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We recently published a paper quantifying the genome-wide consequences of natural selection, including the effects of indirect selection due to the correlation of genetic regions (neutral or selected) with directly selected regions (Gompert et al., 2022). In their critique of our paper, Charlesworth and Jensen (2022) make two main points: (i) indirect selection is equivalent to hitchhiking and thus well documented (i.e., our results are not novel) and (ii) that we do not demonstrate the source of linkage disequilibrium (LD) between SNPs and the Mel-Stripe locus in the Timema cristinae experiment we analyse. As we discuss in detail below, neither of these are substantial criticisms of our work.

The strong reduction in the frequency of recombination in heterozygotes for an inversion and a standard gene arrangement causes inversion and standard haplotypes to become partially isolated, resulting in sequence divergence between them and to changes in the levels of neutral variability at nucleotide sites within each arrangement class, as is also the case for other types of balanced polymorphisms. Previous theoretical studies have either assumed that the population is panmictic or that it is divided into two populations subject to divergent selection. Here, the theory is extended to a model of an arbitrary number of demes connected by migration, using a finite island. Recursion relations for mean pairwise coalescent times are used to obtain simple approximate expressions for diversity and divergence statistics relevant to an inversion polymorphism at equilibrium under recombination and drift, and for the approach to equilibrium following the sweep of an inversion to a stable intermediate frequency. The effects of an inversion polymorphism on patterns of linkage disequilibrium are also examined. The reduction in effective recombination rate caused by population subdivision can have significant effects on these statistics, and hence on estimates of the ages of inversions. The theoretical results are discussed in relation to population genomic data on inversion polymorphisms, with an emphasis onDrosophila melanogaster. Methods are proposed for testing whether or not inversions are close to recombination-drift equilibrium, and for estimating the rate of recombinational exchange in heterozygotes for inversions; difficulties involved in estimating the ages of inversions are also discussed.

It has recently been proposed that lower mutation rates in gene bodies compared with upstream and downstream sequences in Arabidopsis thaliana are the result of an “adaptive” modification of the rate of beneficial and deleterious mutations in these functional regions. This claim was based both on analyses of mutation accumulation lines and on population genomics data. Here, we show that several questionable assumptions were used in the population genomics analyses. In particular, we demonstrate that the difference between gene bodies and less selectively constrained sequences in the magnitude of Tajima's D can in principle be explained by the presence of sites subject to purifying selection and does not require lower mutation rates in regions experiencing selective constraints.

Current procedures for inferring population history generally assume complete neutrality���that is, they neglect both direct selection and the effects of selection on linked sites.We here examine how the presence of direct purifying selection and background selection may bias demographic inference by evaluating two commonly-used methods (MSMC and fastsimcoal2), specifically studying how the underlying shape of the distribution of fitness effects and the fraction of directly selected sites interact with demographic parameter estimation. The results show that, even after masking functional genomic regions, background selection may cause the mis-inference of population growth under models of both constant population size and decline. This effect is amplified as the strength of purifying selection and the density of directly selected sites increases, as indicated by the distortion of the site frequency spectrum and levels of nucleotide diversity at linked neutral sites. We also show how simulated changes in background selection effects caused by population size changes can be predicted analytically.We propose a potential method for correcting for the mis-inference of population growth caused by selection. By treating the distribution of fitness effect as a nuisance parameter and averaging across all potential realizations, we demonstrate that even directly selected sites can be used to infer demographic histories with reasonable accuracy. Key words: demographic inference, background selection, distribution of fitness effects, MSMC, fastsimcoal2, approximate Bayesian computation (ABC).

We discuss the genetic, demographic, and selective forces that are likely to be at play in restricting observed levels of DNA sequence variation in natural populations to a much smaller range of values than would be expected from the distribution of census population sizes alone—Lewontin’s Paradox. While several processes that have previously been strongly emphasized must be involved, including the effects of direct selection and genetic hitchhiking, it seems unlikely that they are sufficient to explain this observation without contributions from other factors. We highlight a potentially important role for the less-appreciated contribution of population size change; specifically, the likelihood that many species and populations may be quite far from reaching the relatively high equilibrium diversity values that would be expected given their current census sizes.

An obituary by Brian Charlesworth of Richard C. Lewontin, who pioneered the study of natural variation at the molecular level.

The relative evolutionary roles of adaptive and non-adaptive processes remain a central question in population genetics. Resolution of this debate has been difficult as an appropriate null model incorporating... The question of the relative evolutionary roles of adaptive and nonadaptive processes has been a central debate in population genetics for nearly a century. While advances have been made in the theoretical development of the underlying models, and statistical methods for estimating their parameters from large-scale genomic data, a framework for an appropriate null model remains elusive. A model incorporating evolutionary processes known to be in constant operation, genetic drift (as modulated by the demographic history of the population) and purifying selection, is lacking. Without such a null model, the role of adaptive processes in shaping within- and between-population variation may not be accurately assessed. Here, we investigate how population size changes and the strength of purifying selection affect patterns of variation at “neutral” sites near functional genomic components. We propose a novel statistical framework for jointly inferring the contribution of the relevant selective and demographic parameters. By means of extensive performance analyses, we quantify the utility of the approach, identify the most important statistics for parameter estimation, and compare the results with existing methods. Finally, we reanalyze genome-wide population-level data from a Zambian population of Drosophila melanogaster, and find that it has experienced a much slower rate of population growth than was inferred when the effects of purifying selection were neglected. Our approach represents an appropriate null model, against which the effects of positive selection can be assessed.

The time taken for a selectively favorable allele to spread through a single population was investigated early in the history of population genetics. The resulting formulas are based on deterministic dynamics, leading to inaccuracies at allele frequencies close to 0 or 1. To remedy this problem, the properties of the stochastic phases at either end point of allele frequency need to be analyzed. This article uses a heuristic approach to determining the expected times spent in the stochastic and deterministic phases of allele frequency trajectories, for a model of weak selection at a single locus that is valid for inbreeding populations and for autosomal and sex-linked inheritance. The net fixation time is surprisingly insensitive to the level of dominance of a favorable mutation, even with random mating. Approximate expressions for the variance of the net fixation time are also obtained, which imply that there can be substantial stochastic effects even in very large populations. The accuracy of the approximations was evaluated by comparisons with computer simulations. The results reveal some areas that need further investigation if a full understanding of selective sweeps is to be obtained, notably the possibility that fixations of slightly deleterious mutations may be affecting variability at closely linked sites.

R.A. Fisher’s 1922 paper On the dominance ratio has a strong claim to be the foundation paper for modern population genetics. It greatly influenced subsequent work by Haldane and Wright, and contributed 3 major innovations to the study of evolution at the genetic level. First, the introduction of a general model of selection at a single locus, which showed how variability could be maintained by heterozygote advantage. Second, the use of the branching process approach to show that a beneficial mutation has a substantial chance of loss from the population, even when the population size is extremely large. Third, the invention of the concept of a probability distribution of allele frequency, caused by random sampling of allele frequencies due to finite population size, and the first use of a diffusion equation to investigate the properties of such a distribution. Although Fisher was motivated by an inference that later turned out to lack strong empirical support (a substantial contribution of dominance to quantitative trait variability), and his use of a diffusion equation was marred by a technical mistake, the paper introduced concepts and methods that pervade much subsequent work in population genetics.

The effects of selection on variability at linked sites have an important influence on levels and patterns of within-population variation across the genome. Most theoretical models of these effects have assumed that selection is sufficiently strong that allele frequency changes at the loci concerned are largely deterministic. These models have led to the conclusion that directional selection for selectively favorable mutations, or against recurrent deleterious mutations, reduces nucleotide site diversity at linked neutral sites. Recent work has shown, however, that fixations of weakly selected mutations, accompanied by significant stochastic changes in allele frequencies, can sometimes cause higher diversity at linked sites when compared with the effects of fixations of neutral mutations. This study extends this work by deriving approximate expressions for the mean conditional times to fixation and loss of mutations subject to selection, and analyzing the conditions under which selection increases rather than reduces these times. Simulations are used to examine the relations between diversity at a neutral site and the fixation and loss times of mutations at a linked site that is subject to selection. It is shown that the long-term level of neutral diversity can be increased over the purely neutral value by recurrent fixations and losses of linked, weakly selected dominant or partially dominant favorable mutations, or linked recessive or partially recessive deleterious mutations. The results are used to examine the conditions under which associative overdominance, as opposed to background selection, is likely to operate.

We write to address recent claims by Gompert et al. (2021) about the potentially important and underappreciated phenomena of “indirect selection”, the observation that neutral regions may be affected by natural selection. We argue both that this phenomenon – generally known as genetic hitchhiking – is neither new nor poorly studied, and that the patterns described by the authors have multiple alternative explanations.

AU The:field Pleaseconfirmthatallheadinglevelsarerepresentedcorrectly of population genomics has grown rapidly in response : to the recent advent of affordable, large-scale sequencing technologies. As opposed to the situation during the majority of the 20th century, in which the development of theoretical and statistical population genetic insights outpaced the generation of data to which they could be applied, genomic data are now being produced at a far greater rate than they can be meaningfully analyzed and interpreted. With this wealth of data has come a tendency to focus on fitting specific (and often rather idiosyncratic) models to data, at the expense of a careful exploration of the range of possible underlying evolutionary processes. For example, the approach of directly investigating models of adaptive evolution in each newly sequenced population or species often neglects the fact that a thorough characterization of ubiquitous nonadaptive processes is a prerequisite for accurate inference. We here describe the perils of these tendencies, present our consensus views on current best practices in population genomic data analysis, and highlight areas of statistical inference and theory that are in need of further attention. Thereby, we argue for the importance of defining a biologically relevant baseline model tuned to the details of each new analysis, of skepticism and scrutiny in interpreting model fitting results, and of carefully defining addressable hypotheses and underlying uncertainties.

Patterns of variation and evolution at a given site in a genome can be strongly influenced by the effects of selection at genetically linked sites. In particular, the recombination rates of genomic regions correlate with their amount of within-population genetic variability, the degree to which the frequency distributions of DNA sequence variants differ from their neutral expectations, and the levels of adaptation of their functional components. We review the major population genetic processes that are thought to lead to these patterns, focusing on their effects on patterns of variability: selective sweeps, background selection, associative overdominance, and Hill–Robertson interference among deleterious mutations. We emphasize the difficulties in distinguishing among the footprints of these processes and disentangling them from the effects of purely demographic factors such as population size changes. We also discuss how interactions between selective and demographic processes can significantly affect patterns of variability within genomes.

There has been a long history of the use of mathematics in genetics, ranging from the use of statistics to analyse genetic data to genetic models of evolutionary processes. Contemporary research into the genomic basis of disease and complex traits exemplifies the importance of statistical methods in genetics. Some examples of the development and application of population genetic models are described, which are intended to highlight the utility of such models for understanding variation and evolution in natural populations. The effects of selection on variability at sites linked to the targets of selection illustrate how fruitful interactions between theory and data can be.

Several recent publications have stated that epistatic fitness interactions cause the fixation of inversions that suppress recombination among the loci involved. Under this type of selection, however, the suppression of recombination in an inversion heterozygote can create a form of heterozygote advantage, which prevents the inversion from becoming fixed by selection. This process has been explicitly modelled by previous workers.

It has previously been shown that, conditional on its fixation, the time to fixation of a semi-dominant deleterious autosomal mutation in a randomly mating population is the same as that of an advantageous mutation. This result implies that deleterious mutations could generate selective sweep-like effects. Although their fixation probabilities greatly differ, the much larger input of deleterious relative to beneficial mutations suggests that this phenomenon could be important. We here examine how the fixation of mildly deleterious mutations affects levels and patterns of polymorphism at linked sites - both in the presence and absence of interference amongst deleterious mutations - and how this class of sites may contribute to divergence between-populations and species. We find that, while deleterious fixations are unlikely to represent a significant proportion of outliers in polymorphism-based genomic scans within populations, minor shifts in the frequencies of deleterious mutations can influence the proportions of private variants and the value ofFSTafter a recent population split. As sites subject to deleterious mutations are necessarily found in functional genomic regions, interpretations in terms of recurrent positive selection may require reconsideration.

To what extent do substitutions in protein-coding versus gene-regulatory regions contribute to fitness change over time? Answering this question requires estimates of the extent of selection acting on beneficial mutations in the two classes of sites. New mutations that have advantageous or deleterious fitness effects can induce selective sweeps and background selection, respectively, causing variation in the level of neutral genetic diversity along the genome. In this study, we analyse the profiles of genetic variability around protein-coding and regulatory elements in the genomes of wild mice to estimate the parameters of positive selection. We find patterns of diversity consistent with the effects of selection at linked sites, which are similar across mouse taxa, despite differences in effective population size and demographic history. By fitting a model that combines the effects of selective sweeps and background selection, we estimate the strength of positive selection and the frequency of advantageous mutations. We find that strong positive selection is required to explain variation in genetic diversity across the murid genome. In particular, we estimate that beneficial mutations in protein-coding regions have stronger effects on fitness than do mutations in gene-regulatory regions, but that mutations in gene-regulatory regions are more common. Overall though, our parameter estimates suggest that the cumulative fitness changes brought about by beneficial mutations in protein-coding may be greater than those in gene-regulatory elements.

Balancing selection (BLS) is the evolutionary force that maintains high levels of genetic variability in many important genes. To further our understanding of its evolutionary significance, we analyze models with BLS acting on a biallelic locus: an equilibrium model with long-term BLS, a model with long-term BLS and recent changes in population size, and a model of recent BLS. Using phase-type theory, a mathematical tool for analyzing continuous time Markov chains with an absorbing state, we examine how BLS affects polymorphism patterns in linked neutral regions, as summarized by nucleotide diversity, the expected number of segregating sites, the site frequency spectrum, and the level of linkage disequilibrium (LD). Long-term BLS affects polymorphism patterns in a relatively small genomic neighborhood, and such selection targets are easier to detect when the equilibrium frequencies of the selected variants are close to 50%, or when there has been a population size reduction. For a new mutation subject to BLS, its initial increase in frequency in the population causes linked neutral regions to have reduced diversity, an excess of both high and low frequency derived variants, and elevated LD with the selected locus. These patterns are similar to those produced by selective sweeps, but the effects of recent BLS are weaker. Nonetheless, compared to selective sweeps, nonequilibrium polymorphism and LD patterns persist for a much longer period under recent BLS, which may increase the chance of detecting such selection targets. An R package for analyzing these models, among others (e.g., isolation with migration), is available.

Population genetics studies often make use of a class of nucleotide site free from selective pressures in order to make inferences about population size changes or natural selection at other sites. If such neutral sites can be identified, they offer the opportunity to avoid any confounding effects of selection. Here we investigate evolution at putatively neutrally evolving short intronic sites in natural populations ofDrosophila melanogasterandD. simulans, in order to understand the properties of spontaneous mutations and the extent of GC-biased gene conversion in these species. Use of data on the genetics of natural populations is advantageous because it integrates information from large numbers of individuals over long timescales. In agreement with direct evidence from observations of spontaneous mutations inDrosophila, we find a bias in the spectrum of mutations towards AT basepairs. In addition, we find that this bias is stronger in theD. melanogasterlineage than theD. simulanslineage. The evidence for GC-biased gene conversion inDrosophilahas been equivocal. Here we provide evidence for a weak force favouring GC in both species, which is stronger inD. simulans.Some homologous short intronic sites have diverged in GC content between the two species, which may have been caused by lineage-specific changes in the extent to which different regions of the genome are subject to a GC (or AT)-favouring force.

R.A. Fisher was one of the greatest scientists of the 20th century, whose scientific contributions ranged over a very wide area of science. He was, however, from an early age a supporter of eugenic ideas, and for this reason has been accused of being a racist and an advocate of forced sterilisation of certain kinds of people. Concerns are now increasingly being raised about historical figures such as Fisher, stimulated by recent abhorrent racially motivated events. A primary aim of this paper is to conduct a careful analysis of Fisher’s writings on eugenics and related areas, in the context of these adverse views. We first review his scientific achievements and then describe his early development of interests in genetics and eugenic ideas. We outline his concerns about the inverse relationship between intellectual ability and fertility, his views on how this might adversely affect the development of human societies, his eugenic proposals for differential family allowances, and his support for voluntary sterilisation for the “feebleminded”. We follow this with an account of Fisher’s interaction with the Nazi-supporting German human geneticist Verschuer, and Fisher’s response to the 1952 UNESCO statement on “The Race Concept”. We finally discuss attitudes to Fisher’s eugenics related activities in a modern context. Our conclusion is that, however much people now reasonably disagree with his stated ideas on eugenics and racial issues, there is no case for dishonouring him and allowing these concerns to outweigh the appreciation of his enormous scientific and humanitarian contributions.

Selective sweeps are thought to play a significant role in shaping patterns of variability across genomes; accurate predictions of their effects are, therefore, important for understanding these patterns. A commonly used model of selective sweeps assumes that alleles sampled at the end of a sweep, and that fail to recombine with wild-type haplotypes during the sweep, coalesce instantaneously, leading to a simple expression for sweep effects on diversity. It is shown here that there can be a significant probability that a pair of alleles sampled at the end of a sweep coalesce during the sweep before a recombination event can occur, reducing their expected coalescent time below that given by the simple approximation. Expressions are derived for the expected reductions in pairwise neutral diversities caused by both single and recurrent sweeps in the presence of such within-sweep coalescence, although the effects of multiple recombination events during a sweep are only treated heuristically. The accuracies of the resulting expressions were checked against the results of simulations. For even moderate ratios of the recombination rate to the selection coefficient, the simple approximation can be substantially inaccurate. The selection model used here can be applied to favorable mutations with arbitrary dominance coefficients, to sex-linked loci with sex-specific selection coefficients, and to inbreeding populations. Using the results from this model, the expected differences between the levels of variability on X chromosomes and autosomes with selection at linked sites are discussed, and compared with data on a population ofDrosophila melanogaster.

Summary Y and W chromosomes start degenerating after they evolve a non-recombining region that is always heterozygous in males (Y) or females (W), sometimes losing almost all genes that were originally present on their X or Z counterparts. A new model for such degeneration involves evolutionary change in regulatory sequences.

A recent article reassessing the Neutral Theory of Molecular Evolution claims that it is no longer as important as is widely believed. The authors argue that "the neutral theory was supported by unreliable theoretical and empirical evidence from the beginning, and that in light of modern, genome-scale data, we can firmly reject its universality." Claiming that "the neutral theory has been overwhelmingly rejected," they propose instead that natural selection is the major force shaping both between-species divergence and within-species variation. Although this is probably a minority view, it is important to evaluate such claims carefully in the context of current knowledge, as inaccuracies can sometimes morph into an accepted narrative for those not familiar with the underlying science. We here critically examine and ultimately reject Kern and Hahn's arguments and assessment, and instead propose that it is now abundantly clear that the foundational ideas presented five decades ago by Kimura and Ohta are indeed correct.

Brian Charlesworth and Anthony W. F. Edwards mark the 100th anniversary of a paper by R. A. Fisher, which introduced the statistical term “variance”. What followed was a whole new field of statistical analysis

We re-examine the model of Kirkpatrick and Barton for the spread of an inversion into a local population. This model assumes that local selection maintains alleles at two or more loci, despite immigration of alternative alleles at these loci from another population. We show that an inversion is favored because it prevents the breakdown of linkage disequilibrium generated by migration; the selective advantage of an inversion is dependent on the amount of recombination between the loci involved, as in other cases where inversions are selected for as a result of their effects on recombination. We derive expressions for the rate of spread of an inversion; when the loci covered by the inversion are tightly linked, these conditions deviate substantially from those proposed previously, and imply that an inversion can then have only a small advantage.

Brian Charlesworth is a Senior Honorary Professorial Fellow at the University of Edinburgh. His work has involved the application of population genetics to a variety of issues in evolutionary biology. His current research is on population genetics theory, molecular evolution and genome evolution. He has published over 300 papers and three books.

Crossing over between homologous chromosomes during meiosis repairs programmed DNA double-strand breaks, ensures proper segregation at meiosis I [1], shapes the genomic distribution of nucleotide variability in populations, and enhances the efficacy of natural selection among genetically linked sites [2]. Between closely related Drosophila species, large differences exist in the rate and chromosomal distribution of crossing over. Little, however, is known about the molecular genetic changes or population genetic forces that mediate evolved differences in recombination between species [3, 4]. Here we show that a meiosis gene with a history of rapid evolution acts as a trans-acting modifier of species differences in crossing over. In transgenic flies, the dicistronic gene, mei-217/mei-218, recapitulates a large part of the species differences in the rate and chromosomal distribution of crossing over. These phenotypic differences appear to result from changes in protein sequence not gene expression. Our population genetics analyses show that the protein-coding sequence of mei-218, but not mei-217, has a history of recurrent positive natural selection. By modulating the intensity of centromeric and telomeric suppression of crossing over, evolution at mei-217/-218 has incidentally shaped gross differences in the chromosomal distribution of nucleotide variability between species. We speculate that recurrent bouts of adaptive evolution at mei-217/-218 might reflect a history of coevolution with selfish genetic elements.

Under the neutral theory, genetic diversity is expected to increase with population size. While comparative analyses have consistently failed to find strong relationships between census population size and genetic diversity, a recent study across animals identified a strong correlation between propagule size and genetic diversity, suggesting that r-strategists that produce many small offspring, have greater long-term population sizes. Here we compare genome-wide genetic diversity across 38 species of European butterflies (Papilionoidea), a group that shows little variation in reproductive strategy. We show that genetic diversity across butterflies varies over an order of magnitude and that this variation cannot be explained by differences in current abundance, propagule size, host or geographic range. Instead, neutral genetic diversity is negatively correlated with body size and positively with the length of the genetic map. This suggests that genetic diversity is determined both by differences in long-term population size and the effect of selection on linked sites., Permissions for field sampling were obtained from the Generalitat de Catalunya (SF/639), the Gobierno de Aragon (INAGA/500201/24/2018/0614 to Karl Wotton) and the Gobierno del Principado de Asturias (014252). This project was supported by an ERC starting grant (ModelGenomLand) and an Independent Research fellowship from the Natural Environmental Research Council (NERC) UK (NE/L011522/1) to K.L.. A.M. was supported by a summer studentship from the Institute of Evolutionary Biology at Edinburgh University, A.H. is supported by a Biotechnology and Biological Sciences Research Council David Phillips fellowship (BB/N020146/1) and R.V. is supported by project CGL2016-76322-P (AEI/FEDER, UE).

Biotechnology companies are process-driven organizations and often struggle with their ability to innovate. Universities, on the other hand, thrive on discovery and variation as a source of innovation. As such, properly structured academic-industry partnerships in medical technology development may enhance and accelerate innovation. Through joint industry-academic efforts, our objective was to develop a technology aimed at global cervical cancer prevention.Our Center for Medical Innovation assembled a multidisciplinary team of students, surgical residents, and clinical faculty to enter in the University of Utah's annual Bench-to-Bedside competition. Bench-to-Bedside is a university program centered on medical innovation. Teams are given access to university resources and are provided $500.00 for prototype development. Participation by team members are on a volunteer basis. Our industry partner presented the validated need and business mentorship. The team studied the therapeutic landscape, environmental constraints, and used simulation to understand human factors design and usage requirements. A physical device was manufactured by first creating a digital image (SOLIDWORKS 3D CAD). Then, using a 3-dimensional printer (Stratasys Objet30 Prime 3D printer), the image was translated into a physical object. Tissue burn depth analysis was performed on raw chicken breasts warmed to room temperature. Varying combinations of time and temperature were tested, and burn depth and diameter were measured 30 min after each trial. An arithmetic mean was calculated for each corresponding time and temperature combination. User comprehension of operation and sterilization was tested via a participant validation study. Clinical obstetricians and gynecologists were given explicit instructions on usage details and then asked to operate the device. Participant behaviors and questions were recorded.Our efforts resulted in a functional battery-powered hand-held thermocoagulation prototype in just 72 d. Total cost of development was$500. Proof of concept trials at 100°C demonstrated an average ablated depth and diameter of 4.7 mm and 23.3 mm, respectively, corresponding to treatment efficacy of all grades of precancerous cervical lesions. User comprehension studies showed variable understanding with respect to operation and sterilization instructions.Our experience with using industry-academic partnerships as a means to create medical technologies resulted in the rapid production of a low-cost device that could potentially serve as an integral piece of the "screen-and-treat" approach to premalignant cervical lesions as outlined by World Health Organization. This case study highlights the impact of accelerating medical advances through industry-academic partnership that leverages their combined resources.

Levels of variability and rates of adaptive evolution may be affected by hitchhiking, the effect of selection on evolution at linked sites. Hitchhiking can be caused either by selective sweeps or by background selection, involving the spread of new favorable alleles or the elimination of deleterious mutations, respectively. Recent analyses of population genomic data have fitted models where both these processes act simultaneously, in order to infer the parameters of selection. Here, we investigate the consequences of relaxing a key assumption of some of these studies – that the time occupied by a selective sweep is negligible compared with the neutral coalescent time. We derive a new expression for the expected level of neutral variability in the presence of recurrent selective sweeps and background selection. We also derive approximate integral expressions for the effects of recurrent selective sweeps. The accuracy of the theoretical predictions was tested against multilocus simulations, with selection, recombination and mutation parameters that are realistic forDrosophila melanogaster. In the presence of crossing over, there is approximate agreement between the theoretical and simulation results. We show that the observed relations between the rate of crossing over and the level of synonymous site diversity and rate of adaptive evolution in Drosophila are probably mainly caused by background selection, whereas selective sweeps and population size changes are needed to produce the observed distortions of the site frequency spectrum.

In the version of this article initially published, reference 10 incorrectly cited Seplyarskiy, V. B. et al. Weghorn, D. et al. is the correct reference. The error has been corrected in the HTML and PDF version of the article.

This paper examines the extent to which empirical estimates of inbreeding depression and inter-population heterosis in subdivided populations, as well as the effects of local population size on mean fitness, can be explained in terms of estimates of mutation rates, and the distribution of selection coefficients against deleterious mutations provided by population genomics data. Using results from 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. 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 analyses, is required to explain the observed patterns. Possible caveats concerning the applicability of the models are discussed.

In its initial formulation by Motoo Kimura, the neutral theory was concerned solely with the level of variability maintained by random genetic drift of selectively neutral mutation, and the rate of molecular evolution caused by the fixation of such mutations. The original theory considered events at a single genetic locus in isolation from the rest of the genome. It did not take long, however, for theoreticians to wonder whether selection at one or more loci might influence neutral variability at linked sites. Once DNA sequence variability could be studied, and especially when resequencing of whole genomes became possible, it became clear that patterns of neutral variability in genomes are affected by selection at linked sites, and that these patterns could advance our understanding of natural selection, and can be used to detect the action of selection in genomic regions, including selection much weaker than could be detected by direct measurements of the relative fitnesses of different genotypes. We outline the different types of processes that have been studied, in approximate order of their historical development.

A faster rate of adaptive evolution of X-linked genes compared with autosomal genes (the faster-X effect) can be caused by the fixation of recessive or partially recessive advantageous mutations. This effect should be largest for advantageous mutations that affect only male fitness, and least for mutations that affect only female fitness. We tested these predictions in Drosophila melanogaster by using coding and functionally significant noncoding sequences of genes with different levels of sex-biased expression. Consistent with theory, nonsynonymous substitutions in most male-biased and unbiased genes show faster adaptive evolution on the X. However, genes with very low recombination rates do not show such an effect, possibly as a consequence of Hill–Robertson interference. Contrary to expectation, there was a substantial faster-X effect for female-biased genes. After correcting for recombination rate differences, however, female-biased genes did not show a faster X-effect. Similar analyses of noncoding UTRs and long introns showed a faster-X effect for all groups of genes, other than introns of female-biased genes. Given the strong evidence that deleterious mutations are mostly recessive or partially recessive, we would expect a slower rate of evolution of X-linked genes for slightly deleterious mutations that become fixed by genetic drift. Surprisingly, we found little evidence for this after correcting for recombination rate, implying that weakly deleterious mutations are mostly close to being semidominant. This is consistent with evidence from polymorphism data, which we use to test how models of selection that assume semidominance with no sex-specific fitness effects may bias estimates of purifying selection.

A faster rate of adaptive evolution of X-linked genes compared with autosomal genes can be caused by the fixation of recessive or partially recessive advantageous mutations, due to the full expression of X-linked mutations in hemizygous males. Other processes, including recombination rate and mutation rate differences between X chromosomes and autosomes, may also cause faster evolution of X-linked genes. We review population genetics theory concerning the expected relative values of variability and rates of evolution of X-linked and autosomal DNA sequences. The theoretical predictions are compared with data from population genomic studies of several species of Drosophila. We conclude that there is evidence for adaptive faster-X evolution of several classes of functionally significant nucleotides. We also find evidence for potential differences in mutation rates between X-linked and autosomal genes, due to differences in mutational bias towards GC to AT mutations. Many aspects of the data are consistent with the male hemizygosity model, although not all possible confounding factors can be excluded.