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.     

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.     

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.     

Evolution at the tip and base of the X chromosome in an African population of Drosophila melanogaster

Hitchhiking effects of advantageous mutations have been invoked to explain reduced polymorphism in regions of low crossing-over in Drosophila. Besides reducing DNA heterozygosity, hitchhiking effects should produce strong linkage disequilibrium and a frequency spectrum skewed toward an excess of rare polymorphisms (compared to the neutral expectation). We measured DNA polymorphism in a Zimbabwe population of D. melanogaster at three loci, yellow, achaete, and suppressor of forked, located in regions of reduced crossing-over. Similar to previously published surveys of these genomic regions in other populations, we observed low levels of nucleotide variability. However, the frequency spectrum was compatible with a neutral model, and there was abundant evidence for recombination in the history of the yellow and ac genes. Thus, some aspects of the data cannot be accounted for by a simple hitchhiking model. An alternative hypothesis, background selection, might be compatible with the observed patterns of linkage disequilibrium and the frequency spectrum. However, this model cannot account for the observed reduction in nucleotide heterozygosity. Thus, there is currently no satisfactory theoretical model for the data from the tip and base of the X chromosome in D. melanogaster.      

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.     

The structure of linkage disequilibrium around a selective sweep

The fixation of advantageous mutations by natural selection has a profound impact on patterns of linked neutral variation. While it has long been appreciated that such selective sweeps influence the frequency spectrum of nearby polymorphism, it has only recently become clear that they also have dramatic effects on local linkage disequilibrium. By extending previous results on the relationship between genealogical structure and linkage disequilibrium, I obtain simple expressions for the influence of a selective sweep on patterns of allelic association. I show that sweeps can increase, decrease, or even eliminate linkage disequilibrium (LD) entirely depending on the relative position of the selected and neutral loci. I also show the importance of the age of the neutral mutations in predicting their degree of association and describe the consequences of such results for the interpretation of empirical data. In particular, I demonstrate that while selective sweeps can eliminate LD, they generate patterns of genetic variation very different from those expected from recombination hotspots.     

Selective sweeps in a 2-locus model for sex-ratio meiotic drive in Drosophila simulans

A way to identify loci subject to positive selection is to detect the signature of selective sweeps in given chromosomal regions. It is revealed by the departure of DNA polymorphism patterns from the neutral equilibrium predicted by coalescent theory. We surveyed DNA sequence variation in a region formerly identified as causing "sex-ratio" meiotic drive in Drosophila simulans. We found evidence that this system evolved by positive selection at 2 neighboring loci, which thus appear to be required simultaneously for meiotic drive to occur. The 2 regions are approximately 150-kb distant, corresponding to a genetic distance of 0.1 cM. The presumably large transmission advantage of chromosomes carrying meiotic drive alleles at both loci has not erased the individual signature of selection at each locus. This chromosome fragment combines a high level of linkage disequilibrium between the 2 critical regions with a high recombination rate. As a result, 2 characteristic traits of selective sweeps--the reduction of variation and the departure from selective neutrality in haplotype tests--show a bimodal pattern. Linkage disequilibrium level indicates that, in the natural population from Madagascar used in this study, the selective sweep may be as recent as 100 years.     

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.     

Selection, recombination and demographic history in Drosophila miranda

Selection, recombination, and the demographic history of a species can all have profound effects on genomewide patterns of variability. To assess the impact of these forces in the genome of Drosophila miranda, we examine polymorphism and divergence patterns at 62 loci scattered across the genome. In accordance with recent findings in D. melanogaster, we find that noncoding DNA generally evolves more slowly than synonymous sites, that the distribution of polymorphism frequencies in noncoding DNA is significantly skewed toward rare variants relative to synonymous sites, and that long introns evolve significantly slower than short introns or synonymous sites. These observations suggest that most noncoding DNA is functionally constrained and evolving under purifying selection. However, in contrast to findings in the D. melanogaster species group, we find little evidence of adaptive evolution acting on either coding or noncoding sequences in D. miranda. Levels of linkage disequilibrium (LD) in D. miranda are comparable to those observed in D. melanogaster, but vary considerably among chromosomes. These patterns suggest a significantly lower rate of recombination on autosomes, possibly due to the presence of polymorphic autosomal inversions and/or differences in chromosome sizes. All chromosomes show significant departures from the standard neutral model, including too much heterogeneity in synonymous site polymorphism relative to divergence among loci and a general excess of rare synonymous polymorphisms. These departures from neutral equilibrium expectations are discussed in the context of nonequilibrium models of demography and selection.     

A genome-wide departure from the standard neutral model in natural populations of Drosophila

We analyze nucleotide polymorphism data for a large number of loci in areas of normal to high recombination in Drosophila melanogaster and D. simulans (24 and 16 loci, respectively). We find a genome-wide, systematic departure from the neutral expectation for a panmictic population at equilibrium in natural populations of both species. The distribution of sequence-based estimates of 2Nc across loci is inconsistent with the assumptions of the standard neutral theory, given the observed levels of nucleotide diversity and accepted values for recombination and mutation rates. Under these assumptions, most estimates of 2Nc are severalfold too low; in other words, both species exhibit greater intralocus linkage disequilibrium than expected. Variation in recombination or mutation rates is not sufficient to account for the excess of linkage disequilibrium. While an equilibrium island model does not seem to account for the data, more complicated forms of population structure may. A proper test of alternative demographic models will require loci to be sampled in a more consistent fashion.     

Linkage disequilibrium testing when linkage phase is unknown

Linkage disequilibrium, the nonrandom association of alleles from different loci, can provide valuable information on the structure of haplotypes in the human genome and is often the basis for evaluating the association of genomic variation with human traits among unrelated subjects. But, linkage phase of genetic markers measured on unrelated subjects is typically unknown, and so measurement of linkage disequilibrium, and testing whether it differs significantly from the null value of zero, requires statistical methods that can account for the ambiguity of unobserved haplotypes. A common method to test whether linkage disequilibrium differs significantly from zero is the likelihood-ratio statistic, which assumes Hardy-Weinberg equilibrium of the marker phenotype proportions. We show, by simulations, that this approach can be grossly biased, with either extremely conservative or liberal type I error rates. In contrast, we use simulations to show that a composite statistic, proposed by Weir and Cockerham, maintains the correct type I error rates, and, when comparisons are appropriate, has similar power as the likelihood-ratio statistic. We extend the composite statistic to allow for more than two alleles per locus, providing a global composite statistic, which is a strong competitor to the usual likelihood-ratio statistic.     

High nucleotide polymorphism and rapid decay of linkage disequilibrium in wild populations of Caenorhabditis remanei

The common ancestor of the self-fertilizing nematodes Caenorhabditis elegans and C. briggsae must have reproduced by obligate outcrossing, like most species in this genus. However, we have only a limited understanding about how genetic variation is patterned in such male-female (gonochoristic) Caenorhabditis species. Here, we report results from surveying nucleotide variation of six nuclear loci in a broad geographic sample of wild isolates of the gonochoristic C. remanei. We find high levels of diversity in this species, with silent-site diversity averaging 4.7%, implying an effective population size close to 1 million. Additionally, the pattern of polymorphisms reveals little evidence for population structure or deviation from neutral expectations, suggesting that the sampled C. remanei populations approximate panmixis and demographic equilibrium. Combined with the observation that linkage disequilibrium between pairs of polymorphic sites decays rapidly with distance, this suggests that C. remanei will provide an excellent system for identifying the genetic targets of natural selection from deviant patterns of polymorphism and linkage disequilibrium. The patterns revealed in this obligately outcrossing species may provide a useful model of the evolutionary circumstances in C. elegans' gonochoristic progenitor. This will be especially important if self-fertilization evolved recently in C. elegans history, because most of the evolutionary time separating C. elegans from its known relatives would have occurred in a state of obligate outcrossing.     

Selection versus random drift: long-term polymorphism persistence in small populations (evidence and modelling)

Our data on a subterranean mammal, Spalax ehrenbergi, and other evidence, indicate that appreciable polymorphism can be preserved in small isolated populations consisting of several dozens of, or a hundred, individuals. Current theoretical models predict fast gene fixation in small panmictic populations without selection, mutation, or gene inflow. Using simple multilocus models, we demonstrate here that moderate stabilizing selection (with stable or fluctuating optimum) for traits controlled by additive genes could oppose random fixation in such isolates during thousands of generations. We also show that in selection-free models polymorphism persists only for a few hundred generations even under high mutation rates. Our multi-chromosome models challenge the hitchhiking hypothesis of polymorphism maintenance for many neutral loci due to close linkage with few selected loci.     

Population structure in admixed populations: effect of admixture dynamics on the pattern of linkage disequilibrium

Gene flow between genetically distinct populations creates linkage disequilibrium (admixture linkage disequilibrium [ALD]) among all loci (linked and unlinked) that have different allele frequencies in the founding populations. We have explored the distribution of ALD by using computer simulation of two extreme models of admixture: the hybrid-isolation (HI) model, in which admixture occurs in a single generation, and the continuous-gene-flow (CGF) model, in which admixture occurs at a steady rate in every generation. Linkage disequilibrium patterns in African American population samples from Jackson, MS, and from coastal South Carolina resemble patterns observed in the simulated CGF populations, in two respects. First, significant association between two loci (FY and AT3) separated by 22 cM was detected in both samples. The retention of ALD over relatively large (>10 cM) chromosomal segments is characteristic of a CGF pattern of admixture but not of an HI pattern. Second, significant associations were also detected between many pairs of unlinked loci, as observed in the CGF simulation results but not in the simulated HI populations. Such a high rate of association between unlinked markers in these populations could result in false-positive linkage signals in an admixture-mapping study. However, we demonstrate that by conditioning on parental admixture, we can distinguish between true linkage and association resulting from shared ancestry. Therefore, populations with a CGF history of admixture not only are appropriate for admixture mapping but also have greater power for detection of linkage disequilibrium over large chromosomal regions than do populations that have experienced a pattern of admixture more similar to the HI model, if methods are employed that detect and adjust for disequilibrium caused by continuous admixture.     

Testing models of selection and demography in Drosophila simulans

We analyze patterns of nucleotide variability at 15 X-linked loci and 14 autosomal loci from a North American population of Drosophila simulans. We show that there is significantly more linkage disequilibrium on the X chromosome than on chromosome arm 3R and much more linkage disequilibrium on both chromosomes than expected from estimates of recombination rates, mutation rates, and levels of diversity. To explore what types of evolutionary models might explain this observation, we examine a model of recurrent, nonoverlapping selective sweeps and a model of a recent drastic bottleneck (e.g., founder event) in the demographic history of North American populations of D. simulans. The simple sweep model is not consistent with the observed patterns of linkage disequilibrium nor with the observed frequencies of segregating mutations. Under a restricted range of parameter values, a simple bottleneck model is consistent with multiple facets of the data. While our results do not exclude some influence of selection on X vs. autosome variability levels, they suggest that demography alone may account for patterns of linkage disequilibrium and the frequency spectrum of segregating mutations in this population of D. simulans.     

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

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