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.     

Hitchhiking: A Comparison of Linkage and Partial Selfing

Genetic hitchhiking occurs when alleles at unselected loci are changed in frequency because of an association with alleles at a selected locus. This association may be mediated either by linkage or partial selfing (inbreeding) and can affect the gene frequency and gametic disequilibrium at the neutral loci. Hitchhiking from partial selfing (unlinked loci) occurs more quickly than linkage hitchhiking and generally has a greater effect. In addition, partial-selfing hitchhiking can cause increases or changes in sign in gametic disequilibrium between neutral loci. The effects of the two types of hitchhiking with different levels of dominance, zygotic frequencies and number of selected loci are also examined. The general conditions for linkage and partial-selfing hitchhiking are outlined and the implications of hitchhiking are discussed for marker or electrophoretic loci.     

Rates of decay of linkage disequilibrium under two-locus models of selection

The effect of selection and linkage on the decay of linkage disequilibrium, D, is investigated for a hierarchy of two-locus models. The method of analysis rests upon a qualitative classification of the dynamic of D under selection relative to the neutral dynamic. To eliminate the confounding effects of gene frequency change, the behavior of D is first studied with gene frequencies fixed at their invariant values. Second, the results are extended to certain special situations where gene frequencies are changing simultaneously.A wide variety of selection regimes can cause an acceleration of the rate of decay of D relative to the neutral rate. Specifically, the asymptotic rate of decay is always faster than the neutral rate in the neighborhood of a stable equilibrium point, when viabilities are additive or only one locus is selected. This is not necessarily the case for models in which there is nonzero additive epistasis. With multiplicative viabilities, decay is always accelerated near a stable boundary equilibrium, but decay is only faster near the stable central equilibrium (with = 0) if linkage is sufficiently loose. In the symmetric viability model, decay may even be retarded near a stable boundary equilibrium. Decay is only accelerated near a stable corner equilibrium when the double homozygote is more fit than the double heterozygotes. Decay near a stable edge equilibrium may be retarded if there is loose linkage. With symmetric viabilities there is usually an acceleration of the decay process for gene frequencies near 1/2 when the central equilibrium (with = 0) is stable. This is always the case when the sign of the epistasis is negative or zero.Conversely, the decay ofD is retarded in the neighborhood of a stable equilibrium in the multiplicative and symmetric viability models if any of the conditions above are violated. Near an unstable equilibrium of any of the models considered,D may either increase or decay at a rate slower than, equal to, or faster than the neutral rate. These analytic results are supplemented by numerical studies of the symmetric viability model.     

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 dynamics of interlocus associations in the three-locus hitchhiking model

The hitchhiking effects of a selected locus upon the dynamics of the pairwise association,D _nn between two neutral loci is examined analytically for the special case where at least one of the neutral loci is in linkage equilibrium with the selected locus. The results apply approximately whenever the product of the pairwise associations between the selected locus and each neutral locus is negligible with respect to the three-way linkage disequilibrium. It is shown that precisely four broad classes of trajectories are possible, whether the selected locus is between (nsn) or to one side (snn) of the neutral loci, and whatever the mode of selection operating.D _nn may: (1) decay rapidly to zero, at a rate faster in each generation than that expected for two isolated neutral loci; (2) monotonically decay to zero at a rate which is slower in every generation than under the usual neutral regime; (3) increase initially and/or in intermediate periods before eventually slowly decaying to zero; or (4) exhibit type 1 behavior in the first segment of the trajectory and either type 2 or 3 behavior in the subsequent generations, with the transition marked by a change in sign. The nature of a given trajectory is largely determined by the direction of gene frequency change at the selected locus, and the initial signs of bothD _nn and the three-way linkage disequilibrium.The single most important consequence of these results is that there is no simple relation between the amount of pairwise association between two neutral markers and the recombination fraction between them. Several factors influencing the magnitude of the hitchhiking effect are also examined. It is shown that, all else being equal, the greater the three-way linkage disequilibrium, the greater the departure ofD _nn from the expected neutral dynamic. Increased recombination among the loci reduces the hitchhiking effect onD _nn . The dependence of the behavior upon the exact position of the selected locus is also determined both within and betweennsn andsnn chromosomal systems. An interesting discovery is that given equivalentnsn andsnn systems, with each having the same recombination between their two neutral loci,D _nn will deviate more from the standard neutral dynamic in thesnn system if its selected locus is sufficiently tightly linked to the neutral loci.     

Perturbation-Reperturbation Test of Selection Vs. Hitchhiking of the Two Major Alleles of Esterase-5 in Drosophila Pseudoobscura

A perturbation-reperturbation tests selective neutrality of 100/100/100/100/100 and 106/100/100/100/100, the two most common alleles at the highly polymorphic X-linked locus Esterase-5 in Drosophila pseudoobscura. A total of 22 replicate populations are set up in cages, 11 start at a high frequency of 76% (U) and 11 at a low frequency of 21% (N) of the 106 allele. Allele frequencies change directionally and decrease in both U and N populations as groups and reach equilibria of 60 and 14%, respectively, after 200-300 days. These changes suggest natural selection. A hypothesis of balancing selection accounts for the pattern and predicts a dynamic equilibrium. A rival neutral hypothesis accounts for the pattern equally well by postulating hitchhiking and breakup of linkage leaving the Est-5 variants to drift at neutral equilibria. A reperturbation of allele frequencies in each population, creating 22 additional reperturbed populations EN and EU, with the original populations as controls, directly addresses the question of balancing selection or hitchhiking and breakup of linkage effects. Allele frequencies do not change directionally among the reperturbed populations as a group. The hypothesis of balancing selection is rejected in favor of the hypothesis of initial hitchhiking and dissipated linkage effects. The power of the experimental design to detect selection is studied by simulation. Within the limits of power set by the design, it is concluded that the 100 and 106 are iso-fitness alleles of Est-5 under the environmental conditions of the laboratory populations. The requirements of a method of perturbation and reperturbation are discussed.     

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 EFFICACY OF DIVERGENCE HITCHHIKING IN GENERATING GENOMIC ISLANDS DURING ECOLOGICAL SPECIATION

Genes under divergent selection flow less readily between populations than other loci. This observation has led to verbal “divergence hitchhiking” models of speciation in which decreased interpopulation gene flow surrounding loci under divergent selection can generate large regions of differentiation within the genome (genomic islands). The efficacy of this model in promoting speciation depends on the size of the region affected by divergence hitchhiking. Empirical evidence is mixed, with examples of both large and small genomic islands. To address these empirical discrepancies and to formalize the theory, we present mathematical models of divergence hitchhiking, which examine neutral differentiation around selected sites. For a single locus under selection, regions of differentiation do not extend far along a chromosome away from a selected site unless both effective population sizes and migration rates are low. When multiple loci are considered, regions of differentiation can be larger. However, with many loci under selection, genome‐wide divergence occurs and genomic islands are erased. The results show that divergence hitchhiking can generate large regions of differentiation, but that the conditions under which this occurs are limited. Thus, speciation may often require multifarious selection acting on many, isolated and physically unlinked genes. How hitchhiking promotes further adaptive divergence warrants consideration.     

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.     

Linkage disequilibrium under genetic hitchhiking in finite populations

The model of genetic hitchhiking predicts a reduction in sequence diversity at a neutral locus closely linked to a beneficial allele. In addition, it has been shown that the same process results in a specific pattern of correlations (linkage disequilibrium) between neutral polymorphisms along the chromosome at the time of fixation of the beneficial allele. During the hitchhiking event, linkage disequilibrium on either side of the beneficial allele is built up whereas it is destroyed across the selected site. We derive explicit formulas for the expectation of the covariance measure D and standardized linkage disequilibrium sigma 2D between a pair of polymorphic sites. For our analysis we use the approximation of a star-like genealogy at the selected site. The resulting expressions are approximately correct in the limit of large selection coefficients. Using simulations we show that the resulting pattern of linkage disequilibrium is quickly-i.e., in <0.1N generations-destroyed after the fixation of the beneficial allele for moderately distant neutral loci, where N is the diploid population size.     

The classical hitchhiking model with continuous mutational pressure and purifying selection

Detecting selective sweeps driven by strong positive selection and localizing the targets of selection in the genome play a major role in modern population genetics and genomics. Most of these analyses are based on the classical model of genetic hitchhiking proposed by Maynard Smith and Haigh (1974, Genetical Research, 23, 23). Here, we consider extensions of the classical two‐locus model. Introducing mutation at the strongly selected site, we analyze the conditions under which soft sweeps may arise. We identify a new parameter (the ratio of the beneficial mutation rate to the selection coefficient) that characterizes the occurrence of multiple‐origin soft sweeps. Furthermore, we quantify the hitchhiking effect when the polymorphism at the linked locus is not neutral but maintained in a mutation‐selection balance. In this case, we find a smaller relative reduction of heterozygosity at the linked site than for a neutral polymorphism. In our analysis, we use a semi‐deterministic approach; i.e., we analyze the frequency process of the beneficial allele in an infinitely large population when its frequency is above a certain threshold; however, for very small frequencies in the initial phase after the onset of selection we rely on diffusion theory.     

Hitchhiking mapping reveals a candidate genomic region for natural selection in three-spined stickleback chromosome VIII

Identification of genes and genomic regions under directional natural selection has become one of the major goals in evolutionary genetics, but relatively little work to this end has been done by applying hitchhiking mapping to wild populations. Hitchhiking mapping starts from a genome scan using a randomly spaced set of molecular markers followed by a fine-scale analysis in the flanking regions of the candidate regions under selection. We used the hitchhiking mapping approach to narrow down a selective sweep in the genomic region flanking a candidate locus (Stn90) in chromosome VIII in the three-spined stickleback (Gasterosteus aculeatus). Twenty-four microsatellite markers were screened in an approximately 800-kb region around the candidate locus in three marine and four freshwater populations. The patterns of genetic diversity and differentiation in the candidate region were compared to those of a putatively neutral set of markers. The Bayesian FST-test indicated an elevated genetic differentiation, deviating significantly from neutral expectations, at a continuous region of approximately 20 kb upstream from the candidate locus. Furthermore, a method developed for an array of microsatellite markers rejected neutrality in a region of approximately 90 kb flanking the candidate locus supporting the selective sweep hypothesis. Likewise, the genomewide pattern of genetic diversity differed from the candidate region in a bottleneck analysis suggesting that selection, rather than demography, explains the reduced genetic diversity at the candidate interval. The neutrality tests suggest that the selective sweep had occurred mainly in the Lake Pulmanki population, but the results from bottleneck analyses indicate that selection might have operated in other populations as well. These results suggest that the narrow interval around locus Stn90 has likely been under directional selection, but the region contains several predicted genes, each of which can be the actual targets of selection. Understanding of the functional significance of this genomic region in an ecological context will require a more detailed sequence analysis.     

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 effect of hitch-hiking on genes linked to a balanced polymorphism in a subdivided population

The effect of multi-allelic balancing selection on nucleotide diversity at linked neutral sites was investigated by simulations of subdivided populations. The motivation is to understand the behaviour of self-recognition systems such as the MHC and plant self-incompatibility. For neutral sites, two types of subdivision are present: (1) into demes (connected by migration), and (2) into classes defined by different functional alleles at the selected locus (connected by recombination). Previous theoretical studies of each type of subdivision separately have shown that each increases diversity, and decreases the relative frequencies of low-frequency variants, at neutral sites or loci. We show here that the two types of subdivision act non-additively when sampling is at the whole population level, and that subdivision produces some non-intuitive results. For instance, in highly subdivided populations, genetic diversity at neutral sites may decrease with tighter linkage to a selected locus or site. Another conclusion is that, if there is population subdivision, balancing selection leads to decreased expected FST values for neutral sites linked to the selected locus. Finally, we show that the ability to detect balancing selection by its effects on linked variation, using tests such as Tajima's D, is reduced when genes in a subdivided population are sampled from the total population, rather than within demes.     

Spatially explicit models of divergence and genome hitchhiking

Strong barriers to genetic exchange can exist at divergently selected loci, whereas alleles at neutral loci flow more readily between populations, thus impeding divergence and speciation in the face of gene flow. However, ‘divergence hitchhiking’ theory posits that divergent selection can generate large regions of differentiation around selected loci. ‘Genome hitchhiking’ theory suggests that selection can also cause reductions in average genome‐wide rates of gene flow, resulting in widespread genomic divergence (rather than divergence only around specific selected loci). Spatial heterogeneity is ubiquitous in nature, yet previous models of genetic barriers to gene flow have explored limited combinations of spatial and selective scenarios. Using simulations of secondary contact of populations, we explore barriers to gene flow in various selective and spatial contexts in continuous, two‐dimensional, spatially explicit environments. In general, the effects of hitchhiking are strongest in environments with regular spatial patterning of starkly divergent habitat types. When divergent selection is very strong, the absence of intermediate habitat types increases the effects of hitchhiking. However, when selection is moderate or weak, regular (vs. random) spatial arrangement of habitat types becomes more important than the presence of intermediate habitats per se. We also document counterintuitive processes arising from the stochastic interplay between selection, gene flow and drift. Our results indicate that generalization of results from two‐deme models requires caution and increase understanding of the genomic and geographic basis of population divergence.     

Polymorphism and divergence at the prune locus in Drosophila melanogaster and D. simulans

The prune locus of Drosophila melanogaster lies at the tip of the X chromosome, in a region of reduced recombination in which nearby loci show reduced variation relative to evolutionary divergence from D. simulans. DNA sequencing of prune alleles from D. melanogaster and D. simulans reveals extremely low variation in D. melanogaster but greater variation in D. simulans. Divergence between the two species is not reduced. This pattern may be explained by either positive selection leading to hitchhiking of neutral variation or background selection against deleterious mutations. The pattern of silent versus replacement polymorphism and divergence at prune is consistent with either a model of weakly deleterious selection against amino acid substitutions or balancing selection.      

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.     

Establishment of new mutations under divergence and genome hitchhiking

Theoretical models addressing genome-wide patterns of divergence during speciation are needed to help us understand the evolutionary processes generating empirical patterns. Here, we examine a critical issue concerning speciation-with-gene flow: to what degree does physical linkage (r < 0.5) of new mutations to already diverged genes aid the build-up of genomic islands of differentiation? We used simulation and analytical approaches to partition the probability of establishment for a new divergently selected mutation when the mutation (i) is the first to arise in an undifferentiated genome (the direct effect of selection), (ii) arises unlinked to any selected loci (r = 0.5), but within a genome that has some already diverged genes (the effect of genome-wide reductions in gene flow for facilitating divergence, which we term 'genome hitchhiking'), and (iii) arises in physical linkage to a diverged locus (divergence hitchhiking). We find that the strength of selection acting directly on a new mutation is generally the most important predictor for establishment, with divergence and genomic hitchhiking having smaller effects. We outline the specific conditions under which divergence and genome hitchhiking can aid mutation establishment. The results generate predictions about genome divergence at different points in the speciation process and avenues for further work.