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.     

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.     

The influence of gene conversion on linkage disequilibrium around a selective sweep

In a 2007 article, McVean studied the effect of recombination on linkage disequilibrium (LD) between two neutral loci located near a third locus that has undergone a selective sweep. The results demonstrated that two loci on the same side of a selected locus might show substantial LD, whereas the expected LD for two loci on opposite sides of a selected locus is zero. In this article, we extend McVean's model to include gene conversion. We show that one of the conclusions is strongly affected by gene conversion: when gene conversion is present, there may be substantial LD between two loci on opposite sides of a selective sweep.     

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.     

Adapt globally, act locally: the effect of selective sweeps on bacterial sequence diversity.

Previous studies have shown that genetic exchange in bacteria is too rare to prevent neutral sequence divergence between ecological populations. That is, despite genetic exchange, each population should diverge into its own DNA sequence-similarity cluster. In those studies, each selective sweep was limited to acting within a single ecological population. Here we postulate the existence of globally adaptive mutations, which may confer a selective advantage to all ecological populations constituting a metapopulation. Such adaptations cause global selective sweeps, which purge the divergence both within and between populations. We found that the effect of recurrent global selective sweeps on neutral sequence divergence is highly dependent on the mechanism of genetic exchange. Global selective sweeps can prevent populations from reaching high levels of neutral sequence divergence, but they cannot cause two populations to become identical in neutral sequence characters. The model supports the earlier conclusion that each ecological population of bacteria should form its own distinct DNA sequence-similarity cluster.     

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.     

Evolution of the ancestral recombination graph along the genome in case of selective sweep

We consider the genome of a sample of n individuals taken at the end of a selective sweep, which is the fixation of an advantageous allele in the population. When the selective advantage is high, the genealogy at a locus under selective sweep can be approximated by a comb with n teeth. However, because of recombinations during the selective sweep, the hitchhiking effect decreases as the distance from the selected site increases, so that far from this locus, the tree can be approximated by a Kingman coalescent tree, as in the neutral case. We first give the distribution of the tree at a given locus. Then we focus on the evolution of this tree along the genome. Since this tree-valued process is not Markovian, we study the evolution of the Ancestral Recombination Graph along the genome in case of selective sweep.     

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.     

Nonadaptive explanations for signatures of partial selective sweeps in Drosophila

A beneficial mutation that has nearly but not yet fixed in a population produces a characteristic haplotype configuration, called a partial selective sweep. Whether nonadaptive processes might generate similar haplotype configurations has not been extensively explored. Here, we consider 5 population genetic data sets taken from regions flanking high-frequency transposable elements in North American strains of Drosophila melanogaster, each of which appears to be consistent with the expectations of a partial selective sweep. We use coalescent simulations to explore whether incorporation of the species' demographic history, purifying selection against the element, or suppression of recombination caused by the element could generate putatively adaptive haplotype configurations. Whereas most of the data sets would be rejected as nonneutral under the standard neutral null model, only the data set for which there is strong external evidence in support of an adaptive transposition appears to be nonneutral under the more complex null model and in particular when demography is taken into account. High-frequency, derived mutations from a recently bottlenecked population, such as we study here, are of great interest to evolutionary genetics in the context of scans for adaptive events; we discuss the broader implications of our findings in this context.     

Pinpointing a selective sweep to the chimpanzee MHC class I region by comparative genomics

Chimpanzees experienced a reduction of the allelic repertoire at the major histocompatibility complex (MHC) class I A and B loci, which may have been caused by a retrovirus belonging to the simian immunodeficiency virus (SIV) family. Extended MHC haplotypes were defined in a pedigreed chimpanzee colony. Comparison of genetic variation at microsatellite markers mapping inside and outside the Mhc region was carried out in humans and chimpanzees to investigate the genomic extent of the repertoire reduction. Multilocus demographic analyses underscored that chimpanzees indeed experienced a selective sweep that mainly targeted the chromosomal segment carrying the Mhc class I region. Probably due to genetic linkage, the sweep also affected other polymorphic loci, mapping in the close vicinity of the Mhc class I region genes. Nevertheless, although the allelic repertoire at particular Mhc class I and II loci appears to be limited, naturally occurring recombination events allowed the establishment of haplotype diversity after the sweep. However, recombination did not have sufficient time to erase the signal of the selective sweep.     

The effect of recurrent mutation on the linkage disequilibrium under a selective sweep

A selective sweep describes the reduction of diversity due to strong positive selection. If the mutation rate to a selectively beneficial allele is sufficiently high, Pennings and Hermisson (Mol Biol Evol 23(5):1076–1084, 2006a) have shown, that it becomes likely, that a selective sweep is caused by several individuals. Such an event is called a soft sweep and the complementary event of a single origin of the beneficial allele, the classical case, a hard sweep. We give analytical expressions for the linkage disequilibrium (LD) between two neutral loci linked to the selected locus, depending on the recurrent mutation to the beneficial allele, measured by D and ${\widehat{\sigma_D^2}}$ , a quantity introduced by Ohta and Kimura (Genetics 63(1):229–238, 1969), and conclude that the LD-pattern of a soft sweep differs substantially from that of a hard sweep due to haplotype structure. The analytical results are compared with simulations.     

Selective sweep at the Drosophila melanogaster Suppressor of Hairless locus and its association with the In(2L)t inversion polymorphism.

The hitchhiking model of population genetics predicts that an allele favored by Darwinian selection can replace haplotypes from the same locus previously established at a neutral mutation-drift equilibrium. This process, known as "selective sweep," was studied by comparing molecular variation between the polymorphic In(2L)t inversion and the standard chromosome. Sequence variation was recorded at the Suppressor of Hairless (Su[H]) gene in an African population of Drosophila melanogaster. We found 47 nucleotide polymorphisms among 20 sequences of 1.2 kb. Neutrality tests were nonsignificant at the nucleotide level. However, these sites were strongly associated, because 290 out of 741 observed pairwise combinations between them were in significant linkage disequilibrium. We found only seven haplotypes, two occurring in the 9 In(2L)t chromosomes, and five in the 11 standard chromosomes, with no shared haplotype. Two haplotypes, one in each chromosome arrangement, made up two-thirds of the sample. This low haplotype diversity departed from neutrality in a haplotype test. This pattern supports a selective sweep hypothesis for the Su(H) chromosome region.     

The effect on neutral gene flow of selection at a linked locus

The effect on gene flow at a neutral locus of a selective cline at a linked locus is investigated. A diffusion approximation for a two-locus island model is derived in which only one locus is subject to selection. The moments of the stationary distribution are obtained and compared to the corresponding moments from a one-locus, neutral island model. This comparison yields an effective migration rate. The effective migration rate is always less than the actual migration rate, but this effect is seen to be small for weak selection and loose linkage in the case of adult migration. The importance of selection at linked loci to the question of genetic differentiation in a subdivided population is discussed.     

Evidence for a selective sweep in the wapl region of Drosophila melanogaster

A scan of the X chromosome of a European Drosophila melanogaster population revealed evidence for the recent action of positive directional selection at individual loci. In this study we analyze one such region that showed no polymorphism in the genome scan (located in cytological division 2C10-2E1). We detect a 60.5-kb stretch of DNA encompassing the genes ph-d, ph-p, CG3835, bcn92, Pgd, wapl, and Cyp4d1, which almost completely lacks variation in the European sample. Loci flanking this region show a skewed frequency spectrum at segregating sites, strong haplotype structure, and high levels of linkage disequilibrium. Neutrality tests reveal that these data are unlikely under both the neutral equilibrium model and the simple bottleneck scenarios. In contrast, newly developed maximum-likelihood ratio tests suggest that strong selection has acted recently on the region under investigation, causing a selective sweep. Evidence that this sweep may have originated in an ancestral population in Africa is presented.     

Conditional gene genealogies under strong purifying selection

The ancestral selection graph, conditioned on the allelic types in the sample, is used to obtain a limiting gene genealogical process under strong selection. In an equilibrium, two-allele system with strong selection, neutral gene genealogies are predicted for random samples and for samples containing at most one unfavorable allele. Samples containing more than one unfavorable allele have gene genealogies that differ greatly from neutral predictions. However, they are related to neutral gene genealogies via the well-known Ewens sampling formula. Simulations show rapid convergence to limiting analytical predictions as the strength of selection increases. These results extend the idea of a soft selective sweep to deleterious alleles and have implications for the interpretation of polymorphism among disease-causing alleles in humans.     

Selective sweep at a quantitative trait locus in the presence of background genetic variation

We model selection at a locus affecting a quantitative trait (QTL) in the presence of genetic variance due to other loci. The dynamics at the QTL are related to the initial genotypic value and to the background genetic variance of the trait, assuming that background genetic values are normally distributed, under three different forms of selection on the trait. Approximate dynamics are derived under the assumption of small mutation effect. For similar strengths of selection on the trait (i.e, gradient of directional selection beta) the way background variation affects the dynamics at the QTL critically depends on the shape of the fitness function. It generally causes the strength of selection on the QTL to decrease with time. The resulting neutral heterozygosity pattern resembles that of a selective sweep with a constant selection coefficient corresponding to the early conditions. The signature of selection may also be blurred by mutation and recombination in the later part of the sweep. We also study the race between the QTL and its genetic background toward a new optimum and find the conditions for a complete sweep. Overall, our results suggest that phenotypic traits exhibiting clear-cut molecular signatures of selection may represent a biased subset of all adaptive traits.     

Molecular Population Genetics of Sex Determination Genes: The Transformer Gene of Drosophila Melanogaster

The transformer locus (tra) produces an RNA processing protein that alternatively splices the doublesex pre-mRNA in the sex determination hierarchy of Drosophila melanogaster. Comparisons of the tra coding region among Drosophila species have revealed an unusually high degree of divergence in synonymous and nonsynonymous sites. In this study, we tested the hypothesis that the tra gene will be polymorphic in synonymous and nonsynonymous sites within species by investigating nucleotide sequence variation in eleven tra alleles within D. melanogaster. Of the 1063 nucleotides examined, two synonymous sites were polymorphic and no amino acid variation was detected. Three statistical tests were used to detect departures from an equilibrium neutral model. Two tests failed to reject a neutral model of molecular evolution because of low statisitical power associated with low levels of genetic variation (Tajima/Fu and Li). The Hudson, Kreitman, and Aguade test rejected a neutral model when the tra region was compared to the 5'-flanking region of alcohol dehydrogenase (Adh). The lack of variability in the tra gene is consistent with a recent selective sweep of a beneficial allele in or near the tra locus.     

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.