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.     

Selective sweeps in the presence of interference among partially linked loci

Recurrent directional selection on a partially recombining chromosome may cause a substantial reduction of standing genetic variation in natural populations. Previous studies of this effect, commonly called selective sweeps, assumed that at most one beneficial allele is on the way to fixation at a given time. However, for a high rate of selected substitutions and a low recombination rate, this assumption can easily be violated. We investigated this problem using full-forward simulations and analytical approximations. We found that interference between linked beneficial alleles causes a reduction of their fixation probabilities. The hitchhiking effect on linked neutral variation for a given substitution also slightly decreases due to interference. As a result, the strength of recurrent selective sweeps is weakened. However, this effect is significant only in chromosomal regions of relatively low recombination rates where the level of variation is greatly reduced. Therefore, previous results on recurrent selective sweeps although derived for a restricted parameter range are still valid. Analytical approximations are obtained for the case of complete linkage for which interference between competing beneficial alleles is maximal.     

The signature of positive selection at randomly chosen loci

In Drosophila and humans, there are accumulating examples of loci with a significant excess of high-frequency-derived alleles or high levels of linkage disequilibrium, relative to a neutral model of a random-mating population of constant size. These are features expected after a recent selective sweep. Their prevalence suggests that positive directional selection may be widespread in both species. However, as I show here, these features do not persist long after the sweep ends: The high-frequency alleles drift to fixation and no longer contribute to polymorphism, while linkage disequilibrium is broken down by recombination. As a result, loci chosen without independent evidence of recent selection are not expected to exhibit either of these features, even if they have been affected by numerous sweeps in their genealogical history. How then can we explain the patterns in the data? One possibility is population structure, with unequal sampling from different subpopulations. Alternatively, positive selection may not operate as is commonly modeled. In particular, the rate of fixation of advantageous mutations may have increased in the recent past.     

Hitchhiking both ways: effect of two interfering selective sweeps on linked neutral variation

The neutral polymorphism pattern in the vicinity of a selective sweep can be altered by both stochastic and deterministic factors. Here, we focus on the impact of another selective sweep in the region of influence of a first one. We study the signature left on neutral polymorphism by positive selection at two closely linked loci, when both beneficial mutations reach fixation. We show that, depending on the timing of selective sweeps and on their selection coefficients, the two hitchhiking effects can interfere with each other, leading to less reduction in heterozygosity than a single selective sweep of the same magnitude and more importantly to an excess of intermediate-frequency variants relative to neutrality under some parameter values. This pattern can be sustained and potentially alter the detection of positive selection, including by provoking spurious detection of balancing selection. In situations where positive selection is suspected a priori at several closely linked loci, the polymorphism pattern in the region may also be informative about their selective histories.     

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.     

Selective sweeps of mitochondrial DNA can drive the evolution of uniparental inheritance

Although the uniparental (or maternal) inheritance of mitochondrial DNA (mtDNA) is widespread, the reasons for its evolution remain unclear. Two main hypotheses have been proposed: selection against individuals containing different mtDNAs (heteroplasmy) and selection against “selfish” mtDNA mutations. Recently, uniparental inheritance was shown to promote adaptive evolution in mtDNA, potentially providing a third hypothesis for its evolution. Here, we explore this hypothesis theoretically and ask if the accumulation of beneficial mutations provides a sufficient fitness advantage for uniparental inheritance to invade a population in which mtDNA is inherited biparentally. In a deterministic model, uniparental inheritance increases in frequency but cannot replace biparental inheritance if only a single beneficial mtDNA mutation sweeps through the population. When we allow successive selective sweeps of mtDNA, however, uniparental inheritance can replace biparental inheritance. Using a stochastic model, we show that a combination of selection and drift facilitates the fixation of uniparental inheritance (compared to a neutral trait) when there is only a single selective mtDNA sweep. When we consider multiple mtDNA sweeps in a stochastic model, uniparental inheritance becomes even more likely to replace biparental inheritance. Our findings thus suggest that selective sweeps of beneficial mtDNA haplotypes can drive the evolution of uniparental inheritance.     

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 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.     

A Coalescent Model for a Sweep of a Unique Standing Variant

The use of genetic polymorphism data to understand the dynamics of adaptation and identify the loci that are involved has become a major pursuit of modern evolutionary genetics. In addition to the classical “hard sweep” hitchhiking model, recent research has drawn attention to the fact that the dynamics of adaptation can play out in a variety of different ways and that the specific signatures left behind in population genetic data may depend somewhat strongly on these dynamics. One particular model for which a large number of empirical examples are already known is that in which a single derived mutation arises and drifts to some low frequency before an environmental change causes the allele to become beneficial and sweeps to fixation. Here, we pursue an analytical investigation of this model, bolstered and extended via simulation study. We use coalescent theory to develop an analytical approximation for the effect of a sweep from standing variation on the genealogy at the locus of the selected allele and sites tightly linked to it. We show that the distribution of haplotypes that the selected allele is present on at the time of the environmental change can be approximated by considering recombinant haplotypes as alleles in the infinite-alleles model. We show that this approximation can be leveraged to make accurate predictions regarding patterns of genetic polymorphism following such a sweep. We then use simulations to highlight which sources of haplotypic information are likely to be most useful in distinguishing this model from neutrality, as well as from other sweep models, such as the classic hard sweep and multiple-mutation soft sweeps. We find that in general, adaptation from a unique standing variant will likely be difficult to detect on the basis of genetic polymorphism data from a single population time point alone, and when it can be detected, it will be difficult to distinguish from other varieties of selective sweeps. Samples from multiple populations and/or time points have the potential to ease this difficulty.     

The signature of positive selection on standing genetic variation

Considerable interest is focused on the use of polymorphism data to identify regions of the genome that underlie recent adaptations. These searches are guided by a simple model of positive selection, in which a mutation is favored as soon as it arises. This assumption may not be realistic, as environmental changes and range expansions may lead previously neutral or deleterious alleles to become beneficial. We examine what effect this mode of selection has on patterns of variation at linked neutral sites by implementing a new coalescent model of positive directional selection on standing variation. In this model, a neutral allele arises and drifts in the population, then at frequency f becomes beneficial, and eventually reaches fixation. Depending on the value of f, this scenario can lead to a large variance in allele frequency spectra and in levels of linkage disequilibrium at linked, neutral sites. In particular, for intermediate f, the beneficial substitution often leads to a loss of rare alleles--a pattern that differs markedly from the signature of directional selection currently relied on by researchers. These findings highlight the importance of an accurate characterization of the effects of positive selection, if we are to reliably identify recent adaptations from polymorphism data.     

Approximate genealogies under genetic hitchhiking

The rapid fixation of an advantageous allele leads to a reduction in linked neutral variation around the target of selection. The genealogy at a neutral locus in such a selective sweep can be simulated by first generating a random path of the advantageous allele's frequency and then a structured coalescent in this background. Usually the frequency path is approximated by a logistic growth curve. We discuss an alternative method that approximates the genealogy by a random binary splitting tree, a so-called Yule tree that does not require first constructing a frequency path. Compared to the coalescent in a logistic background, this method gives a slightly better approximation for identity by descent during the selective phase and a much better approximation for the number of lineages that stem from the founder of the selective sweep. In applications such as the approximation of the distribution of Tajima's D, the two approximation methods perform equally well. For relevant parameter ranges, the Yule approximation is faster.     

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.     

Linkage disequilibrium as a signature of selective sweeps

The hitchhiking effect of a beneficial mutation, or a selective sweep, generates a unique distribution of allele frequencies and spatial distribution of polymorphic sites. A composite-likelihood test was previously designed to detect these signatures of a selective sweep, solely on the basis of the spatial distribution and marginal allele frequencies of polymorphisms. As an excess of linkage disequilibrium (LD) is also known to be a strong signature of a selective sweep, we investigate how much statistical power is increased by the inclusion of information regarding LD. The expected pattern of LD is predicted by a genealogical approach. Both theory and simulation suggest that strong LD is generated in narrow regions at both sides of the location of beneficial mutation. However, a lack of LD is expected across the two sides. We explore various ways to detect this signature of selective sweeps by statistical tests. A new composite-likelihood method is proposed to incorporate information regarding LD. This method enables us to detect selective sweeps and estimate the parameters of the selection model better than the previous composite-likelihood method that does not take LD into account. However, the improvement made by including LD is rather small, suggesting that most of the relevant information regarding selective sweeps is captured by the spatial distribution and marginal allele frequencies of polymorphisms.     

Genetic profile of cosmopolitan populations: effects of hidden subdivision

Natural populations of many organisms exhibit excess of rare alleles in comparison with the predictions of the neutral mutation hypothesis. It has been shown before that either a population bottleneck or the presence of slightly deleterious mutations can explain this phenomenon. A third explanation is presented in this work, showing that hidden subdivision within a population can also lead to an excess of rare alleles in the total population when the expectations of the neutral model are based on the allele frequency profile of the entire population data. With two examples (mitochondrial DNA-morph distribution and isozyme allele frequency distributions), it is shown that most cosmopolitan human populations exhibit excess of rare as well as total allele counts, when these are compared with the expectations of the neutral mutation hypothesis. The mitochondrial data demonstrate that such excesses can be detected from genetic variation at a single locus as well, and this is not due to stochastic error of allele frequency distributions. Contrast of the present observations with the allele frequency profiles in agglomerated tribal populations from South and Central America shows that even when the neutral expectations hold for individual subpopulations, if all subpopulations are grouped into a single population, the pooled data exhibit an excess of total number of alleles that is mainly due to the excess of rare alleles. Therefore, a primary cause of the excess number of rare alleles could be the hidden subdivision, and the magnitude of the excess indicates the extent of substructuring. The two components of hidden subdivision are: 1) Number of subpopulations, and 2) the average genetic distance among them. The implications of this observation in estimating mutation rate are discussed indicating the difficulties of comparing mutation rates from different population surveys.     

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.     

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.     

Origin, fate, and architecture of ecologically relevant genetic variation

Recent advances in molecular genetics combined with field manipulations are yielding new insight into the origin, evolutionary fate, and genetic architecture of phenotypic variation in natural plant populations, with two surprising implications for the evolution of plant genomes. First, genetic loci exhibiting antagonistic pleiotropy across natural environments appear rare relative to loci that are adaptive in one or more environments and neutral elsewhere. These 'conditionally neutral' alleles should sweep to fixation when they arise, yet genome comparisons find little evidence for such selective sweeps. Second, genes under biotic selection tend to be of larger effect than genes under abiotic selection. Recent theory suggests this may be a consequence of high gene flow among populations under selection for local adaptation.