Studying models of balancing selection using phase-type theory

Balancing selection (BLS) is the evolutionary force that maintains high levels of genetic variability in many important genes. To further our understanding of its evolutionary significance, we analyze models with BLS acting on a biallelic locus: an equilibrium model with long-term BLS, a model with long-term BLS and recent changes in population size, and a model of recent BLS. Using phase-type theory, a mathematical tool for analyzing continuous time Markov chains with an absorbing state, we examine how BLS affects polymorphism patterns in linked neutral regions, as summarized by nucleotide diversity, the expected number of segregating sites, the site frequency spectrum, and the level of linkage disequilibrium (LD). Long-term BLS affects polymorphism patterns in a relatively small genomic neighborhood, and such selection targets are easier to detect when the equilibrium frequencies of the selected variants are close to 50%, or when there has been a population size reduction. For a new mutation subject to BLS, its initial increase in frequency in the population causes linked neutral regions to have reduced diversity, an excess of both high and low frequency derived variants, and elevated LD with the selected locus. These patterns are similar to those produced by selective sweeps, but the effects of recent BLS are weaker. Nonetheless, compared to selective sweeps, nonequilibrium polymorphism and LD patterns persist for a much longer period under recent BLS, which may increase the chance of detecting such selection targets. An R package for analyzing these models, among others (e.g., isolation with migration), is available.     

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.     

Contrasting evolutionary histories of two introns of the duchenne muscular dystrophy gene, Dmd, in humans

The Duchenne muscular dystrophy (Dmd) locus lies in a region of the X chromosome that experiences a high rate of recombination and is thus expected to be relatively unaffected by the effects of selection on nearby genes. To provide a picture of nucleotide variability at a high-recombination locus in humans, we sequenced 5. 4 kb from two introns of Dmd in a worldwide sample of 41 alleles from Africa, Asia, Europe, and the Americas. These same regions were also sequenced in one common chimpanzee and one orangutan. Dramatically different patterns of genetic variation were observed at these two introns, which are separated by >500 kb of DNA. Nucleotide diversity at intron 44 pi = 0.141% was more than four times higher than nucleotide diversity at intron 7 pi = 0.034% despite similar levels of divergence for these two regions. Intron 7 exhibited significant linkage disequilibrium extending over 10 kb and also showed a significant excess of rare polymorphisms. In contrast, intron 44 exhibited little linkage disequilibrium and no skew in the frequency distribution of segregating sites. Intron 7 was much more variable in Africa than in other continents, while intron 44 displayed similar levels of variability in different geographic regions. Comparison of intraspecific polymorphism to interspecific divergence using the HKA test revealed a significant reduction in variability at intron 7 relative to intron 44, and this effect was most pronounced in the non-African samples. These results are best explained by positive directional selection acting at or near intron 7 and demonstrate that even genes in regions of high recombination may be influenced by selection at linked sites.     

The effects of Hill-Robertson interference between weakly selected mutations on patterns of molecular evolution and variation

Associations between selected alleles and the genetic backgrounds on which they are found can reduce the efficacy of selection. We consider the extent to which such interference, known as the Hill-Robertson effect, acting between weakly selected alleles, can restrict molecular adaptation and affect patterns of polymorphism and divergence. In particular, we focus on synonymous-site mutations, considering the fate of novel variants in a two-locus model and the equilibrium effects of interference with multiple loci and reversible mutation. We find that weak selection Hill-Robertson (wsHR) interference can considerably reduce adaptation, e.g., codon bias, and, to a lesser extent, levels of polymorphism, particularly in regions of low recombination. Interference causes the frequency distribution of segregating sites to resemble that expected from more weakly selected mutations and also generates specific patterns of linkage disequilibrium. While the selection coefficients involved are small, the fitness consequences of wsHR interference across the genome can be considerable. We suggest that wsHR interference is an important force in the evolution of nonrecombining genomes and may explain the unexpected constancy of codon bias across species of very different census population sizes, as well as several unusual features of codon usage in Drosophila.     

The Evolution of the Y Chromosome with X-Y Recombination

A theoretical population genetic model is developed to explore the consequences of X-Y recombination in the evolution of sex chromosome polymorphism. The model incorporates one sex-determining locus and one locus subject to natural selection. Both loci have two alleles, and the rate of classical meiotic recombination between the loci is r. The alleles at the sex-determining locus specify whether the chromosome is X or Y, and the alleles at the selected locus are arbitrarily labeled A and a. Natural selection is modeled as a process of differential viabilities. The system can be expressed in terms of three recurrence equations, one for the frequency of A on the X-bearing gametes produced by females, one for each of the frequency of A on the X- and Y-bearing gametes produced by males. Several special cases are examined, including X chromosome dominance and symmetric selection. Unusual equilibria are found with the two sexes having very different allele frequencies at the selected locus. A significant finding is that the allowance of recombination results in a much greater opportunity for polymorphism of the Y chromosome. Tighter linkage results in a greater likelihood for equilibria with a large difference between the sex chromosomes in allele frequency.     

Patterns of DNA sequence variation suggest the recent action of positive selection in the janus-ocnus region of Drosophila simulans

Levels of nucleotide polymorphism in three paralogous Drosophila simulans genes, janusA (janA), janusB (janB), and ocnus (ocn), were surveyed by DNA sequencing. The three genes lie in tandem within a 2.5-kb region of chromosome arm 3R. In a sample of eight alleles from a worldwide distribution we found a significant departure from neutrality by several statistical tests. The most striking feature of this sample was that in a 1.7-kb region containing the janA and janB genes, 30 out of 31 segregating sites contained variants present only once in the sample, and 29 of these unique variants were found in the same allele. A restriction survey of an additional 28 lines of D. simulans revealed strong linkage disequilibrium over the janA-janB region and identified six more alleles matching the rare haplotype. Among the rare alleles, the level of DNA sequence variation was typical for D. simulans autosomal genes and showed no departure from neutrality. In addition, the rare haplotype was more similar to the D. melanogaster sequence, indicating that it was the ancestral form. These results suggest that the derived haplotype has risen to high worldwide frequency relatively recently, most likely as a result of natural selection.     

Identifying selected regions from heterozygosity and divergence using a light-coverage genomic dataset from two human populations

When a selective sweep occurs in the chromosomal region around a target gene in two populations that have recently separated, it produces three dramatic genomic consequences: 1) decreased multi-locus heterozygosity in the region; 2) elevated or diminished genetic divergence (F(ST)) of multiple polymorphic variants adjacent to the selected locus between the divergent populations, due to the alternative fixation of alleles; and 3) a consequent regional increase in the variance of F(ST) (S(2)F(ST)) for the same clustered variants, due to the increased alternative fixation of alleles in the loci surrounding the selection target. In the first part of our study, to search for potential targets of directional selection, we developed and validated a resampling-based computational approach; we then scanned an array of 31 different-sized moving windows of SNP variants (5-65 SNPs) across the human genome in a set of European and African American population samples with 183,997 SNP loci after correcting for the recombination rate variation. The analysis revealed 180 regions of recent selection with very strong evidence in either population or both. In the second part of our study, we compared the newly discovered putative regions to those sites previously postulated in the literature, using methods based on inspecting patterns of linkage disequilibrium, population divergence and other methodologies. The newly found regions were cross-validated with those found in nine other studies that have searched for selection signals. Our study was replicated especially well in those regions confirmed by three or more studies. These validated regions were independently verified, using a combination of different methods and different databases in other studies, and should include fewer false positives. The main strength of our analysis method compared to others is that it does not require dense genotyping and therefore can be used with data from population-based genome SNP scans from smaller studies of humans or other species.     

DNA variation in a conifer,Cryptomeria japonica (Cupressaceae sensu lato)

We investigated the nucleotide variation of a conifer, Cryptomeria japonica, and the divergence between this species and its closest relative, Taxodium distichum, at seven nuclear loci (Acl5, Chi1, Ferr, GapC, HemA, Lcyb, and Pat). Samples of C. japonica were collected from three areas, Kantou-Toukai, Hokuriku, and Iwate. No apparent geographic differentiation was found among these samples. However, the frequency spectrum of the nucleotide polymorphism revealed excesses of intermediate-frequency variants, which suggests that the population was not panmictic and a constant size in the past. The average nucleotide diversity, pi, for silent sites was 0.00383. However, values of pi for silent sites vary among loci. Comparisons of polymorphism to divergence among loci (the HKA test) showed that the polymorphism at the Acl5 locus was significantly lower. We also observed a nearly significant excess of replacement polymorphisms at the Lcyb locus. These results suggested possibilities of natural selection acting at some of the loci. Intragenic recombination was detected only once at the Chi1 locus and was not detected at the other loci. The low level of population recombination rate, 4Nr, seemed to be due to both low level of recombination, r, and small population size, N.     

Species and recombination effects on DNA variability in the tomato genus

Population genetics theory predicts that strong selection for rare, beneficial mutations or against frequent, deleterious mutations reduces polymorphism at linked neutral (or weakly selected) sites. The reduction of genetic variation is expected to be more severe when recombination rates are lower. In outbreeding species, low recombination rates are usually confined to certain chromosomal regions, such as centromeres and telomeres. In contrast, in predominantly selfing species, the rarity of double heterozygotes leads to a reduced effective recombination rate in the whole genome. We investigated the effects of restricted recombination on DNA polymorphism in these two cases, analyzing five Lycopersicon species with contrasting mating systems: L. chilense, L. hirsutum, L. peruvianum, L. chmielewskii, and L. pimpinellifolium, of which only the first three species have self-incompatibility alleles. In each species, we determined DNA sequence variation of five single-copy genes located in chromosomal regions with either high or low recombination rate. We found that the mating system has a highly significant effect on the level of polymorphism, whereas recombination has only a weak influence. The effect of recombination on levels of polymorphism in Lycopersicon is much weaker than in other well-studied species, including Drosophila. To explain these observations, we discuss a number of hypotheses, invoking selection, recombination, and demographic factors associated with the mating system. We also provide evidence that L. peruvianum, showing a level of polymorphism (almost 3%) that is comparable to the level of divergence in the whole genus, is the ancestral species from which the other species of the genus Lycopersicon have originated relatively recently.     

Detecting the signature of selection on immune genes in highly structured populations of wild sheep (Ovis dalli)

The confounding effects of population structure complicate efforts to identify regions of the genome under the influence of selection in natural populations. Here we test for evidence of selection in three genes involved in vertebrate immune function - the major histocompatibility complex (MHC), interferon gamma (IFNG) and natural resistance associated macrophage polymorphism (NRAMP) - in highly structured populations of wild thinhorn sheep (Ovis dalli). We examined patterns of variation at microsatellite loci linked to these gene regions and at the DNA sequence level. Simple Watterson's tests indicated balancing selection at all three gene regions. However, evidence for selection was confounded by population structure, as the Watterson's test statistics from linked markers were not outside of the range of values from unlinked and presumably neutral microsatellites. The translated coding sequences of thinhorn IFNG and NRAMP are fixed and identical to those of domestic sheep (Ovis aries). In contrast, the thinhorn MHC DRB locus shows significant evidence of overdominance through both an excess of nonsynonymous substitution and trans-species polymorphism. The failure to detect balancing selection at microsatellite loci linked to the MHC is likely the result of recombination between the markers and expressed gene regions.     

Patterns of variability at the major histocompatibility class II alpha locus in Atlantic salmon contrast with those at the class I locus

In order to investigate the mechanisms creating and maintaining variability at the major histocompatibility (MH) class II alpha (DAA) locus we examined patterns of polymorphism in two isolated Atlantic salmon populations which share a common post-glacial origin. As expected from their common origin, but contrary to the observation at the MH class I locus, these populations shared the majority of DAA alleles: out of 17 sequences observed, 11 were common to both populations. Recombination seems to play a more important role in the origin of new alleles at the class II alpha locus than at the class I locus. A greater than expected proportion of sites inferred to be positively selected (potentially peptide binding residues, PBRs) were found to be involved in recombination events, suggesting a mechanism for increasing MH variability through an interaction between recombination and natural selection. Thus it appears that although selection and recombination are important mechanisms for the evolution of both class II alpha and class I loci in the Atlantic salmon, the pattern of variability differs markedly between these classes of MH loci.     

Recent selection for self‐compatibility in a population of Leavenworthia alabamica

The evolution of self‐compatibility (SC) is the first step in the evolutionary transition in plants from outcrossing enforced by self‐incompatibility (SI) to self‐fertilization. In the Brassicaceae, SI is controlled by alleles of two tightly linked genes at the S‐locus. Despite permitting inbreeding, mutations at the S‐locus leading to SC may be selected if they provide reproductive assurance and/or gain a transmission advantage in a population when SC plants self‐ and outcross. Positive selection can leave a genomic signature in the regions physically linked to the focus of selection when selection has occurred recently. From an SC population of Leavenworthia alabamica with a known nonfunctional mutation at the S‐locus, we collected sequence data from a ～690 Kb region surrounding the S‐locus, as well as from regions not linked to the S‐locus. To test for recent positive selection acting at the S‐locus, we examined polymorphism and the site‐frequency spectra. Using forward simulations, we demonstrate that recent selection of the strength expected for SC at a locus formerly under balancing selection can generate patterns similar to those seen in our empirical data.     

Complex selection on a regulator of social cognition: Evidence of balancing selection,regulatory interactions and population differentiation in the prairie vole Avpr1a locus

Adaptive variation in social behaviour depends upon standing genetic variation, but we know little about how evolutionary forces shape genetic diversity relevant to brain and behaviour. In prairie voles (Microtus ochrogaster), variants at the Avpr1a locus predict expression of the vasopressin 1a receptor in the retrosplenial cortex (RSC), a brain region that mediates spatial and contextual memory; cortical V1aR abundance in turn predicts diversity in space use and sexual fidelity in the field. To examine the potential contributions of adaptive and neutral forces to variation at the Avpr1a locus, we explore sequence diversity at the Avpr1a locus and throughout the genome in two populations of wild prairie voles. First, we refine results demonstrating balancing selection at the locus by comparing the frequency spectrum of variants at the locus to a random sample of the genome. Next, we find that the four single nucleotide polymorphisms that predict high V1aR expression in the RSC are in stronger linkage disequilibrium than expected by chance despite high recombination among intervening variants, suggesting that epistatic selection maintains their association. Analysis of population structure and a haplotype network for two populations revealed that this excessive LD was unlikely to be due to admixture alone. Furthermore, the two populations differed considerably in the region shown to be a regulator of V1aR expression despite the extremely low levels of genomewide genetic differentiation. Together, our data suggest that complex selection on Avpr1a locus favours specific combinations of regulatory polymorphisms, maintains the resulting alleles at population‐specific frequencies, and may contribute to unique patterns of spatial cognition and sexual fidelity among populations.     

Sweeps in time: leveraging the joint distribution of branch lengths

Current methods of identifying positively selected regions in the genome are limited in two key ways: the underlying models cannot account for the timing of adaptive events and the comparison between models of selective sweeps and sequence data is generally made via simple summaries of genetic diversity. Here, we develop a tractable method of describing the effect of positive selection on the genealogical histories in the surrounding genome, explicitly modeling both the timing and context of an adaptive event. In addition, our framework allows us to go beyond analyzing polymorphism data via the site frequency spectrum or summaries thereof and instead leverage information contained in patterns of linked variants. Tests on both simulations and a human data example, as well as a comparison to SweepFinder2, show that even with very small sample sizes, our analytic framework has higher power to identify old selective sweeps and to correctly infer both the time and strength of selection. Finally, we derived the marginal distribution of genealogical branch lengths at a locus affected by selection acting at a linked site. This provides a much-needed link between our analytic understanding of the effects of sweeps on sequence variation and recent advances in simulation and heuristic inference procedures that allow researchers to examine the sequence of genealogical histories along the genome.     

Selective sweep near the In(2L)t inversion breakpoint in an African population of Drosophila melanogaster

Chromosomal inversions largely inhibit recombination and may be associated with selective forces, such as hitch-hiking effects: the effect of positive selection on linked loci. A West African population of Drosophila melanogaster showed a high frequency (0.61) of the In(2L)t inversion. Departure from neutrality statistically associated with the inversion polymorphism was previously recorded at Su(H), a locus distant from the proximal breakpoint of the inversion. These results were consistent with hitch-hiking effects with recombination. The present sequence polymorphism survey involves a 1 kb fragment of the Vha68-1 locus located closer to the proximal breakpoint of the inversion. It shows a significant deficit of polymorphism with respect to divergence when compared with other loci studied in the same population, thus suggesting selective effects. Only 11 polymorphic sites are present in a sample of 20 chromosomes and these sites present a significant excess of rare-frequency variants. The major haplotype shows an unexpectedly high frequency. Our estimate of the background selection effect is not sufficient to account for the observed reduction of polymorphism. Intraspecific variation is structured between inverted and standard chromosomes; there are no shared polymorphisms but also no fixed differences between them. This pattern, together with that found on other loci previously studied near this inversion breakpoint, suggests hitch-hiking effects enhanced by the inversion.     

The implications of intergenic polymorphism for major histocompatibility complex evolution

A systematic survey of six intergenic regions flanking the human HLA-B locus in eight haplotypes reveals the regions to be up to 20 times more polymorphic than the reported average degree of human neutral polymorphism. Furthermore, the extent of polymorphism is directly related to the proximity to the HLA-B locus. Apparently linkage to HLA-B locus alleles, which are under balancing selection, maintains the neutral polymorphism of adjacent regions. For these linked polymorphisms to persist, recombination in the 200-kb interval from HLA-B to TNF must occur at a low frequency. The high degree of polymorphism found distal to HLA-B suggests that recombination is uncommon on both sides of the HLA-B locus. The least-squares estimate is 0.15% per megabase with an estimated range from 0.02 to 0.54%. These findings place strong restrictions on possible recombinational mechanisms for the generation of diversity at the HLA-B.     

Local Patterns of Nucleotide Polymorphism Are Highly Variable in the Selfing Species Arabidopsis thaliana

Neighboring genes predictably share similar evolutionary histories to an extent delineated by recombination. This correlation should extend across multiple linked genes in a selfing species such as Arabidopsis thaliana due to its low effective recombination rate. To test this prediction, we performed a molecular population genetics analysis of nucleotide polymorphism and divergence in chromosomal regions surrounding four low-diversity loci. Three of these loci, At1g67140, At3g03700, and TERMINAL FLOWER1 (TFL1), have been previously implicated as targets of selection and we would predict stronger correlations in polymorphism between neighboring loci due to genetic hitchhiking around these loci. The remaining locus, At1g04300, was identified in a study of linkage disequilibrium surrounding the CRYPTOCHROME2 (CRY2) locus. Although we found broad valleys of reduced nucleotide variation around two of our focal genes, At1g67140 and At3g03700, all chromosomal regions exhibited extreme variation in the patterns of polymorphism and evolution between neighboring loci. Although three of our four regions contained potential targets of selection, application of the composite-likelihood-ratio test of selection in conjunction with a goodness-of-fit test supports the selection hypothesis only for the region containing At3g03700. The degree of discordance in evolutionary histories between linked loci within each region generally correlated with estimates of recombination and linkage disequilibrium for that region, with the exception of the region containing At1g04300. We discuss the implications of these data for future population genetics analyses and genomics studies in A. thaliana. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Recombination rate variation and speciation: theoretical predictions and empirical results from rabbits and mice

Recently diverged taxa may continue to exchange genes. A number of models of speciation with gene flow propose that the frequency of gene exchange will be lower in genomic regions of low recombination and that these regions will therefore be more differentiated. However, several population-genetic models that focus on selection at linked sites also predict greater differentiation in regions of low recombination simply as a result of faster sorting of ancestral alleles even in the absence of gene flow. Moreover, identifying the actual amount of gene flow from patterns of genetic variation is tricky, because both ancestral polymorphism and migration lead to shared variation between recently diverged taxa. New analytic methods have been developed to help distinguish ancestral polymorphism from migration. Along with a growing number of datasets of multi-locus DNA sequence variation, these methods have spawned a renewed interest in speciation models with gene flow. Here, we review both speciation and population-genetic models that make explicit predictions about how the rate of recombination influences patterns of genetic variation within and between species. We then compare those predictions with empirical data of DNA sequence variation in rabbits and mice. We find strong support for the prediction that genomic regions experiencing low levels of recombination are more differentiated. In most cases, reduced gene flow appears to contribute to the pattern, although disentangling the relative contribution of reduced gene flow and selection at linked sites remains a challenge. We suggest fruitful areas of research that might help distinguish between different models.     

Departure from neutrality at the mitochondrial NADH dehydrogenase subunit 2 gene in humans,but not in chimpanzees.

To test whether patterns of mitochondrial DNA (mtDNA) variation are consistent with a neutral model of molecular evolution, nucleotide sequences were determined for the 1041 bp of the NADH dehydrogenase subunit 2 (ND2) gene in 20 geographically diverse humans and 20 common chimpanzees. Contingency tests of neutrality were performed using four mutational categories for the ND2 molecule: synonymous and nonsynonymous mutations in the transmembrane regions, and synonymous and nonsynonymous mutations in the surface regions. The following three topological mutational categories were also used: intraspecific tips, intraspecific interiors, and interspecific fixed differences. The analyses reveal a significantly greater number of nonsynonymous polymorphisms within human transmembrane regions than expected based on interspecific comparisons, and they are inconsistent with a neutral equilibrium model. This pattern of excess nonsynonymous polymorphism is not seen within chimpanzees. Statistical tests of neutrality, such as TAJIMA''s D test, and the D and F tests proposed by FU and LI, indicate an excess of low frequency polymorphisms in the human data, but not in the chimpanzee data. This is consistent with recent directional selection, a population bottleneck or background selection of slightly deleterious mutations in human mtDNA samples. The analyses further support the idea that mitochondrial genome evolution is governed by selective forces that have the potential to affect its use as a "neutral" marker in evolutionary and population genetic studies.