency-Dependent Selection with Mutation from Parental Alleles

Frequency-dependent selection (FDS) remains a common heuristic explanation for the maintenance of genetic variation in natural populations. The pairwise-interaction model (PIM) is a well-studied general model of frequency-dependent selection, which assumes that a genotype’s fitness is a function of within-population intergenotypic interactions. Previous theoretical work indicated that this type of model is able to sustain large numbers of alleles at a single locus when it incorporates recurrent mutation. These studies, however, have ignored the impact of the distribution of fitness effects of new mutations on the dynamics and end results of polymorphism construction. We suggest that a natural way to model mutation would be to assume mutant fitness is related to the fitness of the parental allele, i.e., the existing allele from which the mutant arose. Here we examine the numbers and distributions of fitnesses and alleles produced by construction under the PIM with mutation from parental alleles and the impacts on such measures due to different methods of generating mutant fitnesses. We find that, in comparison with previous results, generating mutants from existing alleles lowers the average number of alleles likely to be observed in a system subject to FDS, but produces polymorphisms that are highly stable and have realistic allele-frequency distributions.     

The impact of random frequency-dependent mutations on the average population fitness

ABSTRACT: BACKGROUND: In addition to selection, the process of evolution is accompanied by stochastic effects, such as changing environmental conditions, genetic drift and mutations. Commonly it is believed that without genetic drift, advantageous mutations quickly fixate in a halpoid population due to strong selection and lead to a continuous increase of the average fitness. This conclusion is based on the assumption of constant fitness. However, for frequency dependent fitness, where the fitness of an individual depends on the interactions with other individuals in the population, this does not hold. RESULTS: We propose a mathematical model that allows to understand the consequences of random frequency dependent mutations on the dynamics of an infinite large population. The frequencies of different types change according to the replicator equations and the fitness of a mutant is random and frequency dependent. To capture the interactions of different types, we employ a payoff matrix of variable size and thus are able to accommodate an arbitrary number of mutations. We assume that at most one mutant type arises at a time. The payoff entries to describe the mutant type are random variables obeying a probability distribution which is related to the fitness of the parent type. CONCLUSIONS: We show that a random mutant can decrease the average fitness under frequency dependent selection, based on analytical results for two types, and on simulations for n types. Interestingly, in the case of at most two types the probabilities to increase or decrease the average fitness are independent of the concrete probability density function. Instead, they only depend on the probability that the payoff entries of the mutant are larger than the payoff entries of the parent type.     

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.     

Mutations as missing data: inferences on the ages and distributions of nonsynonymous and synonymous mutations

This article describes a new Markov chain Monte Carlo (MCMC) method applicable to DNA sequence data, which treats mutations in the genealogy as missing data. The method facilitates inferences regarding the age and identity of specific mutations while taking the full complexities of the mutational process in DNA sequences into account. We demonstrate the utility of the method in three applications. First, we demonstrate how the method can be used to make inferences regarding population genetical parameters such as theta (the effective population size times the mutation rate). Second, we show how the method can be used to estimate the ages of mutations in finite sites models and for making inferences regarding the distribution and ages of nonsynonymous and synonymous mutations. The method is applied to two previously published data sets and we demonstrate that in one of the data sets the average age of nonsynonymous mutations is significantly lower than the average age of synonymous mutations, suggesting the presence of slightly deleterious mutations. Third, we demonstrate how the method in general can be used to evaluate the posterior distribution of a function of a mapping of mutations on a gene genealogy. This application is useful for evaluating the uncertainty associated with methods that rely on mapping mutations on a phylogeny or a gene genealogy.     

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.     

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.     

Analysis of a genetic hitchhiking model, and its application to DNA polymorphism data from Drosophila melanogaster

Begun and Aquadro have demonstrated that levels of nucleotide variation correlate with recombination rate among 20 gene regions from across the genome of Drosophila melanogaster. It has been suggested that this correlation results from genetic hitchhiking associated with the fixation of strongly selected mutants. The hitchhiking process can be described as a series of two-step events. The first step consists of a strongly selected substitution wiping out linked variation in a population; this is followed by a recovery period in which polymorphism can build up via neutral mutations and random genetic drift. Genetic hitchhiking has previously been modeled as a steady-state process driven by recurring selected substitutions. We show here that the characteristic parameter of this steady-state model is alpha v, the product of selection intensity (alpha = 2Ns) and the frequency of beneficial mutations v (where N is population size and s is the selective advantage of the favored allele). We also demonstrate that the steady-state model describes the hitchhiking process adequately, unless the recombination rate is very low. To estimate alpha v, we use the data of DNA sequence variation from 17 D. melanogaster loci from regions of intermediate to high recombination rates. We find that alpha v is likely to be > 1.3 x 10(-8). Additional data are needed to estimate this parameter more precisely. The estimation of alpha v is important, as this parameter determines the shape of the frequency distribution of strongly selected substitutions.      

Functional origins of fitness effect-sizes of compensatory mutations in the DNA bacteriophage phiX174

Abstract Epistasis is an important and poorly understood aspect of mutations and strongly influences the evolutionary impact of genetic variation on adaptation and fitness. Although recent studies have begun to characterize the distribution of epistatic effects between mutations affecting fitness, there is currently a lack of empirical information on the underlying biological causes of these epistatic interactions. What are the functional constraints that determine the effectiveness of a compensatory mutation at restoring fitness? We have measured the effect‐sizes of 52 compensatory mutations affecting nine different deleterious mutations in the major capsid and spike proteins of the DNA bacteriophage X174. On average, an experimentally detectable compensatory mutation recovers about two‐thirds of the fitness cost of the preceding deleterious mutation. Variation in fitness effect‐sizes is only weakly associated with measures of the distance separating the deleterious and compensatory mutations in the amino acid sequence or the folded protein structure. However, there is a strong association of fitness effect‐size with the correlation in the effects of the mutations on the biochemical properties of amino acids. A compensatory mutation has the largest effect‐size, on average, when both the compensatory and deleterious mutations have radical effects on the overall biochemical make‐up of the amino acids. By examining the relative contributions of specific biochemical properties to variation in fitness effect‐size, we find that the area and charge of amino acids have a major influence, which suggests that the complexity of the amino acid phenotype is simplified by selection into a reduced number of phenotypic components.