Distribution Of Selection Coefficients Research Articles

Allele ages provide limited information about the strength of negative selection.

For many problems in population genetics, it is useful to characterize the distribution of fitness effects (DFE) of de novo mutations among a certain class of sites. A DFE is typically estimated by fitting an observed site frequency spectrum (SFS) to an expected SFS given a hypothesized distribution of selection coefficients and demographic history. The development of tools to infer gene trees from haplotype alignments, along with ancient DNA resources, provides us with additional information about the frequency trajectories of segregating mutations. Here, we ask how useful this additional information is for learning about the DFE, using the joint distribution on allele frequency and age to summarize information about the trajectory. To this end, we introduce an accurate and efficient numerical method for computing the density on the age of a segregating variant found at a given sample frequency, given the strength of selection and an arbitrarily complex population size history. We then use this framework to show that the unconditional age distribution of negatively selected alleles is very closely approximated by re-weighting the neutral age distribution in terms of the negatively selected SFS, suggesting that allele ages provide little information about the DFE beyond that already contained in the present day frequency. To confirm this prediction, we extended the standard Poisson Random Field (PRF) method to incorporate the joint distribution of frequency and age in estimating selection coefficients, and test its performance using simulations. We find that when the full SFS is observed and the true allele ages are known, including ages in the estimation provides only small increases in the accuracy of estimated selection coefficients. However, if only sites with frequencies above a certain threshold are observed, then the true ages can provide substantial information about the selection coefficients, especially when the selection coefficient is large. When ages are estimated from haplotype data using state-of-the-art tools, uncertainty about the age abrogates most of the additional information in the fully observed SFS case, while the neutral prior assumed in these tools when estimating ages induces a downward bias in the case of the thresholded SFS.

Hill-Robertson interference may bias the inference of fitness effects of new mutations in highly selfing species.

The accurate estimation of the distribution of fitness effects (DFE) of new mutations is critical for population genetic inference but remains a challenging task. While various methods have been developed for DFE inference using the site frequency spectrum of putatively neutral and selected sites, their applicability in species with diverse life history traits and complex demographic scenarios is not well understood. Selfing is common among eukaryotic species and can lead to decreased effective recombination rates, increasing the effects of selection at linked sites, including interference between selected alleles. We employ forward simulations to investigate the limitations of current DFE estimation approaches in the presence of selfing and other model violations, such as linkage, departures from semidominance, population structure, and uneven sampling. We find that distortions of the site frequency spectrum due to Hill-Robertson interference in highly selfing populations lead to mis-inference of the deleterious DFE of new mutations. Specifically, when inferring the distribution of selection coefficients, there is an overestimation of nearly neutral and strongly deleterious mutations and an underestimation of mildly deleterious mutations when interference between selected alleles is pervasive. In addition, the presence of cryptic population structure with low rates of migration and uneven sampling across subpopulations leads to the false inference of a deleterious DFE skewed towards effectively neutral/mildly deleterious mutations. Finally, the proportion of adaptive substitutions estimated at high rates of selfing is substantially overestimated. Our observations apply broadly to species and genomic regions with little/no recombination and where interference might be pervasive.

Mutation and Selection Induce Correlations between Selection Coefficients and Mutation Rates.

AbstractThe joint distribution of selection coefficients and mutation rates is a key determinant of the genetic architecture of molecular adaptation. Three different distributions are of immediate interest: (1) the "nominal" distribution of possible changes, prior to mutation or selection; (2) the "de novo" distribution of realized mutations; and (3) the "fixed" distribution of selectively established mutations. Here, we formally characterize the relationships between these joint distributions under the strong-selection/weak-mutation (SSWM) regime. The de novo distribution is enriched relative to the nominal distribution for the highest rate mutations, and the fixed distribution is further enriched for the most highly beneficial mutations. Whereas mutation rates and selection coefficients are often assumed to be uncorrelated, we show that even with no correlation in the nominal distribution, the resulting de novo and fixed distributions can have correlations with any combination of signs. Nonetheless, we suggest that natural systems with a finite number of beneficial mutations will frequently have the kind of nominal distribution that induces negative correlations in the fixed distribution. We apply our mathematical framework, along with population simulations, to explore joint distributions of selection coefficients and mutation rates from deep mutational scanning and cancer informatics. Finally, we consider the evolutionary implications of these joint distributions together with two additional joint distributions relevant to parallelism and the rate of adaptation.

Haplotype-based inference of the distribution of fitness effects.

Recent genome sequencing studies with large sample sizes in humans have discovered a vast quantity of low-frequency variants, providing an important source of information to analyze how selection is acting on human genetic variation. In order to estimate the strength of natural selection acting on low-frequency variants, we have developed a likelihood-based method that uses the lengths of pairwise identity-by-state between haplotypes carrying low-frequency variants. We show that in some nonequilibrium populations (such as those that have had recent population expansions) it is possible to distinguish between positive or negative selection acting on a set of variants. With our new framework, one can infer a fixed selection intensity acting on a set of variants at a particular frequency, or a distribution of selection coefficients for standing variants and new mutations. We show an application of our method to the UK10K phased haplotype dataset of individuals.

A Mutation-Selection Model of Protein Evolution under Persistent Positive Selection.

We use first principles of population genetics to model the evolution of proteins under persistent positive selection (PPS). PPS may occur when organisms are subjected to persistent environmental change, during adaptive radiations, or in host–pathogen interactions. Our mutation–selection model indicates protein evolution under PPS is an irreversible Markov process, and thus proteins under PPS show a strongly asymmetrical distribution of selection coefficients among amino acid substitutions. Our model shows the criteria (where ω is the ratio of nonsynonymous over synonymous codon substitution rates) to detect positive selection is conservative and indeed arbitrary, because in real proteins many mutations are highly deleterious and are removed by selection even at positively selected sites. We use a penalized-likelihood implementation of the PPS model to successfully detect PPS in plant RuBisCO and influenza HA proteins. By directly estimating selection coefficients at protein sites, our inference procedure bypasses the need for using ω as a surrogate measure of selection and improves our ability to detect molecular adaptation in proteins.

On the feasibility of saltational evolution

Is evolution always gradual or can it make leaps? We examine a mathematical model of an evolutionary process on a fitness landscape and obtain analytic solutions for the probability of multimutation leaps, that is, several mutations occurring simultaneously, within a single generation in 1 genome, and being fixed all together in the evolving population. The results indicate that, for typical, empirically observed combinations of the parameters of the evolutionary process, namely, effective population size, mutation rate, and distribution of selection coefficients of mutations, the probability of a multimutation leap is low, and accordingly the contribution of such leaps is minor at best. However, we show that, taking sign epistasis into account, leaps could become an important factor of evolution in cases of substantially elevated mutation rates, such as stress-induced mutagenesis in microbes. We hypothesize that stress-induced mutagenesis is an evolvable adaptive strategy.

Mutational load, inbreeding depression and heterosis in subdivided populations.

This paper examines the extent to which empirical estimates of inbreeding depression and interpopulation heterosis in subdivided populations, as well as the effects of local population size on mean fitness, can be explained in terms of current estimates of mutation rates, and the distribution of selection coefficients against deleterious mutations provided by population genomics data. Using population genetics models, numerical predictions of the genetic load, inbreeding depression and heterosis were obtained for a broad range of selection coefficients and mutation rates. The models allowed for the possibility of very high mutation rates per nucleotide site, as is sometimes observed for epiallelic mutations in plants. There was fairly good quantitative agreement between the theoretical predictions and empirical estimates of heterosis and the effects of population size on genetic load, on the assumption that the deleterious mutation rate per individual per generation is approximately one, but there was less good agreement for inbreeding depression. Weak selection, of the order of magnitude suggested by population genomic data, is required to explain the observed patterns. Possible caveats concerning the applicability of the models are discussed.

Exonic splice regulation imposes strong selection at synonymous sites.

What proportion of coding sequence nucleotides have roles in splicing, and how strong is the selection that maintains them? Despite a large body of research into exonic splice regulatory signals, these questions have not been answered. This is because, to our knowledge, previous investigations have not explicitly disentangled the frequency of splice regulatory elements from the strength of the evolutionary constraint under which they evolve. Current data are consistent both with a scenario of weak and diffuse constraint, enveloping large swaths of sequence, as well as with well-defined pockets of strong purifying selection. In the former case, natural selection on exonic splice enhancers (ESEs) might primarily act as a slight modifier of codon usage bias. In the latter, mutations that disrupt ESEs are likely to have large fitness and, potentially, clinical effects. To distinguish between these scenarios, we used several different methods to determine the distribution of selection coefficients for new mutations within ESEs. The analyses converged to suggest that ∼15%–20% of fourfold degenerate sites are part of functional ESEs. Most of these sites are under strong evolutionary constraint. Therefore, exonic splice regulation does not simply impose a weak bias that gently nudges coding sequence evolution in a particular direction. Rather, the selection to preserve these motifs is a strong force that severely constrains the evolution of a substantial proportion of coding nucleotides. Thus synonymous mutations that disrupt ESEs should be considered as a potentially common cause of single-locus genetic disorders.

Inference of the Distribution of Selection Coefficients for New Nonsynonymous Mutations Using Large Samples.

The distribution of fitness effects (DFE) has considerable importance in population genetics. To date, estimates of the DFE come from studies using a small number of individuals. Thus, estimates of the proportion of moderately to strongly deleterious new mutations may be unreliable because such variants are unlikely to be segregating in the data. Additionally, the true functional form of the DFE is unknown, and estimates of the DFE differ significantly between studies. Here we present a flexible and computationally tractable method, called Fit∂a∂i, to estimate the DFE of new mutations using the site frequency spectrum from a large number of individuals. We apply our approach to the frequency spectrum of 1300 Europeans from the Exome Sequencing Project ESP6400 data set, 1298 Danes from the LuCamp data set, and 432 Europeans from the 1000 Genomes Project to estimate the DFE of deleterious nonsynonymous mutations. We infer significantly fewer (0.38–0.84 fold) strongly deleterious mutations with selection coefficient |s| > 0.01 and more (1.24–1.43 fold) weakly deleterious mutations with selection coefficient |s| < 0.001 compared to previous estimates. Furthermore, a DFE that is a mixture distribution of a point mass at neutrality plus a gamma distribution fits better than a gamma distribution in two of the three data sets. Our results suggest that nearly neutral forces play a larger role in human evolution than previously thought.

Estimating the selective effects of heterozygous protein-truncating variants from human exome data.

The dispensability of individual genes for viability has interested generations of geneticists. For some genes it is essential to maintain two functional chromosomal copies, while others may tolerate the loss of one or both copies. Exome sequence data from 60,706 individuals provide sufficient observations of rare protein truncating variants (PTVs) to make genome-wide estimates of selection against heterozygous loss of gene function. The cumulative frequency of rare deleterious PTVs is primarily determined by the balance between incoming mutations and purifying selection rather than genetic drift. This enables the estimation of the genome-wide distribution of selection coefficients for heterozygous PTVs and corresponding Bayesian estimates for individual genes. The strength of selection can discriminate the severity, age of onset, and mode of inheritance in Mendelian exome sequencing cases. We find that genes under the strongest selection are enriched in embryonic lethal mouse knockouts, putatively cell-essential genes, Mendelian disease genes, and regulators of transcription. Screening by essentiality, we find a large set of genes under strong selection that likely have critical function but have not yet been extensively annotated in published literature.

Errors in meta-analyses of selection.

Errors in meta-analyses of selection.

Extensively Parameterized Mutation-Selection Models Reliably Capture Site-Specific Selective Constraint.

The mutation-selection model of coding sequence evolution has received renewed attention for its use in estimating site-specific amino acid propensities and selection coefficient distributions. Two computationally tractable mutation-selection inference frameworks have been introduced: One framework employs a fixed-effects, highly parameterized maximum likelihood approach, whereas the other employs a random-effects Bayesian Dirichlet Process approach. While both implementations follow the same model, they appear to make distinct predictions about the distribution of selection coefficients. The fixed-effects framework estimates a large proportion of highly deleterious substitutions, whereas the random-effects framework estimates that all substitutions are either nearly neutral or weakly deleterious. It remains unknown, however, how accurately each method infers evolutionary constraints at individual sites. Indeed, selection coefficient distributions pool all site-specific inferences, thereby obscuring a precise assessment of site-specific estimates. Therefore, in this study, we use a simulation-based strategy to determine how accurately each approach recapitulates the selective constraint at individual sites. We find that the fixed-effects approach, despite its extensive parameterization, consistently and accurately estimates site-specific evolutionary constraint. By contrast, the random-effects Bayesian approach systematically underestimates the strength of natural selection, particularly for slowly evolving sites. We also find that, despite the strong differences between their inferred selection coefficient distributions, the fixed- and random-effects approaches yield surprisingly similar inferences of site-specific selective constraint. We conclude that the fixed-effects mutation-selection framework provides the more reliable software platform for model application and future development.

Epistasis and the Structure of Fitness Landscapes: Are Experimental Fitness Landscapes Compatible with Fisher's Geometric Model?

The fitness landscape defines the relationship between genotypes and fitness in a given environment and underlies fundamental quantities such as the distribution of selection coefficient and the magnitude and type of epistasis. A better understanding of variation in landscape structure across species and environments is thus necessary to understand and predict how populations will adapt. An increasing number of experiments investigate the properties of fitness landscapes by identifying mutations, constructing genotypes with combinations of these mutations, and measuring the fitness of these genotypes. Yet these empirical landscapes represent a very small sample of the vast space of all possible genotypes, and this sample is often biased by the protocol used to identify mutations. Here we develop a rigorous statistical framework based on Approximate Bayesian Computation to address these concerns and use this flexible framework to fit a broad class of phenotypic fitness models (including Fisher’s model) to 26 empirical landscapes representing nine diverse biological systems. Despite uncertainty owing to the small size of most published empirical landscapes, the inferred landscapes have similar structure in similar biological systems. Surprisingly, goodness-of-fit tests reveal that this class of phenotypic models, which has been successful so far in interpreting experimental data, is a plausible in only three of nine biological systems. More precisely, although Fisher’s model was able to explain several statistical properties of the landscapes—including the mean and SD of selection and epistasis coefficients—it was often unable to explain the full structure of fitness landscapes.

Effective population size does not predict codon usage bias in mammals.

Synonymous codons are not used at equal frequency throughout the genome, a phenomenon termed codon usage bias (CUB). It is often assumed that interspecific variation in the intensity of CUB is related to species differences in effective population sizes (Ne), with selection on CUB operating less efficiently in species with small Ne. Here, we specifically ask whether variation in Ne predicts differences in CUB in mammals and report two main findings. First, across 41 mammalian genomes, CUB was not correlated with two indirect proxies of Ne (body mass and generation time), even though there was statistically significant evidence of selection shaping CUB across all species. Interestingly, autosomal genes showed higher codon usage bias compared to X-linked genes, and high-recombination genes showed higher codon usage bias compared to low recombination genes, suggesting intraspecific variation in Ne predicts variation in CUB. Second, across six mammalian species with genetic estimates of Ne (human, chimpanzee, rabbit, and three mouse species: Mus musculus, M. domesticus, and M. castaneus), Ne and CUB were weakly and inconsistently correlated. At least in mammals, interspecific divergence in Ne does not strongly predict variation in CUB. One hypothesis is that each species responds to a unique distribution of selection coefficients, confounding any straightforward link between Ne and CUB.

A Penalized-Likelihood Method to Estimate the Distribution of Selection Coefficients from Phylogenetic Data

We develop a maximum penalized-likelihood (MPL) method to estimate the fitnesses of amino acids and the distribution of selection coefficients (S = 2Ns) in protein-coding genes from phylogenetic data. This improves on a previous maximum-likelihood method. Various penalty functions are used to penalize extreme estimates of the fitnesses, thus correcting overfitting by the previous method. Using a combination of computer simulation and real data analysis, we evaluate the effect of the various penalties on the estimation of the fitnesses and the distribution of S. We show the new method regularizes the estimates of the fitnesses for small, relatively uninformative data sets, but it can still recover the large proportion of deleterious mutations when present in simulated data. Computer simulations indicate that as the number of taxa in the phylogeny or the level of sequence divergence increases, the distribution of S can be more accurately estimated. Furthermore, the strength of the penalty can be varied to study how informative a particular data set is about the distribution of S. We analyze three protein-coding genes (the chloroplast rubisco protein, mammal mitochondrial proteins, and an influenza virus polymerase) and show the new method recovers a large proportion of deleterious mutations in these data, even under strong penalties, confirming the distribution of S is bimodal in these real data. We recommend the use of the new MPL approach for the estimation of the distribution of S in species phylogenies of protein-coding genes.

Site-heterogeneous mutation-selection models within the PhyloBayes-MPI package

Motivation: In recent years, there has been an increasing interest in the potential of codon substitution models for a variety of applications. However, the computational demands of these models have sometimes lead to the adoption of oversimplified assumptions, questionable statistical methods or a limited focus on small data sets.Results: Here, we offer a scalable, message-passing-interface-based Bayesian implementation of site-heterogeneous codon models in the mutation-selection framework. Our software jointly infers the global mutational parameters at the nucleotide level, the branch lengths of the tree and a Dirichlet process governing across-site variation at the amino acid level. We focus on an example estimation of the distribution of selection coefficients from an alignment of several hundred sequences of the influenza PB2 gene, and highlight the site-specific characterization enabled by such a modeling approach. Finally, we discuss future potential applications of the software for conducting evolutionary inferences.Availability and implementation: The models are implemented within the PhyloBayes-MPI package, (available at phylobayes.org) along with usage details in the accompanying manual.Contact: nicolas.rodrigue@ucalgary.ca

Distortions in Genealogies due to Purifying Selection and Recombination

Purifying selection at many linked sites alters patterns of molecular evolution, reducing overall diversity and distorting the shapes of genealogies. Recombination attenuates these effects; however, purifying selection can significantly distort genealogies even for substantial recombination rates. Here, we show that when selection and/or recombination are sufficiently strong, the genealogy at any single site can be described by a time-dependent effective population size, Ne(t), which has a simple analytic form. Our results illustrate how recombination reduces distortions in genealogies and allow us to quantitatively describe the shapes of genealogies in the presence of strong purifying selection and recombination. We also analyze the effects of a distribution of selection coefficients across the genome.

Purifying Selection in Mammalian Mitochondrial Protein-Coding Genes Is Highly Effective and Congruent with Evolution of Nuclear Genes

The mammalian mitochondrial genomes differ from the nuclear genomes by maternal inheritance, absence of recombination, and higher mutation rate. All these differences decrease the effective population size of mitochondrial genome and make it more susceptible to accumulation of slightly deleterious mutations. It was hypothesized that mitochondrial genes, especially in species with low effective population size, irreversibly degrade leading to decrease of organismal fitness and even to extinction of species through the mutational meltdown. To interrogate this hypothesis, we compared the purifying selections acting on the representative set of mitochondrial (potentially degrading) and nuclear (potentially not degrading) protein-coding genes in species with different effective population size. For 21 mammalian species, we calculated the ratios of accumulation of slightly deleterious mutations approximated by Kn/Ks separately for mitochondrial and nuclear genomes. The 75% of variation in Kn/Ks is explained by two independent variables: type of a genome (mitochondrial or nuclear) and effective population size of species approximated by generation time. First, we observed that purifying selection is more effective in mitochondria than in the nucleus that implies strong evolutionary constraints of mitochondrial genome. Mitochondrial de novo nonsynonymous mutations have at least 5-fold more harmful effect when compared with nuclear. Second, Kn/Ks of mitochondrial and nuclear genomes is positively correlated with generation time of species, indicating relaxation of purifying selection with decrease of species-specific effective population size. Most importantly, the linear regression lines of mitochondrial and nuclear Kn/Ks's from generation times of species are parallel, indicating congruent relaxation of purifying selection in both genomes. Thus, our results reveal that the distribution of selection coefficients of de novo nonsynonymous mitochondrial mutations has a similar shape with the distribution of de novo nonsynonymous nuclear mutations, but its mean is five times smaller. The harmful effect of mitochondrial de novo nonsynonymous mutations triggers highly effective purifying selection, which maintains the fitness of the mammalian mitochondrial genome.

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.

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.