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.     

The Genealogy of Samples in Models with Selection

We introduce the genealogy of a random sample of genes taken from a large haploid population that evolves according to random reproduction with selection and mutation. Without selection, the genealogy is described by Kingman''s well-known coalescent process. In the selective case, the genealogy of the sample is embedded in a graph with a coalescing and branching structure. We describe this graph, called the ancestral selection graph, and point out differences and similarities with Kingman''s coalescent. We present simulations for a two-allele model with symmetric mutation in which one of the alleles has a selective advantage over the other. We find that when the allele frequencies in the population are already in equilibrium, then the genealogy does not differ much from the neutral case. This is supported by rigorous results. Furthermore, we describe the ancestral selection graph for other selective models with finitely many selection classes, such as the K-allele models, infinitely-many-alleles models, DNA sequence models, and infinitely-many-sites models, and briefly discuss the diploid case.     

Patterns of neutral diversity under general models of selective sweeps

Two major sources of stochasticity in the dynamics of neutral alleles result from resampling of finite populations (genetic drift) and the random genetic background of nearby selected alleles on which the neutral alleles are found (linked selection). There is now good evidence that linked selection plays an important role in shaping polymorphism levels in a number of species. One of the best-investigated models of linked selection is the recurrent full-sweep model, in which newly arisen selected alleles fix rapidly. However, the bulk of selected alleles that sweep into the population may not be destined for rapid fixation. Here we develop a general model of recurrent selective sweeps in a coalescent framework, one that generalizes the recurrent full-sweep model to the case where selected alleles do not sweep to fixation. We show that in a large population, only the initial rapid increase of a selected allele affects the genealogy at partially linked sites, which under fairly general assumptions are unaffected by the subsequent fate of the selected allele. We also apply the theory to a simple model to investigate the impact of recurrent partial sweeps on levels of neutral diversity and find that for a given reduction in diversity, the impact of recurrent partial sweeps on the frequency spectrum at neutral sites is determined primarily by the frequencies rapidly achieved by the selected alleles. Consequently, recurrent sweeps of selected alleles to low frequencies can have a profound effect on levels of diversity but can leave the frequency spectrum relatively unperturbed. In fact, the limiting coalescent model under a high rate of sweeps to low frequency is identical to the standard neutral model. The general model of selective sweeps we describe goes some way toward providing a more flexible framework to describe genomic patterns of diversity than is currently available.     

Transposable elements in natural populations with a mixture of selected and neutral insertion sites.

This paper examines models of the population dynamics of transposable elements when chromosomal sites vary with respect to the effect on fitness of mutations caused by element insertions. Element abundance is assumed to be stabilised solely by the joint results of transposition, excision, and selection against insertional mutations. When there are only two classes of site, selected and neutral, it is hard to find parameter values for which numbers of elements are maintained that match the findings from surveys of Drosophila populations, as elements tend to accumulate at high frequencies at the neutral sites. It is similarly hard to produce realistic equilibria with three classes of site (strongly selected, weakly selected, and neutral), when elements can transpose out of the neutral sites. If transposition from neutral sites is impossible, as might be the case for elements inserted into centric heterochromatin, then realistic equilibria can be generated if there is very weak selection against elements inserted into the majority of non-neutral sites. This model predicts a modest over-representation of elements at the neutral sites. It also predicts that elements should be under-represented on the X chromosome compared with the autosomes, but this is not generally found to be the case. It is concluded that selection against insertional mutations is unlikely to be the major factor involved in the containment of element abundance.     

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.     

A multi-dimensional coalescent process applied to multi-allelic selection models and migration models

For a sample of two genes from a population divided into an arbitrary number of allele classes, a general mathematical framework is developed to address the expectation and variance of the time of the most recent common ancestor. Depending on the meaning of allele classes and the manner in which genes can change among them, this framework can be applied to a diversity of population genetic models. By adoption of the infinite sites model, the effect on heterozygosity is modelled for balancing selection among allele classes, mutation between allele classes, migration among populations, and gene conversion between loci. Most results are described for a continuous time approximation to a discrete generation model. It is also shown how the discrete generation model can be used to study the hitch-hiking effect of favorable mutations.     

Genealogies and weak purifying selection

The assumption that selection alters the genealogical tree of a sample of alleles from a population relative to the neutral expectation underlies several "tests of neutrality." Two recent papers have studied the effect of purifying selection; their suggestive but incomplete results indicate that, in the single site case, the shape of a gene genealogy for a locus may differ only from the neutral expectation. We verify this finding for weak selection using the "ancestral selection graph." We consider a wider range of models, including both a four-allele single-site model and an infinite-sites model. Our results confirm the previous claim for the symmetric-mutation single site model. We emphasize, however, that a neutral-seeming genealogy is consistent with detectable effects of selection on the distribution of allele frequences within the sample. With selection operating, the information about a sample cannot be reduced to the genealogy. As a result, a distinction needs to be made between the selected sites themselves, for which the genealogy offers insufficient information, and linked neutral variation. This distinction seems to have been overlooked in previous papers, yet it has significant implications for the interpretation of data on DNA sequence variation. In particular, it predicts that under purifying selection, the frequency spectrum of neutral mutations will not reflect the skew toward rare polymorphisms at replacement sites even if there is no recombination between them. We caution, however, that the effect of weak selection on the genealogy is specific to the model; a (more realistic) model of multiple linked sites could lead to a more distorted genealogy than is observed for a single site.     

The effects of multilocus balancing selection on neutral variability

We studied the effect of multilocus balancing selection on neutral nucleotide variability at linked sites by simulating a model where diallelic polymorphisms are maintained at an arbitrary number of selected loci by means of symmetric overdominance. Different combinations of alleles define different genetic backgrounds that subdivide the population and strongly affect variability. Several multilocus fitness regimes with different degrees of epistasis and gametic disequilibrium are allowed. Analytical results based on a multilocus extension of the structured coalescent predict that the expected linked neutral diversity increases exponentially with the number of selected loci and can become extremely large. Our simulation results show that although variability increases with the number of genetic backgrounds that are maintained in the population, it is reduced by random fluctuations in the frequencies of those backgrounds and does not reach high levels even in very large populations. We also show that previous results on balancing selection in single-locus systems do not extend to the multilocus scenario in a straightforward way. Different patterns of linkage disequilibrium and of the frequency spectrum of neutral mutations are expected under different degrees of epistasis. Interestingly, the power to detect balancing selection using deviations from a neutral distribution of allele frequencies seems to be diminished under the fitness regime that leads to the largest increase of variability over the neutral case. This and other results are discussed in the light of data from the Mhc.     

The effect of selection on genealogies

The coalescent process can describe the effects of selection at linked loci only if selection is so strong that genotype frequencies evolve deterministically. Here, we develop methods proposed by Kaplan, Darden, and Hudson to find the effects of weak selection. We show that the overall effect is given by an extension to Price's equation: the change in properties such as moments of coalescence times is equal to the covariance between those properties and the fitness of the sample of genes. The distribution of coalescence times differs substantially between allelic classes, even in the absence of selection. However, the average coalescence time between randomly chosen genes is insensitive to the current allele frequency and is affected significantly by purifying selection only if deleterious mutations are common and selection is strong (i.e., the product of population size and selection coefficient, Ns>3). Balancing selection increases mean coalescence times, but the effect becomes large only when mutation rates between allelic classes are low and when selection is extremely strong. Our analysis supports previous simulations that show that selection has surprisingly little effect on genealogies. Moreover, small fluctuations in allele frequency due to random drift can greatly reduce any such effects. This will make it difficult to detect the action of selection from neutral variation alone.     

THE MAINTENANCE OF GENETIC VARIATION FOR OVIPOSITION RATE IN TWO‐SPOTTED SPIDER MITES: INFERENCES FROM ARTIFICIAL SELECTION

Despite the directional selection acting on life‐history traits, substantial amounts of standing variation for these traits have frequently been found. This variation may result from balancing selection (e.g., through genetic trade‐offs) or from mutation‐selection balance. These mechanisms affect allele frequencies in different ways: Under balancing selection alleles are maintained at intermediate frequencies, whereas under mutation‐selection balance variation is generated by deleterious mutations and removed by directional selection, which leads to asymmetry in the distribution of allele frequencies. To investigate the importance of these two mechanisms in maintaining heritable variation in oviposition rate of the two‐spotted spider mite, we analyzed the response to artificial selection. In three replicate experiments, we selected for higher and lower oviposition rate, compared to control lines. A response to selection only occurred in the downward direction. Selection for lower oviposition rate did not lead to an increase in any other component of fitness, but led to a decline in female juvenile survival. The results suggest standing variation for oviposition rate in this population consists largely of deleterious alleles, as in a mutation‐selection balance. Consequently, the standing variation for this trait does not appear to be indicative of its adaptive potential.     

Evidence for convergent nucleotide evolution and high allelic turnover rates at the complementary sex determiner gene of Western and Asian honeybees

Our understanding of the impact of recombination, mutation, genetic drift, and selection on the evolution of a single gene is still limited. Here we investigate the impact of all these evolutionary forces at the complementary sex determiner (csd) gene that evolves under a balancing mode of selection. Females are heterozygous at the csd gene and males are hemizygous; diploid males are lethal and occur when csd is homozygous. Rare alleles thus have a selective advantage, are seldom lost by the effect of genetic drift, and are maintained over extended periods of time when compared with neutral polymorphisms. Here, we report on the analysis of 17, 19, and 15 csd alleles of Apis cerana, Apis dorsata, and Apis mellifera honeybees, respectively. We observed great heterogeneity of synonymous (piS) and nonsynonymous (piN) polymorphisms across the gene, with a consistent peak in exons 6 and 7. We propose that exons 6 and 7 encode the potential specifying domain (csd-PSD) that has accumulated elevated nucleotide polymorphisms over time by balancing selection. We observed no direct evidence that balancing selection favors the accumulation of nonsynonymous changes at csd-PSD (piN/piS ratios are all <1, ranging from 0.6 to 0.95). We observed an excess of shared nonsynonymous changes, which suggest that strong evolutionary constraints are operating at csd-PSD resulting in the independent accumulation of the same nonsynonymous changes in different alleles across species (convergent evolution). Analysis of csd-PSD genealogy revealed relatively short average coalescence times ( approximately 6 Myr), low average synonymous nucleotide diversity (piS < 0.09), and a lack of trans-specific alleles that substantially contrasts with previously analyzed loci under strong balancing selection. We excluded the possibility of a burst of diversification after population bottlenecking and intragenic recombination as explanatory factors, leaving high turnover rates as the explanation for this observation. By comparing observed allele richness and average coalescence times with a simplified model of csd-coalescence, we found that small long-term population sizes (i.e., N(e) < 10(4)), but not high mutation rates, can explain short maintenance times, implicating a strong historical impact of genetic drift on the molecular evolution of highly social honeybees.     

The probability and chromosomal extent of trans-specific polymorphism

Balancing selection may result in trans-specific polymorphism: the maintenance of allelic classes that transcend species boundaries by virtue of being more ancient than the species themselves. At the selected site, gene genealogies are expected not to reflect the species tree. Because of linkage, the same will be true for part of the surrounding chromosomal region. Here we obtain various approximations for the distribution of the length of this region and discuss the practical implications of our results. Our main finding is that the trans-specific region surrounding a single-locus balanced polymorphism is expected to be quite short, probably too short to be readily detectable. Thus lack of obvious trans-specific polymorphism should not be taken as evidence against balancing selection. When trans-specific polymorphism is obvious, on the other hand, it may be reasonable to argue that selection must be acting on multiple sites or that recombination is suppressed in the surrounding region.     

Extending the coalescent to multilocus systems: the case of balancing selection

Natural populations are structured spatially into local populations and genetically into diverse 'genetic backgrounds' defined by different combinations of selected alleles. If selection maintains genetic backgrounds at constant frequency then neutral diversity is enhanced. By contrast, if background frequencies fluctuate then diversity is reduced. Provided that the population size of each background is large enough, these effects can be described by the structured coalescent process. Almost all the extant results based on the coalescent deal with a single selected locus. Yet we know that very large numbers of genes are under selection and that any substantial effects are likely to be due to the cumulative effects of many loci. Here, we set up a general framework for the extension of the coalescent to multilocus scenarios and we use it to study the simplest model, where strong balancing selection acting on a set of n loci maintains 2n backgrounds at constant frequencies and at linkage equilibrium. Analytical results show that the expected linked neutral diversity increases exponentially with the number of selected loci and can become extremely large. However, simulation results reveal that the structured coalescent approach breaks down when the number of backgrounds approaches the population size, because of stochastic fluctuations in background frequencies. A new method is needed to extend the structured coalescent to cases with large numbers of backgrounds.     

Evaluating outlier loci and their effect on the identification of pedigree errors

Homozygosity outlier loci, which show patterns of variation that are extremely divergent from the rest of the genome, can be evaluated by comparison of the homozygosity under Hardy-Weinberg proportions (the sum of the squares of allele frequencies) with the expected homozygosity under neutrality. Such outlier loci are potentially under selection (balancing selection or directional selection) when genome-wide effects (such as bottleneck and rapid population growth) are excluded. Outlier loci show skewed allele frequencies with respect to neutrality and may therefore affect the identification of pedigree errors. However, choosing neutral markers (excluding outlier loci) for the identification of pedigree errors has been neglected thus far. Our results showed that 4.1%, 5.5%, and 1.5% of the microsatellite markers, Illumina single-nucleotide polymorphisms (SNPs), and Affymetrix SNPs, respectively, on the autosomes appear to be under balancing selection (p or=40%) appear to be under balancing selection. Pedigree structure errors in 15 of 143 pedigrees were detected using microsatellite markers from the autosomes and/or selected SNPs from chromosomes 1 to 18 of the Illumina and/or selected SNPs from chromosomes 1 to 16 of the Affymetrix. Outlier loci did not make a major difference to the identification of pedigree errors. The Collaborative Study on the Genetics of Alcoholism data has pedigree errors and some of them may be due to sample mix up.     

The stationary distribution of allele frequencies when selection acts at unlinked loci

We consider population genetics models where selection acts at a set of unlinked loci. It is known that if the fitness of an individual is multiplicative across loci, then these loci are independent. We consider general selection models, but assume parent-independent mutation at each locus. For such a model, the joint stationary distribution of allele frequencies is proportional to the stationary distribution under neutrality multiplied by a known function of the mean fitness of the population. We further show how knowledge of this stationary distribution enables direct simulation of the genealogy of a sample at a single-locus. For a specific selection model appropriate for complex disease genes, we use simulation to determine what features of the genealogy differ between our general selection model and a multiplicative model.     

Partial protection from cyclical selection generates a high level of polymorphism at multiple non‐neutral sites

Temporally varying selection is known to maintain genetic polymorphism under certain restricted conditions. However, if part of a population can escape from selective pressure, a condition called the “storage effect” is produced, which greatly promotes balanced polymorphism. We investigate whether seasonally fluctuating selection can maintain polymorphism at multiple loci, if cyclically fluctuating selection is not acting on a subpopulation called a “refuge.” A phenotype with a seasonally oscillating optimum is determined by alleles at multiple sites, across which the effects of mutations on phenotype are distributed randomly. This model resulted in long‐term polymorphism at multiple sites, during which allele frequencies oscillate heavily, greatly increasing the level of nonneutral polymorphism. The level of polymorphism at linked neutral sites was either higher or lower than expected for unlinked neutral loci. Overall, these results suggest that for a protein‐coding sequence, the nonsynonymous‐to‐synonymous ratio of polymorphism may exceed one. In addition, under randomly perturbed environmental oscillation, different sets of sites may take turns harboring long‐term polymorphism, thus making trans‐species polymorphism (which has been predicted as a classical signature of balancing selection) less likely.     

The origin of selection signatures on bovine chromosome 6

The extent and pattern of linkage disequilibrium (LD) between closely spaced markers contain information about population history, including past population size and selection history. Selection signatures can be identified by comparing the LD surrounding a putative selected allele at a locus to the putative non-selected allele. In livestock populations, locations of selection signatures identified in this way should be correlated with QTL affecting production traits, as the populations have been under strong artificial selection for these traits. We used a dense SNP map of bovine chromosome 6 to characterize the pattern of LD on this chromosome in Norwegian Red cattle, a breed which has been strongly selected for milk production. The pattern of LD was generally consistent with strong selection in regions containing QTL affecting milk production traits, including a strong selection signature in a region containing a mutation known to affect milk production. The results demonstrate that in livestock populations, the origin of selection signatures will often be QTL for livestock production traits, and illustrate the value of selection signatures in uncovering new mutations with potential effects on quantitative traits.     

Balancing selection at a frog antimicrobial peptide locus: fluctuating immune effector alleles?

Balancing selection is common on many defense genes, but it has rarely been reported for immune effector proteins such as antimicrobial peptides (AMPs). We describe genetic diversity at a brevinin-1 AMP locus in three species of leopard frogs (Rana pipiens, Rana blairi, and Rana palustris). Several highly divergent allelic lineages are segregating at this locus. That this unusual pattern results from balancing selection is demonstrated by multiple lines of evidence, including a ratio of nonsynonymous/synonymous polymorphism significantly higher than 1, the ZnS test, incongruence between the number of segregating sites and haplotype diversity, and significant Tajima's D values. Our data are more consistent with a model of fluctuating selection in which alleles change frequencies over time than with a model of stable balancing selection such as overdominance. Evidence for fluctuating selection includes skewed allele frequencies, low levels of synonymous variation, nonneutral values of Tajima's D within allelic lineages, an inverse relationship between the frequency of an allelic lineage and its degree of polymorphism, and divergent allele frequencies among populations. AMP loci could be important sites of adaptive genetic diversity, with consequences for host-pathogen coevolution and the ability of species to resist disease epidemics.     

Recombination, balancing selection and phylogenies in MHC and self-incompatibility genes.

Using a coalescent model of multiallelic balancing selection with recombination, the genealogical process as a function of recombinational distance from a site under selection is investigated. We find that the shape of the phylogenetic tree is independent of the distance to the site under selection. Only the timescale changes from the value predicted by Takahata's allelic genealogy at the site under selection, converging with increasing recombination to the timescale of the neutral coalescent. However, if nucleotide sequences are simulated over a recombining region containing a site under balancing selection, a phylogenetic tree constructed while ignoring such recombination is strongly affected. This is true even for small rates of recombination. Published studies of multiallelic balancing selection, i.e., the major histocompatibility complex (MHC) of vertebrates, gametophytic and sporophytic self-incompatibility of plants, and incompatibility of fungi, all observe allelic genealogies with unexpected shapes. We conclude that small absolute levels of recombination are compatible with these observed distortions of the shape of the allelic genealogy, suggesting a possible cause of these observations. Furthermore, we illustrate that the variance in the coalescent with recombination process makes it difficult to locate sites under selection and to estimate the selection coefficient from levels of variability.