Allele frequency distribution under recurrent selective sweeps

The allele frequency of a neutral variant in a population is pushed either upward or downward by directional selection on a linked beneficial mutation ("selective sweeps"). DNA sequences sampled after the fixation of the beneficial allele thus contain an excess of rare neutral alleles. This study investigates the allele frequency distribution under selective sweep models using analytic approximation and simulation. First, given a single selective sweep at a fixed time, I derive an expression for the sampling probabilities of neutral mutants. This solution can be used to estimate the time of the fixation of a beneficial allele from sequence data. Next, I obtain an approximation to mean allele frequencies under recurrent selective sweeps. Under recurrent sweeps, the frequency spectrum is skewed toward rare alleles. However, the excess of high-frequency derived alleles, previously shown to be a signature of single selective sweeps, disappears with recurrent sweeps. It is shown that, using this approximation and multilocus polymorphism data, genomewide parameters of directional selection can be estimated.     

Patterns of neutral diversity under general models of selective sweeps

Two major sources of stochasticity in the dynamics of neutral alleles result from resampling of finite populations (genetic drift) and the random genetic background of nearby selected alleles on which the neutral alleles are found (linked selection). There is now good evidence that linked selection plays an important role in shaping polymorphism levels in a number of species. One of the best-investigated models of linked selection is the recurrent full-sweep model, in which newly arisen selected alleles fix rapidly. However, the bulk of selected alleles that sweep into the population may not be destined for rapid fixation. Here we develop a general model of recurrent selective sweeps in a coalescent framework, one that generalizes the recurrent full-sweep model to the case where selected alleles do not sweep to fixation. We show that in a large population, only the initial rapid increase of a selected allele affects the genealogy at partially linked sites, which under fairly general assumptions are unaffected by the subsequent fate of the selected allele. We also apply the theory to a simple model to investigate the impact of recurrent partial sweeps on levels of neutral diversity and find that for a given reduction in diversity, the impact of recurrent partial sweeps on the frequency spectrum at neutral sites is determined primarily by the frequencies rapidly achieved by the selected alleles. Consequently, recurrent sweeps of selected alleles to low frequencies can have a profound effect on levels of diversity but can leave the frequency spectrum relatively unperturbed. In fact, the limiting coalescent model under a high rate of sweeps to low frequency is identical to the standard neutral model. The general model of selective sweeps we describe goes some way toward providing a more flexible framework to describe genomic patterns of diversity than is currently available.     

The Hill-Robertson effect and the evolution of recombination

In finite populations, genetic drift generates interference between selected loci, causing advantageous alleles to be found more often on different chromosomes than on the same chromosome, which reduces the rate of adaptation. This "Hill-Robertson effect" generates indirect selection to increase recombination rates. We present a new method to quantify the strength of this selection. Our model represents a new beneficial allele (A) entering a population as a single copy, while another beneficial allele (B) is sweeping at another locus. A third locus affects the recombination rate between selected loci. Using a branching process model, we calculate the probability distribution of the number of copies of A on the different genetic backgrounds, after it is established but while it is still rare. Then, we use a deterministic model to express the change in frequency of the recombination modifier, due to hitchhiking, as A goes to fixation. We show that this method can give good estimates of selection for recombination. Moreover, it shows that recombination is selected through two different effects: it increases the fixation probability of new alleles, and it accelerates selective sweeps. The relative importance of these two effects depends on the relative times of occurrence of the beneficial alleles.     

Reductions in genetic variation inDrosophila andE. coli caused by selection at linked sites

Selection at linked sites has important consequences for the properties of neutral variation and for tests of the predictions of the neutral theory of molecular evolution. We review the theory of the effect of adaptive gene substitutions on neutral variability at linked sites (hitchhiking or selective sweeps) and discuss theoretical results on the effect of selection against deleterious alleles on variation at linked sites (background selection). InDrosophila melanogaster there is a clear relation between the frequency of recombination in a given region of the chromosome and the amount of natural variability in that region. Attempts to predict this relation have given rise to models of selective sweeps and background selection. We describe possible methods of discriminating between these models, and also discuss the probable strong influence of selective sweeps on variation in largely nonrecombining genomes, with particular reference toEscherichia coll. Finally we present some unresolved questions and possible directions for future research.     

Hitchhiking of Deleterious Alleles and the Cost of Adaptation in Partially Selfing Species

Self-fertilization is generally seen to be disadvantageous in the long term. It increases genetic drift, which subsequently reduces polymorphism and the efficiency of selection, which also challenges adaptation. However, high selfing rates can increase the fixation probability of recessive beneficial mutations, but existing theory has generally not accounted for the effect of linked sites. Here, we analyze a model for the fixation probability of deleterious mutants that hitchhike with selective sweeps in diploid, partially selfing populations. Approximate analytical solutions show that, conditional on the sweep not being lost by drift, higher inbreeding rates increase the fixation probability of the deleterious allele, due to the resulting reduction in polymorphism and effective recombination. When extending the analysis to consider a distribution of deleterious alleles, as well as the average fitness increase after a sweep, we find that beneficial alleles generally need to be more recessive than the previously assumed dominance threshold (h < 1/2) for selfing to be beneficial from one-locus theory. Our results highlight that recombination aiding the efficiency of selection on multiple loci amplifies the fitness benefits of outcrossing over selfing, compared to results obtained from one-locus theory. This effect additionally increases the parameter range under which obligate outcrossing is beneficial over partial selfing.     

Soft sweeps: molecular population genetics of adaptation from standing genetic variation

A population can adapt to a rapid environmental change or habitat expansion in two ways. It may adapt either through new beneficial mutations that subsequently sweep through the population or by using alleles from the standing genetic variation. We use diffusion theory to calculate the probabilities for selective adaptations and find a large increase in the fixation probability for weak substitutions, if alleles originate from the standing genetic variation. We then determine the parameter regions where each scenario-standing variation vs. new mutations-is more likely. Adaptations from the standing genetic variation are favored if either the selective advantage is weak or the selection coefficient and the mutation rate are both high. Finally, we analyze the probability of "soft sweeps," where multiple copies of the selected allele contribute to a substitution, and discuss the consequences for the footprint of selection on linked neutral variation. We find that soft sweeps with weaker selective footprints are likely under both scenarios if the mutation rate and/or the selection coefficient is high.     

The effect of deleterious alleles on adaptation in asexual populations

We calculate the fixation probability of a beneficial allele that arises as the result of a unique mutation in an asexual population that is subject to recurrent deleterious mutation at rate U. Our analysis is an extension of previous works, which make a biologically restrictive assumption that selection against deleterious alleles is stronger than that on the beneficial allele of interest. We show that when selection against deleterious alleles is weak, beneficial alleles that confer a selective advantage that is small relative to U have greatly reduced probabilities of fixation. We discuss the consequences of this effect for the distribution of effects of alleles fixed during adaptation. We show that a selective sweep will increase the fixation probabilities of other beneficial mutations arising during some short interval afterward. We use the calculated fixation probabilities to estimate the expected rate of fitness improvement in an asexual population when beneficial alleles arise continually at some low rate proportional to U. We estimate the rate of mutation that is optimal in the sense that it maximizes this rate of fitness improvement. Again, this analysis relaxes the assumption made previously that selection against deleterious alleles is stronger than on beneficial alleles.     

Soft sweeps II--molecular population genetics of adaptation from recurrent mutation or migration

In the classical model of molecular adaptation, a favored allele derives from a single mutational origin. This ignores that beneficial alleles can enter a population recurrently, either by mutation or migration, during the selective phase. In this case, descendants of several of these independent origins may contribute to the fixation. As a consequence, all ancestral haplotypes that are linked to any of these copies will be retained in the population, affecting the pattern of a selective sweep on linked neutral variation. In this study, we use analytical calculations based on coalescent theory and computer simulations to analyze molecular adaptation from recurrent mutation or migration. Under the assumption of complete linkage, we derive a robust analytical approximation for the number of ancestral haplotypes and their distribution in a sample from the population. We find that so-called "soft sweeps," where multiple ancestral haplotypes appear in a sample, are likely for biologically realistic values of mutation or migration rates.     

The First Steps of Adaptation of Escherichia coli to the Gut Are Dominated by Soft Sweeps

The accumulation of adaptive mutations is essential for survival in novel environments. However, in clonal populations with a high mutational supply, the power of natural selection is expected to be limited. This is due to clonal interference - the competition of clones carrying different beneficial mutations - which leads to the loss of many small effect mutations and fixation of large effect ones. If interference is abundant, then mechanisms for horizontal transfer of genes, which allow the immediate combination of beneficial alleles in a single background, are expected to evolve. However, the relevance of interference in natural complex environments, such as the gut, is poorly known. To address this issue, we have developed an experimental system which allows to uncover the nature of the adaptive process as Escherichia coli adapts to the mouse gut. This system shows the invasion of beneficial mutations in the bacterial populations and demonstrates the pervasiveness of clonal interference. The observed dynamics of change in frequency of beneficial mutations are consistent with soft sweeps, where different adaptive mutations with similar phenotypes, arise repeatedly on different haplotypes without reaching fixation. Despite the complexity of this ecosystem, the genetic basis of the adaptive mutations revealed a striking parallelism in independently evolving populations. This was mainly characterized by the insertion of transposable elements in both coding and regulatory regions of a few genes. Interestingly, in most populations we observed a complete phenotypic sweep without loss of genetic variation. The intense clonal interference during adaptation to the gut environment, here demonstrated, may be important for our understanding of the levels of strain diversity of E. coli inhabiting the human gut microbiota and of its recombination rate.     

The Pattern of Neutral Molecular Variation under the Background Selection Model

Stochastic simulations of the infinite sites model were used to study the behavior of genetic diversity at a neutral locus in a genomic region without recombination, but subject to selection against deleterious alleles maintained by recurrent mutation (background selection). In large populations, the effect of background selection on the number of segregating sites approaches the effct on nucleotide site diversity, i.e., the reduction in genetic variability caused by background selection resembles that caused by a simple reduction in effective population size. We examined, by coalescence-based methods, the power of several tests for the departure from neutral expectation of the frequency spectra of alleles in samples from randomly mating populations (TAJIMA's, FU and LI's, and WATTERSON's tests). All of the tests have low power unless the selection against mutant alleles is extremely weak. In Drosophila, significant TAJIMA's tests are usually not obtained with empirical data sets from loci in genomic regions with restricted recombination frequencies and that exhibit low genetic diversity. This is consistent with the operation of background selection as opposed to selective sweeps. It remains to be decided whether background selection is sufficient to explain the observed extent of reduction in diversity in regions of restricted recombination.     

Genetic hitchhiking

Selection on one or more genes inevitably perturbs other genes, even when those genes have no direct effect on fitness. This article reviews the theory of such genetic hitchhiking, concentrating on effects on neutral loci. Maynard Smith and Haigh introduced the classical case where the perturbation is due to a single favourable mutation. This is contrasted with the apparently distinct effects of inherited variation in fitness due to loosely linked loci. A model of fluctuating selection is analysed which bridges these alternative treatments. When alleles sweep between extreme frequencies at a rate lambda, the rate of drift is increased by a factor (1 + E[1/pq]lambda/(2(2lambda + r))), where the recombination rate r is much smaller than the strength of selection. In spatially structured populations, the effects of any one substitution are weaker, and only cause a local increase in the frequency of a neutral allele. This increase depends primarily on the rate of recombination relative to selection (r/s), and more weakly, on the neighbourhood size, Nb = 4(pi rho sigma)2. Spatial subdivision may allow local selective sweeps to occur more frequently than is indicated by the overall rate of molecular evolution. However, it seems unlikely that such sweeps can be sufficiently frequent to increase significantly the drift of neutral alleles.     

Beneficial mutations, hitchhiking and the evolution of mutation rates in sexual populations

Natural selection acts in three ways on heritable variation for mutation rates. A modifier allele that increases the mutation rate is (i) disfavored due to association with deleterious mutations, but is also favored due to (ii) association with beneficial mutations and (iii) the reduced costs of lower fidelity replication. When a unique beneficial mutation arises and sweeps to fixation, genetic hitchhiking may cause a substantial change in the frequency of a modifier of mutation rate. In previous studies of the evolution of mutation rates in sexual populations, this effect has been underestimated. This article models the long-term effect of a series of such hitchhiking events and determines the resulting strength of indirect selection on the modifier. This is compared to the indirect selection due to deleterious mutations, when both types of mutations are randomly scattered over a given genetic map. Relative to an asexual population, increased levels of recombination reduce the effects of beneficial mutations more rapidly than those of deleterious mutations. However, the role of beneficial mutations in determining the evolutionarily stable mutation rate may still be significant if the function describing the cost of high-fidelity replication has a shallow gradient.     

Weak seed banks influence the signature and detectability of selective sweeps

Seed banking (or dormancy) is a widespread bet-hedging strategy, generating a form of population overlap, which decreases the magnitude of genetic drift. The methodological complexity of integrating this trait implies it is ignored when developing tools to detect selective sweeps. But, as dormancy lengthens the ancestral recombination graph (ARG), increasing times to fixation, it can change the genomic signatures of selection. To detect genes under positive selection in seed banking species it is important to (1) determine whether the efficacy of selection is affected, and (2) predict the patterns of nucleotide diversity at and around positively selected alleles. We present the first tree sequence-based simulation program integrating a weak seed bank to examine the dynamics and genomic footprints of beneficial alleles in a finite population. We find that seed banking does not affect the probability of fixation and confirm expectations of increased times to fixation. We also confirm earlier findings that, for strong selection, the times to fixation are not scaled by the inbreeding effective population size in the presence of seed banks, but are shorter than would be expected. As seed banking increases the effective recombination rate, footprints of sweeps appear narrower around the selected sites and due to the scaling of the ARG are detectable for longer periods of time. The developed simulation tool can be used to predict the footprints of selection and draw statistical inference of past evolutionary events in plants, invertebrates, or fungi with seed banks.     

Multiple signatures of positive selection downstream of notch on the X chromosome in Drosophila melanogaster

To identify genomic regions affected by the rapid fixation of beneficial mutations (selective sweeps), we performed a scan of microsatellite variability across the Notch locus region of Drosophila melanogaster. Nine microsatellites spanning 60 kb of the X chromosome were surveyed for variation in one African and three non-African populations of this species. The microsatellites identified an approximately 14-kb window for which we observed relatively low levels of variability and/or a skew in the frequency spectrum toward rare alleles, patterns predicted at regions linked to a selective sweep. DNA sequence polymorphism data were subsequently collected within this 14-kb region for three of the D. melanogaster populations. The sequence data strongly support the initial microsatellite findings; in the non-African populations there is evidence of a recent selective sweep downstream of the Notch locus near or within the open reading frames CG18508 and Fcp3C. In addition, we observe a significant McDonald-Kreitman test result suggesting too many amino acid fixations species wide, presumably due to positive selection, at the unannotated open reading frame CG18508. Thus, we observe within this small genomic region evidence for both recent (skew toward rare alleles in non-African populations) and recurring (amino acid evolution at CG18508) episodes of positive selection.     

The structure of linkage disequilibrium around a selective sweep

The fixation of advantageous mutations by natural selection has a profound impact on patterns of linked neutral variation. While it has long been appreciated that such selective sweeps influence the frequency spectrum of nearby polymorphism, it has only recently become clear that they also have dramatic effects on local linkage disequilibrium. By extending previous results on the relationship between genealogical structure and linkage disequilibrium, I obtain simple expressions for the influence of a selective sweep on patterns of allelic association. I show that sweeps can increase, decrease, or even eliminate linkage disequilibrium (LD) entirely depending on the relative position of the selected and neutral loci. I also show the importance of the age of the neutral mutations in predicting their degree of association and describe the consequences of such results for the interpretation of empirical data. In particular, I demonstrate that while selective sweeps can eliminate LD, they generate patterns of genetic variation very different from those expected from recombination hotspots.     

Recombination Speeds Adaptation by Reducing Competition between Beneficial Mutations in Populations of Escherichia coli

Identification of the selective forces contributing to the origin and maintenance of sex is a fundamental problem in biology. The Fisher–Muller model proposes that sex is advantageous because it allows beneficial mutations that arise in different lineages to recombine, thereby reducing clonal interference and speeding adaptation. I used the F plasmid to mediate recombination in the bacterium Escherichia coli and measured its effect on adaptation at high and low mutation rates. Recombination increased the rate of adaptation ∼3-fold more in the high mutation rate treatment, where beneficial mutations had to compete for fixation. Sequencing of candidate loci revealed the presence of a beneficial mutation in six high mutation rate lines. In the absence of recombination, this mutation took longer to fix and, over the course of its substitution, conferred a reduced competitive advantage, indicating interference between competing beneficial mutations. Together, these results provide experimental support for the Fisher–Muller model and demonstrate that plasmid-mediated gene transfer can accelerate bacterial adaptation.     

Clonal interference and the periodic selection of new beneficial mutations in Escherichia coli

The conventional model of adaptation in asexual populations implies sequential fixation of new beneficial mutations via rare selective sweeps that purge all variation and preserve the clonal genotype. However, in large populations multiple beneficial mutations may co-occur, causing competition among them, a phenomenon called "clonal interference." Clonal interference is thus expected to lead to longer fixation times and larger fitness effects of mutations that ultimately become fixed, as well as to a genetically more diverse population. Here, we study the significance of clonal interference in populations consisting of mixtures of differently marked wild-type and mutator strains of Escherichia coli that adapt to a minimal-glucose environment for 400 generations. We monitored marker frequencies during evolution and measured the competitive fitness of random clones from each marker state after evolution. The results demonstrate the presence of multiple beneficial mutations in these populations and slower and more erratic invasion of mutants than expected by the conventional model, showing the signature of clonal interference. We found that a consequence of clonal interference is that fitness estimates derived from invasion trajectories were less than half the magnitude of direct estimates from competition experiments, thus revealing fundamental problems with this fitness measure. These results force a reevaluation of the conventional model of periodic selection for asexual microbes.     

Palliating the impact of fixation of a major gene on the genetic variation of artificially selected polygenes

Selective sweeps of variation caused by fixation of major genes may have a dramatic impact on the genetic gain from background polygenic variation, particularly in the genome regions closely linked to the major gene. The response to selection can be restrained because of the reduced selection intensity and the reduced effective population size caused by the increase in frequency of the major gene. In the context of a selected population where fixation of a known major gene is desired, the question arises as to which is the optimal path of increase in frequency of the gene so that the selective sweep of variation resulting from its fixation is minimized. Using basic theoretical arguments we propose a frequency path that maximizes simultaneously the effective population size applicable to the selected background and the selection intensity on the polygenic variation by minimizing the average squared selection intensity on the major gene over generations up to a given fixation time. We also propose the use of mating between carriers and non-carriers of the major gene, in order to promote the effective recombination between the major gene and its linked polygenic background. Using a locus-based computer simulation assuming different degrees of linkage, we show that the path proposed is more effective than a similar path recently published, and that the combination of the selection and mating methods provides an efficient way to palliate the negative effects of a selective sweep.