The signature of positive selection on standing genetic variation

Considerable interest is focused on the use of polymorphism data to identify regions of the genome that underlie recent adaptations. These searches are guided by a simple model of positive selection, in which a mutation is favored as soon as it arises. This assumption may not be realistic, as environmental changes and range expansions may lead previously neutral or deleterious alleles to become beneficial. We examine what effect this mode of selection has on patterns of variation at linked neutral sites by implementing a new coalescent model of positive directional selection on standing variation. In this model, a neutral allele arises and drifts in the population, then at frequency f becomes beneficial, and eventually reaches fixation. Depending on the value of f, this scenario can lead to a large variance in allele frequency spectra and in levels of linkage disequilibrium at linked, neutral sites. In particular, for intermediate f, the beneficial substitution often leads to a loss of rare alleles--a pattern that differs markedly from the signature of directional selection currently relied on by researchers. These findings highlight the importance of an accurate characterization of the effects of positive selection, if we are to reliably identify recent adaptations from polymorphism data.     

Allele frequency distribution under recurrent selective sweeps

The allele frequency of a neutral variant in a population is pushed either upward or downward by directional selection on a linked beneficial mutation ("selective sweeps"). DNA sequences sampled after the fixation of the beneficial allele thus contain an excess of rare neutral alleles. This study investigates the allele frequency distribution under selective sweep models using analytic approximation and simulation. First, given a single selective sweep at a fixed time, I derive an expression for the sampling probabilities of neutral mutants. This solution can be used to estimate the time of the fixation of a beneficial allele from sequence data. Next, I obtain an approximation to mean allele frequencies under recurrent selective sweeps. Under recurrent sweeps, the frequency spectrum is skewed toward rare alleles. However, the excess of high-frequency derived alleles, previously shown to be a signature of single selective sweeps, disappears with recurrent sweeps. It is shown that, using this approximation and multilocus polymorphism data, genomewide parameters of directional selection can be estimated.     

Fixation probability in a two-locus model by the ancestral recombination-selection graph

We use the ancestral influence graph (AIG) for a two-locus, two-allele selection model in the limit of a large population size to obtain an analytic approximation for the probability of ultimate fixation of a single mutant allele A. We assume that this new mutant is introduced at a given locus into a finite population in which a previous mutant allele B is already segregating with a wild type at another linked locus. We deduce that the fixation probability increases as the recombination rate increases if allele A is either in positive epistatic interaction with B and allele B is beneficial or in no epistatic interaction with B and then allele A itself is beneficial. This holds at least as long as the recombination fraction and the selection intensity are small enough and the population size is large enough. In particular this confirms the Hill-Robertson effect, which predicts that recombination renders more likely the ultimate fixation of beneficial mutants at different loci in a population in the presence of random genetic drift even in the absence of epistasis. More importantly, we show that this is true from weak negative epistasis to positive epistasis, at least under weak selection. In the case of deleterious mutants, the fixation probability decreases as the recombination rate increases. This supports Muller's ratchet mechanism to explain the accumulation of deleterious mutants in a population lacking recombination.     

A haplotype map of allohexaploid wheat reveals distinct patterns of selection on homoeologous genomes

BackgroundBread wheat is an allopolyploid species with a large, highly repetitive genome. To investigate the impact of selection on variants distributed among homoeologous wheat genomes and to build a foundation for understanding genotype-phenotype relationships, we performed population-scale re-sequencing of a diverse panel of wheat lines.ResultsA sample of 62 diverse lines was re-sequenced using the whole exome capture and genotyping-by-sequencing approaches. We describe the allele frequency, functional significance, and chromosomal distribution of 1.57 million single nucleotide polymorphisms and 161,719 small indels. Our results suggest that duplicated homoeologous genes are under purifying selection. We find contrasting patterns of variation and inter-variant associations among wheat genomes; this, in addition to demographic factors, could be explained by differences in the effect of directional selection on duplicated homoeologs. Only a small fraction of the homoeologous regions harboring selected variants overlapped among the wheat genomes in any given wheat line. These selected regions are enriched for loci associated with agronomic traits detected in genome-wide association studies.ConclusionsEvidence suggests that directional selection in allopolyploids rarely acted on multiple parallel advantageous mutations across homoeologous regions, likely indicating that a fitness benefit could be obtained by a mutation at any one of the homoeologs. Additional advantageous variants in other homoelogs probably either contributed little benefit, or were unavailable in populations subjected to directional selection. We hypothesize that allopolyploidy may have increased the likelihood of beneficial allele recovery by broadening the set of possible selection targets.

Electronic supplementary material

The online version of this article (doi:10.1186/s13059-015-0606-4) contains supplementary material, which is available to authorized users.     

Estimating the time since the fixation of a beneficial allele

The fixation of a beneficial allele in a population leaves a well-characterized signature in patterns of nucleotide variation at linked sites. This signature can be used to estimate the time since fixation from patterns of polymorphism in extant individuals. I introduce a method to assess the support in polymorphism data for a recent episode of directional positive selection and to estimate the time since fixation. I summarize the polymorphism data by three statistics that carry information about levels of diversity, the allele frequency spectrum, and the extent of allelic associations. Simulations are then used to obtain a sample from the posterior distribution of the time since fixation, conditional on the observed summaries. I test the performance of the approach on simulated data and apply it to the gene tb1 in maize. The data support the recent fixation of a favored allele, consistent with what is known about the importance of tb1 in the domestication process of maize.     

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.     

Selective sweeps in the presence of interference among partially linked loci

Recurrent directional selection on a partially recombining chromosome may cause a substantial reduction of standing genetic variation in natural populations. Previous studies of this effect, commonly called selective sweeps, assumed that at most one beneficial allele is on the way to fixation at a given time. However, for a high rate of selected substitutions and a low recombination rate, this assumption can easily be violated. We investigated this problem using full-forward simulations and analytical approximations. We found that interference between linked beneficial alleles causes a reduction of their fixation probabilities. The hitchhiking effect on linked neutral variation for a given substitution also slightly decreases due to interference. As a result, the strength of recurrent selective sweeps is weakened. However, this effect is significant only in chromosomal regions of relatively low recombination rates where the level of variation is greatly reduced. Therefore, previous results on recurrent selective sweeps although derived for a restricted parameter range are still valid. Analytical approximations are obtained for the case of complete linkage for which interference between competing beneficial alleles is maximal.     

Linking genetic mechanisms of heterozygosity-fitness correlations to footprints of selection at single loci

Investigations of heterozygosity-fitness correlations (HFCs) are central to the understanding how genetic diversity is maintained in natural populations. Advanced genome-wide approaches will enrich the number of functional loci to be tested. We argue that a combined analysis of the genetic mechanisms of HFCs and selection signals at single loci will allow researchers to better understand the micro-evolutionary basis of HFCs. Different dominance relationships among the alleles at the locus can lead to positive, negative or null HFCs depending on the allele frequency distribution. These scenarios differ in the temporal stability of the HFCs and in the patterns of allele frequency changes over time. Here, we describe a simple theoretical framework that links the analyses of heterozygosity-fitness associations (ecological timescale) with tests for selection signals (evolutionary timescale). Different genomic footprints of selection can be expected for the different underlying genetic mechanisms of HFCs, and this information can be independently used for the classification of HFCs. We suggest that in addition to inbreeding and single-locus overdominant effects also loci under directional selection could play a significant role in the development of heterozygosity-fitness effects in large natural populations under recent or fluctuating ecological changes.     

Genetic analysis of differentiation among breeding ponds reveals a candidate gene for local adaptation in Rana arvalis

One of the main questions in evolutionary and conservation biology is how geographical and environmental features of the landscape shape neutral and adaptive genetic variation in natural populations. The identification of genomic polymorphisms that account for adaptive variation can aid in finding candidate loci for local adaptation. Consequently, a comparison of spatial patterns in neutral markers and loci under selection may help disentangle the effects of gene flow, genetic drift and selection at the landscape scale. Many amphibians breed in wetlands, which differ in environmental conditions and in the degree of isolation, enhancing the potential for local adaptation. We used microsatellite markers to measure genetic differentiation among 17 local populations of Rana arvalis breeding in a network of wetlands. We found that locus RC08604 deviated from neutral expectations, suggesting that it is a good candidate for directional selection. We used a genetic network analysis to show that the allele distribution in this locus is correlated with habitat characteristics, whereas this was not the case at neutral markers that displayed a different allele distribution and population network in the study area. The graph approach illustrated the genomic heterogeneity (neutral loci vs. the candidate locus for directional selection) of gene exchange and genetic divergence among populations under directional selection. Limited gene flow between wetlands was only observed at the candidate genomic region under directional selection. RC08604 is partially located inside an up‐regulated thyroid‐hormone receptor (TRβ) gene coordinating the expression of other genes during metamorphosis and appears to be linked with variation in larval life‐history traits found among R. arvalis populations. We suggest that directional selection on genes coding larval life‐history traits is strong enough to maintain the divergence in these genomic regions, reducing the effective recombination of locally adapted alleles but not in other regions of the genome. Integrating this knowledge into conservation plans at the landscape scale will improve the design of management strategies to preserve adaptive genetic diversity in wetland networks.     

The effect of deleterious alleles on adaptation in asexual populations

We calculate the fixation probability of a beneficial allele that arises as the result of a unique mutation in an asexual population that is subject to recurrent deleterious mutation at rate U. Our analysis is an extension of previous works, which make a biologically restrictive assumption that selection against deleterious alleles is stronger than that on the beneficial allele of interest. We show that when selection against deleterious alleles is weak, beneficial alleles that confer a selective advantage that is small relative to U have greatly reduced probabilities of fixation. We discuss the consequences of this effect for the distribution of effects of alleles fixed during adaptation. We show that a selective sweep will increase the fixation probabilities of other beneficial mutations arising during some short interval afterward. We use the calculated fixation probabilities to estimate the expected rate of fitness improvement in an asexual population when beneficial alleles arise continually at some low rate proportional to U. We estimate the rate of mutation that is optimal in the sense that it maximizes this rate of fitness improvement. Again, this analysis relaxes the assumption made previously that selection against deleterious alleles is stronger than on beneficial alleles.     

The fixation of locally beneficial alleles in a metapopulation

Extinction, recolonization, and local adaptation are common in natural spatially structured populations. Understanding their effect upon genetic variation is important for systems such as genetically modified organism management or avoidance of drug resistance. Theoretical studies on the effect of extinction and recolonization upon genetic variance started appearing in the 1970s, but the role of local adaptation still has no good theoretical basis. Here we develop a model of a haploid species in a metapopulation in which a locally adapted beneficial allele is introduced. We study the effect of different spatial patterns of local adaptation, and different metapopulation dynamics, upon the fixation probability of the beneficial allele. Controlling for the average selection pressure, we find that a small area of positive selection can significantly increase the global probability of fixation. However, local adaptation becomes less important as extinction rate increases. Deme extinction and recolonization have a spatial smoothing effect that effectively reduces spatial variation in fitness.     

Using path analysis to measure natural selection

We expand current methods for calculating selection coefficients using path analysis and demonstrate how to analyse nonlinear selection. While this incorporation is a straightforward extension of current procedures, the rules for combining these traits to calculate selection coefficients can be complex. We demonstrate our method with an analysis of selection in an experimental population of Arabidopsis thaliana consisting of 289 individuals. Multiple regression analyses found positive directional selection and positive nonlinear selection only for inflorescence height. In contrast, the path analyses also revealed positive directional selection for number of rosette leaves and positive nonlinear selection for leaf number and time of inflorescence initiation. These changes in conclusions came about because indirect selection was converted into direct selection with the change in causal structure. Path analysis has great promise for improving our understanding of natural selection but must be used with caution since coefficient estimates depend on the assumed causal structure.     

Two steps forward, one step back: the pleiotropic effects of favoured alleles

Pleiotropy is one of the most commonly observed attributes of genes. Yet the extent and influence of pleiotropy have been underexplored in population genetics models. In this paper, I quantify the extent to which pleiotropy inhibits the spread of alleles in response to directional selection on a focal trait. Under the assumption that pleiotropic effects are extensive and deleterious, the fraction of alleles that are beneficial overall is severely limited by pleiotropy and rises nearly linearly with the strength of directional selection on the focal trait. Over a broad class of distribution of pleiotropic effects, the mean selective effect of those alleles that are beneficial overall is halved, on average, by pleiotropy. The fraction of new mutant alleles that are beneficial overall and that succeed in fixing within a population is even more severely limited when directional selection is weak, but it rises quadratically with the strength of directional selection. Finally, the mean selective effect of mutant alleles that are beneficial and succeed in fixing is reduced by one-third, on average, by pleiotropy. These results help to shape our understanding of the evolutionary inertia caused by pleiotropy.     

Evidence for complex selection on four‐fold degenerate sites in Drosophila melanogaster

We considered genome‐wide four‐fold degenerate sites from an African Drosophila melanogaster population and compared them to short introns. To include divergence and to polarize the data, we used its close relatives Drosophila simulans, Drosophila sechellia, Drosophila erecta and Drosophila yakuba as outgroups. In D. melanogaster, the GC content at four‐fold degenerate sites is higher than in short introns; compared to its relatives, more AT than GC is fixed. The former has been explained by codon usage bias (CUB) favouring GC; the latter by decreased intensity of directional selection or by increased mutation bias towards AT. With a biallelic equilibrium model, evidence for directional selection comes mostly from the GC‐rich ancestral base composition. Together with a slight mutation bias, it leads to an asymmetry of the unpolarized allele frequency spectrum, from which directional selection is inferred. Using a quasi‐equilibrium model and polarized spectra, however, only purifying and no directional selection is detected. Furthermore, polarized spectra are proportional to those of the presumably unselected short introns. As we have no evidence for a decrease in effective population size, relaxed CUB must be due to a reduction in the selection coefficient. Going beyond the biallelic model and considering all four bases, signs of directional selection are stronger. In contrast to short introns, complementary bases show strand specificity and allele frequency spectra depend on mutation directions. Hence, the traditional biallelic model to describe the evolution of four‐fold degenerate sites should be replaced by more complex models assuming only quasi‐equilibrium and accounting for all four bases.     

Operational sex ratio, sexual conflict and the intensity of sexual selection

Modern sexual selection theory indicates that reproductive costs rather than the operational sex ratio predict the intensity of sexual selection. We investigated sexual selection in the polygynandrous common lizard Lacerta vivipara . This species shows male aggression, causing high mating costs for females when adult sex ratios (ASR) are male-biased. We manipulated ASR in 12 experimental populations and quantified the intensity of sexual selection based on the relationship between reproductive success and body size. In sharp contrast to classical sexual selection theory predictions, positive directional sexual selection on male size was stronger and positive directional selection on female size weaker in female-biased populations than in male-biased populations. Thus, consistent with modern theory, directional sexual selection on male size was weaker in populations with higher female mating costs. This suggests that the costs of breeding, but not the operational sex ratio, correctly predicted the strength of sexual selection.     

Genomic effects of nucleotide substitutions in Drosophila simulans

Selective fixation of beneficial mutations reduces levels of linked, neutral variation. The magnitude of this "hitchhiking effect" is determined by the strength of selection and the recombination rate between selected and neutral sites. Thus, depending on the values of these parameters and the frequency with which directional selection occurs, the genomic scale over which directional selection reduces levels of linked variation may vary widely. Here we present a permutation-based analysis of nucleotide polymorphisms and fixations in Drosophila simulans. We show evidence of pervasive small-scale hitchhiking effects in this lineage. Furthermore, our results reveal that different types of fixations are associated with different levels of linked variation.     

A Model-Based Approach for Identifying Signatures of Ancient Balancing Selection in Genetic Data

While much effort has focused on detecting positive and negative directional selection in the human genome, relatively little work has been devoted to balancing selection. This lack of attention is likely due to the paucity of sophisticated methods for identifying sites under balancing selection. Here we develop two composite likelihood ratio tests for detecting balancing selection. Using simulations, we show that these methods outperform competing methods under a variety of assumptions and demographic models. We apply the new methods to whole-genome human data, and find a number of previously-identified loci with strong evidence of balancing selection, including several HLA genes. Additionally, we find evidence for many novel candidates, the strongest of which is FANK1, an imprinted gene that suppresses apoptosis, is expressed during meiosis in males, and displays marginal signs of segregation distortion. We hypothesize that balancing selection acts on this locus to stabilize the segregation distortion and negative fitness effects of the distorter allele. Thus, our methods are able to reproduce many previously-hypothesized signals of balancing selection, as well as discover novel interesting candidates.     

On the fixation process of a beneficial mutation in a variable environment

A population that adapts to gradual environmental change will typically experience temporal variation in its population size and the selection pressure. On the basis of the mathematical theory of inhomogeneous branching processes, we present a framework to describe the fixation process of a single beneficial allele under these conditions. The approach allows for arbitrary time-dependence of the selection coefficient s(t) and the population size N(t), as may result from an underlying ecological model. We derive compact analytical approximations for the fixation probability and the distribution of passage times for the beneficial allele to reach a given intermediate frequency. We apply the formalism to several biologically relevant scenarios, such as linear or cyclic changes in the selection coefficient, and logistic population growth. Comparison with computer simulations shows that the analytical results are accurate for a large parameter range, as long as selection is not very weak.     

Selective sweeps for recessive alleles and for other modes of dominance

A selective sweep describes the reduction of linked genetic variation due to strong positive selection. If s is the fitness advantage of a homozygote for the beneficial allele and h its dominance coefficient, it is usually assumed that h = 1/2, i.e. the beneficial allele is co-dominant. We complement existing theory for selective sweeps by assuming that h is any value in [0, 1]. We show that genetic diversity patterns under selective sweeps with strength s and dominance 0 < h < 1 are similar to co-dominant sweeps with selection strength 2hs. Moreover, we focus on the case h = 0 of a completely recessive beneficial allele. We find that the length of the sweep, i.e. the time from occurrence until fixation of the beneficial allele, is of the order of \({\sqrt{N/s}}\) generations, if N is the population size. Simulations as well as our results show that genetic diversity patterns in the recessive case h = 0 greatly differ from all other cases.     

Directional evolution for microsatellite size in maize

Directional evolution in microsatellites is the tendency for microsatellites either to increase or to decrease in size over time between populations. We analyzed 99 microsatellite loci in a sample of 193 maize plants representing the entire pre-Columbian range of this crop for evidence of directional evolution. We took advantage of the known phylogeographic history of maize with the independent movement of maize from its ancestral location in Mexico to North and South America. We show that there is an increase in the average allele size of microsatellites in the geographically derived North and South American groups relative to the ancestral Mexican group. We also show that there is a negative correlation between average allele size and altitude in all three groups. Directional evolution in maize microsatellites can be explained by changes in the mutation rate over time and space, changes in the degree of mutational bias to a larger allele, demographic differences between the ancestral and geographically derived populations, and/or scenarios involving selection on microsatellite size. The occurrence of directional evolution for microsatellite size indicates that the estimation of population parameters with microsatellite data in maize should be done with caution.