Joint effects of genetic hitchhiking and background selection on neutral variation

Due to relatively high rates of strongly selected deleterious mutations, directional selection on favorable alleles (causing hitchhiking effects on linked neutral polymorphisms) is expected to occur while a deleterious mutation-selection balance is present in a population. We analyze this interaction of directional selection and background selection and study their combined effects on neutral variation, using a three-locus model in which each locus is subjected to either deleterious, favorable, or neutral mutations. Average heterozygosity is measured by simulations (1) at the stationary state under the assumption of recurrent hitchhiking events and (2) as a transient level after a single hitchhiking event. The simulation results are compared to theoretical predictions. It is shown that known analytical solutions describing the hitchhiking effect without background selection can be modified such that they accurately predict the joint effects of hitchhiking and background on linked, neutral variation. Generalization of these results to a more appropriate multilocus model (such that background selection can occur at multiple sites) suggests that, in regions of very low recombination rates, stationary levels of nucleotide diversity are primarily determined by hitchhiking, whereas in regions of high recombination, background selection is the dominant force. The implications of these results on the identification and estimation of the relevant parameters of the model are discussed.     

The effects of weak selection on neutral diversity at linked sites

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.     

Natural selection at linked sites in humans

Theoretical and empirical work indicates that patterns of neutral polymorphism can be affected by linked, selected mutations. Under background selection, deleterious mutations removed from a population by purifying selection cause a reduction in linked neutral diversity. Under genetic hitchhiking, the rise in frequency and fixation of beneficial mutations also reduces the level of linked neutral polymorphism. Here we review the evidence that levels of neutral polymorphism in humans are affected by selection at linked sites. We then discuss four approaches for distinguishing between background selection and genetic hitchhiking based on (i) the relationship between polymorphism level and recombination rate for neutral loci with high mutation rates, (ii) relative levels of variation on the X chromosome and the autosomes, (iii) the frequency distribution of neutral polymorphisms, and (iv) population-specific patterns of genetic variation. Although the evidence for selection at linked sites in humans is clear, current methods and data do not allow us to clearly assess the relative importance of background selection and genetic hitchhiking in humans. These results contrast with those obtained for Drosophila, where the signals of positive selection are stronger.     

Hitchhiking effect of a beneficial mutation spreading in a subdivided population

A central problem in population genetics is to detect and analyze positive natural selection by which beneficial mutations are driven to fixation. The hitchhiking effect of a rapidly spreading beneficial mutation, which results in local removal of standing genetic variation, allows such an analysis using DNA sequence polymorphism. However, the current mathematical theory that predicts the pattern of genetic hitchhiking relies on the assumption that a beneficial mutation increases to a high frequency in a single random-mating population, which is certainly violated in reality. Individuals in natural populations are distributed over a geographic space. The spread of a beneficial allele can be delayed by limited migration of individuals over the space and its hitchhiking effect can also be affected. To study this effect of geographic structure on genetic hitchhiking, we analyze a simple model of directional selection in a subdivided population. In contrast to previous studies on hitchhiking in subdivided populations, we mainly investigate the range of sufficiently high migration rates that would homogenize genetic variation at neutral loci. We provide a heuristic mathematical analysis that describes how the genealogical structure at a neutral locus linked to the locus under selection is expected to change in a population divided into two demes. Our results indicate that the overall strength of genetic hitchhiking--the degree to which expected heterozygosity decreases--is diminished by population subdivision, mainly because opportunity for the breakdown of hitchhiking by recombination increases as the spread of the beneficial mutation across demes is delayed when migration rate is much smaller than the strength of selection. Furthermore, the amount of genetic variation after a selective sweep is expected to be unequal over demes: a greater reduction in expected heterozygosity occurs in the subpopulation from which the beneficial mutation originates than in its neighboring subpopulations. This raises a possibility of detecting a "hidden" geographic structure of population by carefully analyzing the pattern of a selective sweep.     

The Hitchhiking Effect on the Site Frequency Spectrum of DNA Polymorphisms

The level of DNA sequence variation is reduced in regions of the Drosophila melanogaster genome where the rate of crossing over per physical distance is also reduced. This observation has been interpreted as support for the simple model of genetic hitchhiking, in which directional selection on rare variants, e.g., newly arising advantageous mutants, sweeps linked neutral alleles to fixation, thus eliminating polymorphisms near the selected site. However, the frequency spectra of segregating sites of several loci from some populations exhibiting reduced levels of nucleotide diversity and reduced numbers of segregating sites did not appear different from what would be expected under a neutral equilibrium model. Specifically, a skew toward an excess of rare sites was not observed in these samples, as measured by Tajima's D. Because this skew was predicted by a simple hitchhiking model, yet it had never been expressed quantitatively and compared directly to DNA polymorphism data, this paper investigates the hitchhiking effect on the site frequency spectrum, as measured by Tajima's D and several other statistics, using a computer simulation model based on the coalescent process and recurrent hitchhiking events. The results presented here demonstrate that under the simple hitchhiking model (1) the expected value of Tajima's D is large and negative (indicating a skew toward rare variants), (2) that Tajima's test has reasonable power to detect a skew in the frequency spectrum for parameters comparable to those from actual data sets, and (3) that the Tajima's Ds observed in several data sets are very unlikely to have been the result of simple hitchhiking. Consequently, the simple hitchhiking model is not a sufficient explanation for the DNA polymorphism at those loci exhibiting a decreased number of segregating sites yet not exhibiting a skew in the frequency spectrum.     

The hitchhiking effect on linkage disequilibrium between linked neutral loci

We analyzed a three-locus model of genetic hitchhiking with one locus experiencing positive directional selection and two partially linked neutral loci. Following the original hitchhiking approach by Maynard Smith and Haigh, our analysis is purely deterministic. In the first half of the selected phase after a favored mutation has entered the population, hitchhiking may lead to a strong increase of linkage disequilibrium (LD) between the two neutral sites if both are <0.1 s away from the selected site (where s is the selection coefficient). In the second half of the selected phase, the main effect of hitchhiking is to destroy LD. This occurs very quickly (before the end of the selected phase) when the selected site is between both neutral loci. This pattern cannot be attributed to the well-known variation-reducing effect of hitchhiking but is a consequence of secondary hitchhiking effects on the recombinants created in the selected phase. When the selected site is outside the neutral loci (which are, say, <0.1s apart), however, a fast decay of LD is observed only if the selected site is in the immediate neighborhood of one of the neutral sites (i.e., if the recombination rate r between the selected site and one of the neutral sites satisfies r<0.1 s). If the selected site is far away from the neutral sites (say, r > 0.3 s), the decay rate of LD approaches that of neutrality. Averaging over a uniform distribution of initial gamete frequencies shows that the expected LD at the end of the hitchhiking phase is driven toward zero, while the variance is increased when the selected site is well outside the two neutral sites. When the direction of LD is polarized with respect to the more common allele at each neutral site, hitchhiking creates more positive than negative linkage disequilibrium. Thus, hitchhiking may have a distinctively patterned LD-reducing effect, in particular near the target of selection.     

Variation after a selective sweep in a subdivided population

The effect of genetic hitchhiking on neutral variation is analyzed in subdivided populations with differentiated demes. After fixation of a favorable mutation, the consequences on particular subpopulations can be radically different. In the subpopulation where the mutation first appeared by mutation, variation at linked neutral loci is expected to be reduced, as predicted by the classical theory. However, the effect in the other subpopulations, where the mutation is introduced by migration, can be the opposite. This effect depends on the level of genetic differentiation of the subpopulations, the selective advantage of the mutation, the recombination frequency, and the population size, as stated by analytical derivations and computer simulations. The characteristic outcomes of the effect are three. First, the genomic region of reduced variation around the selected locus is smaller than that predicted in a panmictic population. Second, for more distant neutral loci, the amount of variation increases over the level they had before the hitchhiking event. Third, for these loci, the spectrum of gene frequencies is dominated by an excess of alleles at intermediate frequencies when compared with the neutral theory. At these loci, hitchhiking works like a system that takes variation from the between-subpopulation component and introduces it into the subpopulations. The mechanism can also operate in other systems in which the genetic variation is distributed in clusters with limited exchange of variation, such as chromosome arrangements or genomic regions closely linked to targets of balancing selection.     

The mean and variance of the number of segregating sites since the last hitchhiking event

 Tight linkage may cause a reduction of nucleotide diversity in a chromosomal region if an advantageous mutation appears in that region which is driven to fixation by directional selection. This process is usually called genetic hitchhiking. If selection is strong, the entire process takes place during a time period of length 2s ln (2N) that is very short relative to 2N generations [s is the selection coefficient of the advantageous mutation and N the effective diploid population size]. On the time scale of 2N generations, which is characteristic for neutral evolution, we may therefore call this process a hitchhiking event. Using coalescent methods, we analyzed a model in which a hitchhiking event occurred in a chromosomal region of zero-recombination in the past at time x. Such a hitchhiking “catastrophe” wipes out completely genetic variation that existed in a population before that time. Standing variation observed at present must therefore be due to mutations that have arisen since time point x. Assuming that all newly arising mutations are neutral, we derived expressions for the expectation, variance and also for the higher moments of the number of nucleotide sites segregating in a sample of n genes as a function of x. The result for the first moment is then used to estimate the time back to the last hitchhiking event based on DNA polymorphism data from Drosophila. Assuming that directional selection is the sole determinant of the level of genetic variation in the gene regions surveyed, we obtained estimates of x that were typically in the order of 0.1N generations. Received 14 May 1996; received in revised form 26 August 1996     

Selection at linked sites in the partial selfer Caenorhabditis elegans

Natural selection can produce a correlation between local recombination rates and levels of neutral DNA polymorphism as a consequence of genetic hitchhiking and background selection. Theory suggests that selection at linked sites should affect patterns of neutral variation in partially selfing populations more dramatically than in outcrossing populations. However, empirical investigations of selection at linked sites have focused primarily on outcrossing species. To assess the potential role of selection as a determinant of neutral polymorphism in the context of partial self-fertilization, we conducted a multivariate analysis of single-nucleotide polymorphism (SNP) density throughout the genome of the nematode Caenorhabditis elegans. We based the analysis on a published SNP data set and partitioned the genome into windows to calculate SNP densities, recombination rates, and gene densities across all six chromosomes. Our analyses identify a strong, positive correlation between recombination rate and neutral polymorphism (as estimated by noncoding SNP density) across the genome of C. elegans. Furthermore, we find that levels of neutral polymorphism are lower in gene-dense regions than in gene-poor regions in some analyses. Analyses incorporating local estimates of divergence between C. elegans and C. briggsae indicate that a mutational explanation alone is unlikely to explain the observed patterns. Consequently, we interpret these findings as evidence that natural selection shapes genome-wide patterns of neutral polymorphism in C. elegans. Our study provides the first demonstration of such an effect in a partially selfing animal. Explicit models of genetic hitchhiking and background selection can each adequately describe the relationship between recombination rate and SNP density, but only when they incorporate selfing rate. Clarification of the relative roles of genetic hitchhiking and background selection in C. elegans awaits the development of specific theoretical predictions that account for partial self-fertilization and biased sex ratios.     

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.     

Hitchhiking under positive Darwinian selection

Positive selection can be inferred from its effect on linked neutral variation. In the restrictive case when there is no recombination, all linked variation is removed. If recombination is present but rare, both deterministic and stochastic models of positive selection show that linked variation hitchhikes to either low or high frequencies. While the frequency distribution of variation can be influenced by a number of evolutionary processes, an excess of derived variants at high frequency is a unique pattern produced by hitchhiking (derived refers to the nonancestral state as determined from an outgroup). We adopt a statistic, H, to measure an excess of high compared to intermediate frequency variants. Only a few high-frequency variants are needed to detect hitchhiking since not many are expected under neutrality. This is of particular utility in regions of low recombination where there is not much variation and in regions of normal or high recombination, where the hitchhiking effect can be limited to a small (<1 kb) region. Application of the H test to published surveys of Drosophila variation reveals an excess of high frequency variants that are likely to have been influenced by positive selection.     

Detecting a local signature of genetic hitchhiking along a recombining chromosome

The theory of genetic hitchhiking predicts that the level of genetic variation is greatly reduced at the site of strong directional selection and increases as the recombinational distance from the site of selection increases. This characteristic pattern can be used to detect recent directional selection on the basis of DNA polymorphism data. However, the large variance of nucleotide diversity in samples of moderate size imposes difficulties in detecting such patterns. We investigated the patterns of genetic variation along a recombining chromosome by constructing ancestral recombination graphs that are modified to incorporate the effect of genetic hitchhiking. A statistical method is proposed to test the significance of a local reduction of variation and a skew of the frequency spectrum caused by a hitchhiking event. This method also allows us to estimate the strength and the location of directional selection from DNA sequence data.     

High DNA sequence diversity in pericentromeric genes of the plant Arabidopsis lyrata

Differences in neutral diversity at different loci are predicted to arise due to differences in mutation rates and from the "hitchhiking" effects of natural selection. Consistent with hitchhiking models, Drosophila melanogaster chromosome regions with very low recombination have unusually low nucleotide diversity. We compared levels of diversity from five pericentromeric regions with regions of normal recombination in Arabidopsis lyrata, an outcrossing close relative of the highly selfing A. thaliana. In contrast with the accepted theoretical prediction, and the pattern in Drosophila, we found generally high diversity in pericentromeric genes, which is consistent with the observation in A. thaliana. Our data rule out balancing selection in the pericentromeric regions, suggesting that hitchhiking is more strongly reducing diversity in the chromosome arms than the pericentromere regions.     

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.     

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.     

Analysis of a genetic hitchhiking model, and its application to DNA polymorphism data from Drosophila melanogaster

Begun and Aquadro have demonstrated that levels of nucleotide variation correlate with recombination rate among 20 gene regions from across the genome of Drosophila melanogaster. It has been suggested that this correlation results from genetic hitchhiking associated with the fixation of strongly selected mutants. The hitchhiking process can be described as a series of two-step events. The first step consists of a strongly selected substitution wiping out linked variation in a population; this is followed by a recovery period in which polymorphism can build up via neutral mutations and random genetic drift. Genetic hitchhiking has previously been modeled as a steady-state process driven by recurring selected substitutions. We show here that the characteristic parameter of this steady-state model is alpha v, the product of selection intensity (alpha = 2Ns) and the frequency of beneficial mutations v (where N is population size and s is the selective advantage of the favored allele). We also demonstrate that the steady-state model describes the hitchhiking process adequately, unless the recombination rate is very low. To estimate alpha v, we use the data of DNA sequence variation from 17 D. melanogaster loci from regions of intermediate to high recombination rates. We find that alpha v is likely to be > 1.3 x 10(-8). Additional data are needed to estimate this parameter more precisely. The estimation of alpha v is important, as this parameter determines the shape of the frequency distribution of strongly selected substitutions.      

Evidence for hitchhiking of deleterious mutations within the human genome

Deleterious mutations present a significant obstacle to adaptive evolution. Deleterious mutations can inhibit the spread of linked adaptive mutations through a population; conversely, adaptive substitutions can increase the frequency of linked deleterious mutations and even result in their fixation. To assess the impact of adaptive mutations on linked deleterious mutations, we examined the distribution of deleterious and neutral amino acid polymorphism in the human genome. Within genomic regions that show evidence of recent hitchhiking, we find fewer neutral but a similar number of deleterious SNPs compared to other genomic regions. The higher ratio of deleterious to neutral SNPs is consistent with simulated hitchhiking events and implies that positive selection eliminates some deleterious alleles and increases the frequency of others. The distribution of disease-associated alleles is also altered in hitchhiking regions. Disease alleles within hitchhiking regions have been associated with auto-immune disorders, metabolic diseases, cancers, and mental disorders. Our results suggest that positive selection has had a significant impact on deleterious polymorphism and may be partly responsible for the high frequency of certain human disease alleles.     

Regions of lower crossing over harbor more rare variants in African populations of Drosophila melanogaster

A correlation between diversity levels and rates of recombination is predicted both by models of positive selection, such as hitchhiking associated with the rapid fixation of advantageous mutations, and by models of purifying selection against strongly deleterious mutations (commonly referred to as "background selection"). With parameter values appropriate for Drosophila populations, only the first class of models predicts a marked skew in the frequency spectrum of linked neutral variants, relative to a neutral model. Here, we consider 29 loci scattered throughout the Drosophila melanogaster genome. We show that, in African populations, a summary of the frequency spectrum of polymorphic mutations is positively correlated with the meiotic rate of crossing over. This pattern is demonstrated to be unlikely under a model of background selection. Models of weakly deleterious selection are not expected to produce both the observed correlation and the extent to which nucleotide diversity is reduced in regions of low (but nonzero) recombination. Thus, of existing models, hitchhiking due to the recurrent fixation of advantageous variants is the most plausible explanation for the data.     

The ``hitchhiking Effect'''' Revisited

The number of selectively neutral polymorphic sites in a random sample of genes can be affected by ancestral selectively favored substitutions at linked loci. The degree to which this happens depends on when in the history of the sample the selected substitutions happen, the strength of selection and the amount of crossing over between the sampled locus and the loci at which the selected substitutions occur. This phenomenon is commonly called hitchhiking. Using the coalescent process for a random sample of genes from a selectively neutral locus that is linked to a locus at which selection is taking place, a stochastic, finite population model is developed that describes the steady state effect of hitchhiking on the distribution of the number of selectively neutral polymorphic sites in a random sample. A prediction of the model is that, in regions of low crossing over, strongly selected substitutions in the history of the sample can substantially reduce the number of polymorphic sites in a random sample of genes from that expected under a neutral model.     

Evidence for genetic hitchhiking effect associated with insecticide resistance in Aedes aegypti.

Information on genetic variation within and between populations is critical for understanding the evolutionary history of mosquito populations and disease epidemiology. Previous studies with Drosophila suggest that genetic variation of selectively neutral loci in a large fraction of genome may be constrained by fixation of advantageous mutations associated with hitchhiking effect. This study examined restriction fragment length polymorphisms of four natural Aedes aegypti mosquito populations from Trinidad and Tobago, at 16 loci. These populations have been subjected to organophosphate (OP) insecticide treatments for more than two decades, while dichlor-diphenyltrichlor (DDT) was the insecticide of choice prior to this period. We predicted that genes closely linked to the OP target loci would exhibit reduced genetic variation as a result of the hitchhiking effect associated with intensive OP insecticide selection. We also predicted that genetic variability of the genes conferring resistance to DDT and loci near the target site would be similar to other unlinked loci. As predicted, reduced genetic variation was found for loci in the general chromosomal region of a putative OP target site, and these loci generally exhibited larger F(ST) values than other random loci. In contrast, the gene conferring resistance to DDT and its linked loci show polymorphisms and genetic differentiation similar to other random loci. The reduced genetic variability and apparent gene deletion in some regions of chromosome 1 likely reflect the hitchhiking effect associated with OP insecticide selection.