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.     

Linkage disequilibria and the site frequency spectra in the su(s) and su(w(a)) regions of the Drosophila melanogaster X chromosome

Over the last decade, surveys of DNA sequence variation in natural populations of several Drosophila species and other taxa have established that polymorphism is reduced in genomic regions characterized by low rates of crossing over per physical length. Parallel studies have also established that divergence between species is not reduced in these same genomic regions, thus eliminating explanations that rely on a correlation between the rates of mutation and crossing over. Several theoretical models (directional hitchhiking, background selection, and random environment) have been proposed as population genetic explanations. In this study samples from an African population (n = 50) and a European population (n = 51) were surveyed at the su(s) (1955 bp) and su(w(a)) (3213 bp) loci for DNA sequence polymorphism, utilizing a stratified SSCP/DNA sequencing protocol. These loci are located near the telomere of the X chromosome, in a region of reduced crossing over per physical length, and exhibit a significant reduction in DNA sequence polymorphism. Unlike most previously surveyed, these loci reveal substantial skews toward rare site frequencies, consistent with the predictions of directional hitchhiking and random environment models and inconsistent with the general predictions of the background selection model (or neutral theory). No evidence for excess geographic differentiation at these loci is observed. Although linkage disequilibrium is observed between closely linked sites within these loci, many recombination events in the genealogy of the sampled alleles can be inferred and the genomic scale of linkage disequilibrium, measured in base pairs between sites, is the same as that observed for loci in regions of normal crossing over. We conclude that gene conversion must be high in these regions of low crossing over.     

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.     

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.     

The Effect of Adaptive Mutagenesis on Genetic Variation at a Linked, Neutral Locus

Based on recent studies in single-celled organisms, it has been argued that a fitness benefit associated with a mutation will increase the probability of that mutation occurring. This increase is independent of mutation rates at other loci and is called adaptive mutagenesis. We modeled the effect of adaptive mutagenesis on populations of haploid organisms with adaptive mutation rates ranging from 0 to 1 X 10(-5). Allele frequencies at the selected locus and a neutral linked locus were tracked. We also observed the amount of linkage disequilibrium during the selective sweep and the final heterozygosity after the sweep. The presence of adaptive mutagenesis increases the number of genetic backgrounds carrying the new fitter allele, making the outcomes more representative of the population before the selection. Therefore, more neutral genetic variation is preserved in simulations with adaptive mutagenesis than in those without it due to hitchhiking. Since adaptive mutagenesis is time-dependent, it can generate mutants when other mechanisms of mutation cannot. In addition, adaptive mutagenesis has the potential to confound both phylogeny construction and the detection of natural selection from patterns of nucleotide variation.     

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.     

The Effect of a Selected Locus on Linked Neutral Loci

The effects produced on linked neutral loci as a selected locus evolves towards its equilibrium value are considered. Significant effects on the neutral loci arise if the recombination fraction between the neutral and selected loci is smaller than the order of magnitude of the selective differences at the selected locus. The effect on gene frequencies at the neutral loci, that is, the hitchhiking effect, is determined, as well as the linkage disequilibrium generated by this hitchhiking effect. One of the more important findings is that significant disequilibrium can be generated between two neutral loci by the evolution of a linked selected locus. Consideration is given to the problem of determining how the effect of selection operating in natural populations can be detected, the question of the establishment of inversions in populations, and also to the nonequilibrium properties of populations.     

DNA sequence polymorphism and divergence at the erect wing and suppressor of sable loci of Drosophila melanogaster and D. simulans

Several evolutionary models of linked selection (e.g., genetic hitchhiking, background selection, and random environment) predict a reduction in polymorphism relative to divergence in genomic regions where the rate of crossing over per physical distance is restricted. We tested this prediction near the telomere of the Drosophila melanogaster and D. simulans X chromosome at two loci, erect wing (ewg) and suppressor of sable [su(s)]. Consistent with this prediction, polymorphism is reduced at both loci, while divergence is normal. The reduction is greater at ewg, the more distal of the two regions. Two models can be discriminated by comparing the observed site frequency spectra with those predicted by the models. The hitchhiking model predicts a skew toward rare variants in a sample, while the spectra under the background-selection model are similar to those of the neutral model of molecular evolution. Statistical tests of the fit to the predictions of these models require many sampled alleles and segregating sites. Thus we used SSCP and stratified DNA sequencing to cover a large number of randomly sampled alleles (approximately 50) from each of three populations. The result is a clear trend toward negative values of Tajima's D, indicating an excess of rare variants at ewg, the more distal of the two loci. One fixed difference among the populations and high FST values indicate strong population subdivision among the three populations at ewg. These results indicate genetic hitchhiking at ewg, in particular, geographically localized hitchhiking events within Africa. The reduction of polymorphism at su(s) combined with the excess of high-frequency variants in D. simulans is inconsistent with the hitchhiking and background-selection models.     

Hitchhiking and associative overdominance at a microsatellite locus

The possible effects of a selected locus on a closely linked microsatellite locus are discussed and analyzed in terms of coalescent theory and models of the mutation process. Background selection caused by recurrent deleterious mutations will reduce the variance of allele size at a microsatellite locus. The occasional substitution of advantageous alleles (genetic hitchhiking) will also reduce the variance, but a high mutation rate at a microsatellite locus can restore the variance relatively rapidly. Overdominance at the selected locus will increase the variance at the microsatellite locus and create partitioning of the variation in allele size among gametes carrying one or the other of the overdominant alleles. These results suggest that neutral microsatellite loci can provide indicators of selective processes at closely linked loci.      

GENETIC HITCHHIKING AND THE DYNAMIC BUILDUP OF GENOMIC DIVERGENCE DURING SPECIATION WITH GENE FLOW

A major issue in evolutionary biology is explaining patterns of differentiation observed in population genomic data, as divergence can be due to both direct selection on a locus and genetic hitchhiking. “Divergence hitchhiking” (DH) theory postulates that divergent selection on a locus reduces gene flow at physically linked sites, facilitating the formation of localized clusters of tightly linked, diverged loci. “Genome hitchhiking” (GH) theory emphasizes genome‐wide effects of divergent selection. Past theoretical investigations of DH and GH focused on static snapshots of divergence. Here, we used simulations assessing a variety of strengths of selection, migration rates, population sizes, and mutation rates to investigate the relative importance of direct selection, GH, and DH in facilitating the dynamic buildup of genomic divergence as speciation proceeds through time. When divergently selected mutations were limiting, GH promoted divergence, but DH had little measurable effect. When populations were small and divergently selected mutations were common, DH enhanced the accumulation of weakly selected mutations, but this contributed little to reproductive isolation. In general, GH promoted reproductive isolation by reducing effective migration rates below that due to direct selection alone, and was important for genome‐wide “congealing” or “coupling” of differentiation (F_ST) across loci as speciation progressed.     

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.     

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.     

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.      

THE DISTINCTIVE FOOTPRINTS OF LOCAL HITCHHIKING IN A VARIED ENVIRONMENT AND GLOBAL HITCHHIKING IN A SUBDIVIDED POPULATION

Loci with higher levels of population differentiation than the neutral expectation are traditionally interpreted as evidence of ongoing selection that varies in space. This article emphasizes an alternative explanation that has been largely overlooked to date: in species subdivided into large subpopulations, enhanced differentiation can also be the signature left by the fixation of an unconditionally favorable mutation on its chromosomal neighborhood. This is because the hitchhiking effect is expected to diminish as the favorable mutation spreads from the deme in which it originated to other demes. To discriminate among the two alternative scenarios one needs to investigate how genetic structure varies along the chromosomal region of the locus. Local hitchhiking is shown to generate a single sharp peak of differentiation centered on the adaptive polymorphism and the standard signature of a selective sweep only in those subpopulations in which the allele is favored. Global hitchhiking produces two domes of differentiation on either side of the fixed advantageous mutation and signatures of a selective sweep in every subpopulation, albeit of different magnitude. Investigating population differentiation around a locus that strongly differentiates two otherwise genetically similar populations of the marine mussel Mytilus edulis, plausible evidence for the global hitchhiking hypothesis has been obtained. Global hitchhiking is a neglected phenomenon that might prove to be important in species with large population sizes such as many marine invertebrates.     

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.     

Divergent selection and heterogeneous genomic divergence

Levels of genetic differentiation between populations can be highly variable across the genome, with divergent selection contributing to such heterogeneous genomic divergence. For example, loci under divergent selection and those tightly physically linked to them may exhibit stronger differentiation than neutral regions with weak or no linkage to such loci. Divergent selection can also increase genome‐wide neutral differentiation by reducing gene flow (e.g. by causing ecological speciation), thus promoting divergence via the stochastic effects of genetic drift. These consequences of divergent selection are being reported in recently accumulating studies that identify: (i) ‘outlier loci’ with higher levels of divergence than expected under neutrality, and (ii) a positive association between the degree of adaptive phenotypic divergence and levels of molecular genetic differentiation across population pairs [‘isolation by adaptation’ (IBA)]. The latter pattern arises because as adaptive divergence increases, gene flow is reduced (thereby promoting drift) and genetic hitchhiking increased. Here, we review and integrate these previously disconnected concepts and literatures. We find that studies generally report 5–10% of loci to be outliers. These selected regions were often dispersed across the genome, commonly exhibited replicated divergence across different population pairs, and could sometimes be associated with specific ecological variables. IBA was not infrequently observed, even at neutral loci putatively unlinked to those under divergent selection. Overall, we conclude that divergent selection makes diverse contributions to heterogeneous genomic divergence. Nonetheless, the number, size, and distribution of genomic regions affected by selection varied substantially among studies, leading us to discuss the potential role of divergent selection in the growth of regions of differentiation (i.e. genomic islands of divergence), a topic in need of future investigation.     

A regression-based approach to selection mapping

Selection mapping applies the population genetics theory of hitchhiking to the localization of genomic regions containing genes under selection. This approach predicts that neutral loci linked to genes under positive selection will have reduced diversity due to their shared history with a selected locus, and thus, genome scans of diversity levels can be used to identify regions containing selected loci. Most previous approaches to this problem ignore the spatial genomic pattern of diversity expected under selection. The regression-based approach advocated in this paper takes into account the expected pattern of decreasing genetic diversity with increased proximity to a selected locus. Simulated data are used to examine the patterns of diversity under different scenarios, in order to assess the power of a regression-based approach to the identification of regions under selection. Application of this method to both simulated and empirical data demonstrates its potential to detect selection. In contrast to some other methods, the regression approach described in this paper can be applied to any marker type. Results also suggest that this approach may give more precise estimates of the location of the selected locus than alternative methods, although the power is slightly lower in some cases.     

Genetic drift in an infinite population. The pseudohitchhiking model

Selected substitutions at one locus can induce stochastic dynamics that resemble genetic drift at a closely linked neutral locus. The pseudohitchhiking model is a one-locus model that approximates these effects and can be used to describe the major consequences of linked selection. As the changes in neutral allele frequencies when hitchhiking are rapid, diffusion theory is not appropriate for studying neutral dynamics. A stationary distribution and some results on substitution processes are presented that use the theory of continuous-time Markov processes with discontinuous sample paths. The coalescent of the pseudohitchhiking model is shown to have a random number of branches at each node, which leads to a frequency spectrum that is different from that of the equilibrium neutral model. If genetic draft, the name given to these induced stochastic effects, is a more important stochastic force than genetic drift, then a number of paradoxes that have plagued population genetics disappear.     

The coalescent process in models with selection, recombination and geographic subdivision

A population genetic model with a single locus at which balancing selection acts and many linked loci at which neutral mutations can occur is analysed using the coalescent approach. The model incorporates geographic subdivision with migration, as well as mutation, recombination, and genetic drift of neutral variation. It is found that geographic subdivision can affect genetic variation even with high rates of migration, providing that selection is strong enough to maintain different allele frequencies at the selected locus. Published sequence data from the alcohol dehydrogenase locus of Drosophila melanogaster are found to fit the proposed model slightly better than a similar model without subdivision.     

How closely does genetic diversity in finite populations conform to predictions of neutral theory? Large deficits in regions of low recombination

Levels of genetic diversity in finite populations are crucial in conservation and evolutionary biology. Genetic diversity is required for populations to evolve and its loss is related to inbreeding in random mating populations, and thus to reduced population fitness and increased extinction risk. Neutral theory is widely used to predict levels of genetic diversity. I review levels of genetic diversity in finite populations in relation to predictions of neutral theory. Positive associations between genetic diversity and population size, as predicted by neutral theory, are observed for microsatellites, allozymes, quantitative genetic variation and usually for mitochondrial DNA (mtDNA). However, there are frequently significant deviations from neutral theory owing to indirect selection at linked loci caused by balancing selection, selective sweeps and background selection. Substantially lower genetic diversity than predicted under neutrality was found for chromosomes with low recombination rates and high linkage disequilibrium (compared with 'normally' recombining chromosomes within species and adjusted for different copy numbers and mutation rates), including W (median 100% lower) and Y (89% lower) chromosomes, dot fourth chromosomes in Drosophila (94% lower) and mtDNA (67% lower). Further, microsatellite genetic and allelic diversity were lost at 12 and 33% faster rates than expected in populations adapting to captivity, owing to widespread selective sweeps. Overall, neither neutral theory nor most versions of the genetic draft hypothesis are compatible with all empirical results.