Patterns of neutral diversity under general models of selective sweeps

The impacts of positive selection on genomic variation in Drosophila serrata: Insights from a deep learning approach

This study explores the impact of positive selection on the genetic composition of a Drosophila serrata population in eastern Australia through a comprehensive analysis of 110 whole genome sequences. Utilizing an advanced deep learning algorithm (partialS/HIC) and a range of inferred demographic histories, we identified that approximately 14% of the genome is directly affected by sweeps, with soft sweeps being more prevalent (10.6%) than hard sweeps (2.1%), and partial sweeps being uncommon (1.3%). The algorithm demonstrated robustness to demographic assumptions in classifying complete sweeps but faced challenges in distinguishing neutral regions from partial sweeps and linked regions under demographic misspecification. The findings reveal the indirect influence of sweeps on nearly two-thirds of the genome through linkage, with an over-representation of putatively deleterious variants suggesting that positive selection drags deleterious variants to higher frequency due to hitchhiking with beneficial loci. Gene ontology enrichment analysis further supported our confidence in the accuracy of sweep detection as several traits expected to be under positive selection due to evolutionary arms races (e.g. immunity) were detected in hard sweeps. This study provides valuable insights into the direct and indirect contributions of positive selection in shaping genomic variation in natural populations.

Pervasive conservation of intron number and other genetic elements revealed by a chromosome-level genomic assembly of the hyper-polymorphic nematode Caenorhabditis brenneri

With within-species genetic diversity estimates that span the gambit of that seen across the entirety of animals, the Caenorhabditis genus of nematodes holds unique potential to provide insights into how population size and reproductive strategies influence gene and genome organization and evolution. Our study focuses on Caenorhabditis brenneri, currently known as one of the most genetically diverse nematodes within its genus and metazoan phyla. Here, we present a high-quality gapless genome assembly and annotation for C. brenneri, revealing a common nematode chromosome arrangement characterized by gene-dense central regions and repeat rich peripheral parts. Comparison of C. brenneri with other nematodes from the 'Elegans' group revealed conserved macrosynteny but a lack of microsynteny, characterized by frequent rearrangements and low correlation iof orthogroup sizes, indicative of high rates of gene turnover. We also assessed genome organization within corresponding syntenic blocks in selfing and outcrossing species, affirming that selfing species predominantly experience loss of both genes and intergenic DNA. Comparison of gene structures revealed strikingly small number of shared introns across species, yet consistent distributions of intron number and length, regardless of population size or reproductive mode, suggesting that their evolutionary dynamics are primarily reflective of functional constraints. Our study provides valuable insights into genome evolution and expands the nematode genome resources with the highly genetically diverse C. brenneri, facilitating research into various aspects of nematode biology and evolutionary processes.

Sweepstakes reproduction facilitates rapid adaptation in highly fecund populations

Adaptation enables natural populations to survive in a changing environment. Understanding the mechanics of adaptation is therefore crucial for learning about the evolution and ecology of natural populations. We focus on the impact of random sweepstakes on selection in highly fecund haploid and diploid populations partitioned into two genetic types, with one type conferring selective advantage. For the diploid populations, we incorporate various dominance mechanisms. We assume that the populations may experience recurrent bottlenecks. In random sweepstakes, the distribution of individual recruitment success is highly skewed, resulting in a huge variance in the number of offspring contributed by the individuals present in any given generation. Using computer simulations, we investigate the joint effects of random sweepstakes, recurrent bottlenecks and dominance mechanisms on selection. In our framework, bottlenecks allow random sweepstakes to have an effect on the time to fixation, and in diploid populations, the effect of random sweepstakes depends on the dominance mechanism. We describe selective sweepstakes that are approximated by recurrent sweeps of strongly beneficial allelic types arising by mutation. We demonstrate that both types of sweepstakes reproduction may facilitate rapid adaptation (as defined based on the average time to fixation of a type conferring selective advantage conditioned on fixation of the type). However, whether random sweepstakes cause rapid adaptation depends also on their interactions with bottlenecks and dominance mechanisms. Finally, we review a case study in which a model of recurrent sweeps is shown to essentially explain population genomic data from Atlantic cod.

The pseudoentropy of allele frequency trajectories, the persistence of variation, and the effective population size

To concisely describe how genetic variation, at individual loci or across whole genomes, changes over time, and to follow transitory allelic changes, we introduce a quantity related to entropy, that we term pseudoentropy. This quantity emerges in a diffusion analysis of the mean time a mutation segregates in a population. For a neutral locus with an arbitrary number of alleles, the mean time of segregation is generally proportional to the pseudoentropy of initial allele frequencies. After the initial time point, pseudoentropy generally decreases, but other behaviours are possible, depending on the genetic diversity and selective forces present. For a biallelic locus, pseudoentropy and entropy coincide, but they are distinct quantities with more than two alleles. Thus for populations with multiple biallelic loci, the language of entropy suffices. Then entropy, combined across loci, serves as a concise description of genetic variation. We used individual based simulations to explore how this entropy behaves under different evolutionary scenarios. In agreement with predictions, the entropy associated with unlinked neutral loci decreases over time. However, deviations from free recombination and neutrality have clear and informative effects on the entropy's behaviour over time. Analysis of publicly available data of a natural D. melanogaster population, that had been sampled over seven years, using a sliding-window approach, yielded considerable variation in entropy trajectories of different genomic regions. These mostly follow a pattern that suggests a substantial effective population size and a limited effect of positive selection on genome-wide diversity over short time scales.

Genomic diversity landscapes in outcrossing and selfing Caenorhabditis nematodes

Caenorhabditis nematodes form an excellent model for studying how the mode of reproduction affects genetic diversity, as some species reproduce via outcrossing whereas others can self-fertilize. Currently, chromosome-level patterns of diversity and recombination are only available for self-reproducing Caenorhabditis, making the generality of genomic patterns across the genus unclear given the profound potential influence of reproductive mode. Here we present a whole-genome diversity landscape, coupled with a new genetic map, for the outcrossing nematode C. remanei. We demonstrate that the genomic distribution of recombination in C. remanei, like the model nematode C. elegans, shows high recombination rates on chromosome arms and low rates toward the central regions. Patterns of genetic variation across the genome are also similar between these species, but differ dramatically in scale, being tenfold greater for C. remanei. Historical reconstructions of variation in effective population size over the past million generations echo this difference in polymorphism. Evolutionary simulations demonstrate how selection, recombination, mutation, and selfing shape variation along the genome, and that multiple drivers can produce patterns similar to those observed in natural populations. The results illustrate how genome organization and selection play a crucial role in shaping the genomic pattern of diversity whereas demographic processes scale the level of diversity across the genome as a whole.

Sweepstakes reproductive success via pervasive and recurrent selective sweeps

Highly fecund natural populations characterized by high early mortality abound, yet our knowledge about their recruitment dynamics is somewhat rudimentary. This knowledge gap has implications for our understanding of genetic variation, population connectivity, local adaptation, and the resilience of highly fecund populations. The concept of sweepstakes reproductive success, which posits a considerable variance and skew in individual reproductive output, is key to understanding the distribution of individual reproductive success. However, it still needs to be determined whether highly fecund organisms reproduce through sweepstakes and, if they do, the relative roles of neutral and selective sweepstakes. Here, we use coalescent-based statistical analysis of population genomic data to show that selective sweepstakes likely explain recruitment dynamics in the highly fecund Atlantic cod. We show that the Kingman coalescent (modelling no sweepstakes) and the Xi-Beta coalescent (modelling random sweepstakes), including complex demography and background selection, do not provide an adequate fit for the data. The Durrett-Schweinsberg coalescent, in which selective sweepstakes result from recurrent and pervasive selective sweeps of new mutations, offers greater explanatory power. Our results show that models of sweepstakes reproduction and multiple-merger coalescents are relevant and necessary for understanding genetic diversity in highly fecund natural populations. These findings have fundamental implications for understanding the recruitment variation of fish stocks and general evolutionary genomics of high-fecundity organisms.

Spatial structure alters the site frequency spectrum produced by hitchhiking

The reduction of genetic diversity due to genetic hitchhiking is widely used to find past selective sweeps from sequencing data, but very little is known about how spatial structure affects hitchhiking. We use mathematical modeling and simulations to find the unfolded site frequency spectrum left by hitchhiking in the genomic region of a sweep in a population occupying a 1D range. For such populations, sweeps spread as Fisher waves, rather than logistically. We find that this leaves a characteristic 3-part site frequency spectrum at loci very close to the swept locus. Very low frequencies are dominated by recent mutations that occurred after the sweep and are unaffected by hitchhiking. At moderately low frequencies, there is a transition zone primarily composed of alleles that briefly "surfed" on the wave of the sweep before falling out of the wavefront, leaving a spectrum close to that expected in well-mixed populations. However, for moderate-to-high frequencies, there is a distinctive scaling regime of the site frequency spectrum produced by alleles that drifted to fixation in the wavefront and then were carried throughout the population. For loci slightly farther away from the swept locus on the genome, recombination is much more effective at restoring diversity in 1D populations than it is in well-mixed ones. We find that these signatures of space can be strong even in apparently well-mixed populations with negligible spatial genetic differentiation, suggesting that spatial structure may frequently distort the signatures of hitchhiking in natural populations.

Linkage disequilibrium between rare mutations

The statistical associations between mutations, collectively known as linkage disequilibrium, encode important information about the evolutionary forces acting within a population. Yet in contrast to single-site analogues like the site frequency spectrum, our theoretical understanding of linkage disequilibrium remains limited. In particular, little is currently known about how mutations with different ages and fitness costs contribute to expected patterns of linkage disequilibrium, even in simple settings where recombination and genetic drift are the major evolutionary forces. Here, I introduce a forward-time framework for predicting linkage disequilibrium between pairs of neutral and deleterious mutations as a function of their present-day frequencies. I show that the dynamics of linkage disequilibrium become much simpler in the limit that mutations are rare, where they admit a simple heuristic picture based on the trajectories of the underlying lineages. I use this approach to derive analytical expressions for a family of frequency-weighted linkage disequilibrium statistics as a function of the recombination rate, the frequency scale, and the additive and epistatic fitness costs of the mutations. I find that the frequency scale can have a dramatic impact on the shapes of the resulting linkage disequilibrium curves, reflecting the broad range of time scales over which these correlations arise. I also show that the differences between neutral and deleterious linkage disequilibrium are not purely driven by differences in their mutation frequencies and can instead display qualitative features that are reminiscent of epistasis. I conclude by discussing the implications of these results for recent linkage disequilibrium measurements in bacteria. This forward-time approach may provide a useful framework for predicting linkage disequilibrium across a range of evolutionary scenarios.

Polygenic adaptation after a sudden change in environment

Polygenic adaptation is thought to be ubiquitous, yet remains poorly understood. Here, we model this process analytically, in the plausible setting of a highly polygenic, quantitative trait that experiences a sudden shift in the fitness optimum. We show how the mean phenotype changes over time, depending on the effect sizes of loci that contribute to variance in the trait, and characterize the allele dynamics at these loci. Notably, we describe the two phases of the allele dynamics: The first is a rapid phase, in which directional selection introduces small frequency differences between alleles whose effects are aligned with or opposed to the shift, ultimately leading to small differences in their probability of fixation during a second, longer phase, governed by stabilizing selection. As we discuss, key results should hold in more general settings and have important implications for efforts to identify the genetic basis of adaptation in humans and other species.

A continent-wide high genetic load in African buffalo revealed by clines in the frequency of deleterious alleles, genetic hitchhiking and linkage disequilibrium

A high genetic load can negatively affect population viability and increase susceptibility to diseases and other environmental stressors. Prior microsatellite studies of two African buffalo (Syncerus caffer) populations in South Africa indicated substantial genome-wide genetic load due to high-frequency occurrence of deleterious alleles. The occurrence of these alleles, which negatively affect male body condition and bovine tuberculosis resistance, throughout most of the buffalo's range were evaluated in this study. Using available microsatellite data (2-17 microsatellite loci) for 1676 animals from 34 localities (from 25°S to 5°N), we uncovered continent-wide frequency clines of microsatellite alleles associated with the aforementioned male traits. Frequencies decreased over a south-to-north latitude range (average per-locus Pearson r = -0.22). The frequency clines coincided with a multilocus-heterozygosity cline (adjusted R2 = 0.84), showing up to a 16% decrease in southern Africa compared to East Africa. Furthermore, continent-wide linkage disequilibrium (LD) at five linked locus pairs was detected, characterized by a high fraction of positive interlocus associations (0.66, 95% CI: 0.53, 0.77) between male-deleterious-trait-associated alleles. Our findings suggest continent-wide and genome-wide selection of male-deleterious alleles driven by an earlier observed sex-chromosomal meiotic drive system, resulting in frequency clines, reduced heterozygosity due to hitchhiking effects and extensive LD due to male-deleterious alleles co-occurring in haplotypes. The selection pressures involved must be high to prevent destruction of allele-frequency clines and haplotypes by LD decay. Since most buffalo populations are stable, these results indicate that natural mammal populations, depending on their genetic background, can withstand a high genetic load.

Quantifying the relationship between genetic diversity and population size suggests natural selection cannot explain Lewontin's Paradox

Neutral theory predicts that genetic diversity increases with population size, yet observed levels of diversity across metazoans vary only two orders of magnitude while population sizes vary over several. This unexpectedly narrow range of diversity is known as Lewontin's Paradox of Variation (1974). While some have suggested selection constrains diversity, tests of this hypothesis seem to fall short. Here, I revisit Lewontin's Paradox to assess whether current models of linked selection are capable of reducing diversity to this extent. To quantify the discrepancy between pairwise diversity and census population sizes across species, I combine previously-published estimates of pairwise diversity from 172 metazoan taxa with newly derived estimates of census sizes. Using phylogenetic comparative methods, I show this relationship is significant accounting for phylogeny, but with high phylogenetic signal and evidence that some lineages experience shifts in the evolutionary rate of diversity deep in the past. Additionally, I find a negative relationship between recombination map length and census size, suggesting abundant species have less recombination and experience greater reductions in diversity due to linked selection. However, I show that even assuming strong and abundant selection, models of linked selection are unlikely to explain the observed relationship between diversity and census sizes across species.

Recombination Rate Variation and Infrequent Sex Influence Genetic Diversity in Chlamydomonas reinhardtii

Recombination confers a major evolutionary advantage by breaking up linkage disequilibrium between harmful and beneficial mutations, thereby facilitating selection. However, in species that are only periodically sexual, such as many microbial eukaryotes, the realized rate of recombination is also affected by the frequency of sex, meaning that infrequent sex can increase the effects of selection at linked sites despite high recombination rates. Despite this, the rate of sex of most facultatively sexual species is unknown. Here, we use genomewide patterns of linkage disequilibrium to infer fine-scale recombination rate variation in the genome of the facultatively sexual green alga Chlamydomonas reinhardtii. We observe recombination rate variation of up to two orders of magnitude and find evidence of recombination hotspots across the genome. Recombination rate is highest flanking genes, consistent with trends observed in other nonmammalian organisms, though intergenic recombination rates vary by intergenic tract length. We also find a positive relationship between nucleotide diversity and physical recombination rate, suggesting a widespread influence of selection at linked sites in the genome. Finally, we use estimates of the effective rate of recombination to calculate the rate of sex that occurs in natural populations, estimating a sexual cycle roughly every 840 generations. We argue that the relatively infrequent rate of sex and large effective population size creates a population genetic environment that increases the influence of selection on linked sites across the genome.

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.

Discovery of Ongoing Selective Sweeps within Anopheles Mosquito Populations Using Deep Learning

Identification of partial sweeps, which include both hard and soft sweeps that have not currently reached fixation, provides crucial information about ongoing evolutionary responses. To this end, we introduce partialS/HIC, a deep learning method to discover selective sweeps from population genomic data. partialS/HIC uses a convolutional neural network for image processing, which is trained with a large suite of summary statistics derived from coalescent simulations incorporating population-specific history, to distinguish between completed versus partial sweeps, hard versus soft sweeps, and regions directly affected by selection versus those merely linked to nearby selective sweeps. We perform several simulation experiments under various demographic scenarios to demonstrate partialS/HIC's performance, which exhibits excellent resolution for detecting partial sweeps. We also apply our classifier to whole genomes from eight mosquito populations sampled across sub-Saharan Africa by the Anopheles gambiae 1000 Genomes Consortium, elucidating both continent-wide patterns as well as sweeps unique to specific geographic regions. These populations have experienced intense insecticide exposure over the past two decades, and we observe a strong overrepresentation of sweeps at insecticide resistance loci. Our analysis thus provides a list of candidate adaptive loci that may be relevant to mosquito control efforts. More broadly, our supervised machine learning approach introduces a method to distinguish between completed and partial sweeps, as well as between hard and soft sweeps, under a variety of demographic scenarios. As whole-genome data rapidly accumulate for a greater diversity of organisms, partialS/HIC addresses an increasing demand for useful selection scan tools that can track in-progress evolutionary dynamics.

How Good Are Predictions of the Effects of Selective Sweeps on Levels of Neutral Diversity?

Selective sweeps are thought to play a significant role in shaping patterns of variability across genomes; accurate predictions of their effects are, therefore, important for understanding these patterns. A commonly used model of selective sweeps assumes that alleles sampled at the end of a sweep, and that fail to recombine with wild-type haplotypes during the sweep, coalesce instantaneously, leading to a simple expression for sweep effects on diversity. It is shown here that there can be a significant probability that a pair of alleles sampled at the end of a sweep coalesce during the sweep before a recombination event can occur, reducing their expected coalescent time below that given by the simple approximation. Expressions are derived for the expected reductions in pairwise neutral diversities caused by both single and recurrent sweeps in the presence of such within-sweep coalescence, although the effects of multiple recombination events during a sweep are only treated heuristically. The accuracies of the resulting expressions were checked against the results of simulations. For even moderate ratios of the recombination rate to the selection coefficient, the simple approximation can be substantially inaccurate. The selection model used here can be applied to favorable mutations with arbitrary dominance coefficients, to sex-linked loci with sex-specific selection coefficients, and to inbreeding populations. Using the results from this model, the expected differences between the levels of variability on X chromosomes and autosomes with selection at linked sites are discussed, and compared with data on a population of Drosophila melanogaster.

How Much Does Ne Vary Among Species?

Genetic drift is an important evolutionary force of strength inversely proportional to Ne , the effective population size. The impact of drift on genome diversity and evolution is known to vary among species, but quantifying this effect is a difficult task. Here we assess the magnitude of variation in drift power among species of animals via its effect on the mutation load - which implies also inferring the distribution of fitness effects of deleterious mutations. To this aim, we analyze the nonsynonymous (amino-acid changing) and synonymous (amino-acid conservative) allele frequency spectra in a large sample of metazoan species, with a focus on the primates vs. fruit flies contrast. We show that a Gamma model of the distribution of fitness effects is not suitable due to strong differences in estimated shape parameters among taxa, while adding a class of lethal mutations essentially solves the problem. Using the Gamma + lethal model and assuming that the mean deleterious effects of nonsynonymous mutations is shared among species, we estimate that the power of drift varies by a factor of at least 500 between large-Ne and small-Ne species of animals, i.e., an order of magnitude more than the among-species variation in genetic diversity. Our results are relevant to Lewontin's paradox while further questioning the meaning of the Ne parameter in population genomics.

Variation in breeding practices and geographic isolation drive subpopulation differentiation, contributing to the loss of genetic diversity within dog breed lineages

Background

Discrete breed ideals are not restricted to delimiting dog breeds from another, but also are key drivers of subpopulation differentiation. As genetic differentiation due to population fragmentation results in increased rates of inbreeding and loss of genetic diversity, detecting and alleviating the reasons of population fragmentation can provide effective tools for the maintenance of healthy dog breeds.

Results

Using a genome-wide SNP array, we detected genetic differentiation to subpopulations in six breeds, Belgian Shepherd, English Greyhound, Finnish Lapphund, Italian Greyhound, Labrador Retriever and Shetland Sheepdog, either due to geographical isolation or as a result of differential breeding strategies. The subpopulation differentiation was strongest in show dog lineages.

Conclusions

Besides geographical differentiation caused by founder effect and lack of gene flow, selection on champion looks or restricted pedigrees is a strong driver of population fragmentation. Artificial barriers for gene flow between the different subpopulations should be recognized, their necessity evaluated critically and perhaps abolished in order to maintain genetic diversity within a breed. Subpopulation differentiation might also result in false positive signals in genome-wide association studies of different traits.

Lay summary

Purebred dogs are, by definition, reproductively isolated from other breeds. However, similar isolation can also occur within a breed due to conflicting breeder ideals and geographic distances between the dog populations. We show here that both of these examples can contribute to breed division, with subsequent loss of genetic variation in the resulting breed lineages. Breeders should avoid creating unnecessary boundaries between breed lineages and facilitate the exchange of dogs between countries.

The determinants of genetic diversity in butterflies

Under the neutral theory, genetic diversity is expected to increase with population size. While comparative analyses have consistently failed to find strong relationships between census population size and genetic diversity, a recent study across animals identified a strong correlation between propagule size and genetic diversity, suggesting that r-strategists that produce many small offspring, have greater long-term population sizes. Here we compare genome-wide genetic diversity across 38 species of European butterflies (Papilionoidea), a group that shows little variation in reproductive strategy. We show that genetic diversity across butterflies varies over an order of magnitude and that this variation cannot be explained by differences in current abundance, propagule size, host or geographic range. Instead, neutral genetic diversity is negatively correlated with body size and positively with the length of the genetic map. This suggests that genetic diversity is determined both by differences in long-term population size and the effect of selection on linked sites.

Understanding the Factors That Shape Patterns of Nucleotide Diversity in the House Mouse Genome

A major goal of population genetics has been to determine the extent by which selection at linked sites influences patterns of neutral nucleotide diversity in the genome. Multiple lines of evidence suggest that diversity is influenced by both positive and negative selection. For example, in many species there are troughs in diversity surrounding functional genomic elements, consistent with the action of either background selection (BGS) or selective sweeps. In this study, we investigated the causes of the diversity troughs that are observed in the wild house mouse genome. Using the unfolded site frequency spectrum, we estimated the strength and frequencies of deleterious and advantageous mutations occurring in different functional elements in the genome. We then used these estimates to parameterize forward-in-time simulations of chromosomes, using realistic distributions of functional elements and recombination rate variation in order to determine whether selection at linked sites can explain the observed patterns of nucleotide diversity. The simulations suggest that BGS alone cannot explain the dips in diversity around either exons or conserved noncoding elements. A combination of BGS and selective sweeps produces deeper dips in diversity than BGS alone, but the inferred parameters of selection cannot fully explain the patterns observed in the genome. Our results provide evidence of sweeps shaping patterns of nucleotide diversity across the mouse genome and also suggest that infrequent, strongly advantageous mutations play an important role in this. The limitations of using the unfolded site frequency spectrum for inferring the frequency and effects of advantageous mutations are discussed.

Widespread selection and gene flow shape the genomic landscape during a radiation of monkeyflowers

Speciation genomic studies aim to interpret patterns of genome-wide variation in light of the processes that give rise to new species. However, interpreting the genomic "landscape" of speciation is difficult, because many evolutionary processes can impact levels of variation. Facilitated by the first chromosome-level assembly for the group, we use whole-genome sequencing and simulations to shed light on the processes that have shaped the genomic landscape during a radiation of monkeyflowers. After inferring the phylogenetic relationships among the 9 taxa in this radiation, we show that highly similar diversity (π) and differentiation (FST) landscapes have emerged across the group. Variation in these landscapes was strongly predicted by the local density of functional elements and the recombination rate, suggesting that the landscapes have been shaped by widespread natural selection. Using the varying divergence times between pairs of taxa, we show that the correlations between FST and genome features arose almost immediately after a population split and have become stronger over time. Simulations of genomic landscape evolution suggest that background selection (BGS; i.e., selection against deleterious mutations) alone is too subtle to generate the observed patterns, but scenarios that involve positive selection and genetic incompatibilities are plausible alternative explanations. Finally, tests for introgression among these taxa reveal widespread evidence of heterogeneous selection against gene flow during this radiation. Combined with previous evidence for adaptation in this system, we conclude that the correlation in FST among these taxa informs us about the processes contributing to adaptation and speciation during a rapid radiation.

Extreme Lewontin's Paradox in Ubiquitous Marine Phytoplankton Species

Larger populations are expected to have larger genetic diversity. However, as pointed out by Lewontin in 1974, the range of population sizes exceeds the range of genetic diversity by many orders of magnitude (a.k.a. "Lewontin's paradox," LP). The reasons for LP remain obscure. Here, This paper reports an extreme case of LP in astronomically large populations of the ubiquitous unicellular marine phytoplankton species Emiliania huxleyi (Haptophyta)-the species that accounts for 10-20% of primary productivity in the oceans and its blooms are so extensive that they are visible from space. This study demonstrates that despite the wide distribution and enormous population size, the world-wide sample of E. huxleyi strains with sequenced genomes represents a single cohesive species and contains surprisingly limited genetic diversity (π ∼ 0.006 per silent site). The patterns of polymorphism reveal even larger populations in the past, and frequent recombination (ρ ∼ 0.006) throughout the genome, ruling out demographic history and asexual reproduction as possible causes of low polymorphism in E. huxleyi. Natural selection wiping out genetic diversity at linked sites (a.k.a. "genetic draft") must be strong and frequent to account for low polymorphism in E. huxleyi. This study sheds the first light on poorly understood evolutionary genetic processes in astronomically large populations of marine microplankton.

Methods for Estimating Demography and Detecting Between-Locus Differences in the Effective Population Size and Mutation Rate

It is known that the effective population size (N_e) and the mutation rate (u) vary across the genome. Here, we show that ignoring this heterogeneity may lead to biased estimates of past demography. To solve the problem, we develop new methods for jointly inferring past changes in population size and detecting variation in N_e and u between loci. These methods rely on either polymorphism data alone or both polymorphism and divergence data. In addition to inferring demography, we can use the methods to study a variety of questions: 1) comparing sex chromosomes with autosomes (for finding evidence for male-driven evolution, an unequal sex ratio, or sex-biased demographic changes) and 2) analyzing multilocus data from within autosomes or sex chromosomes (for studying determinants of variability in N_e and u). Simulations suggest that the methods can provide accurate parameter estimates and have substantial statistical power for detecting difference in N_e and u. As an example, we use the methods to analyze a polymorphism data set from Drosophila simulans. We find clear evidence for rapid population expansion. The results also indicate that the autosomes have a higher mutation rate than the X chromosome and that the sex ratio is probably female-biased. The new methods have been implemented in a user-friendly package.

The Effects on Neutral Variability of Recurrent Selective Sweeps and Background Selection

Levels of variability and rates of adaptive evolution may be affected by hitchhiking, the effect of selection on evolution at linked sites. Hitchhiking can be caused either by "selective sweeps" or by background selection, involving the spread of new favorable alleles or the elimination of deleterious mutations, respectively. Recent analyses of population genomic data have fitted models where both these processes act simultaneously, to infer the parameters of selection. Here, we investigate the consequences of relaxing a key assumption of some of these studies, that the time occupied by a selective sweep is negligible compared with the neutral coalescent time. We derive a new expression for the expected level of neutral variability in the presence of recurrent selective sweeps and background selection. We also derive approximate integral expressions for the effects of recurrent selective sweeps. The accuracy of the theoretical predictions was tested against multilocus simulations, with selection, recombination, and mutation parameters that are realistic for Drosophila melanogaster In the presence of crossing over, there is approximate agreement between the theoretical and simulation results. We show that the observed relationships between the rate of crossing over, and the level of synonymous site diversity and rate of adaptive evolution in Drosophila are probably mainly caused by background selection, whereas selective sweeps and population size changes are needed to produce the observed distortions of the site frequency spectrum.

ABLE: blockwise site frequency spectra for inferring complex population histories and recombination

We introduce ABLE (Approximate Blockwise Likelihood Estimation), a novel simulation-based composite likelihood method that uses the blockwise site frequency spectrum to jointly infer past demography and recombination. ABLE is explicitly designed for a wide variety of data from unphased diploid genomes to genome-wide multi-locus data (for example, RADSeq) and can also accommodate arbitrarily large samples. We use simulations to demonstrate the accuracy of this method to infer complex histories of divergence and gene flow and reanalyze whole genome data from two species of orangutan. ABLE is available for download at https://github.com/champost/ABLE.

Nonequilibrium Neutral Theory for Hitchhikers

Selective sweep is a phenomenon of reduced variation at presumably neutrally evolving sites (hitchhikers) in the genome that is caused by the spread of a selected allele at a linked focal site, and is widely used to test for action of positive selection. Nonetheless, selective sweep may also provide an unprecedented opportunity for studying nonequilibrium properties of the neutral variation itself. We have demonstrated this possibility in relation to ancient selective sweep for modern human-specific changes and ongoing selective sweep for local population-specific changes.

Detecting positive selection in the genome

Population geneticists have long sought to understand the contribution of natural selection to molecular evolution. A variety of approaches have been proposed that use population genetics theory to quantify the rate and strength of positive selection acting in a species’ genome. In this review we discuss methods that use patterns of between-species nucleotide divergence and within-species diversity to estimate positive selection parameters from population genomic data. We also discuss recently proposed methods to detect positive selection from a population’s haplotype structure. The application of these tests has resulted in the detection of pervasive adaptive molecular evolution in multiple species.

Estimating the parameters of background selection and selective sweeps in Drosophila in the presence of gene conversion

We used whole-genome resequencing data from a population of Drosophila melanogaster to investigate the causes of the negative correlation between the within-population synonymous nucleotide site diversity (π_S ) of a gene and its degree of divergence from related species at nonsynonymous nucleotide sites (K_A ). By using the estimated distributions of mutational effects on fitness at nonsynonymous and UTR sites, we predicted the effects of background selection at sites within a gene on π_S and found that these could account for only part of the observed correlation between π_S and K_A We developed a model of the effects of selective sweeps that included gene conversion as well as crossing over. We used this model to estimate the average strength of selection on positively selected mutations in coding sequences and in UTRs, as well as the proportions of new mutations that are selectively advantageous. Genes with high levels of selective constraint on nonsynonymous sites were found to have lower strengths of positive selection and lower proportions of advantageous mutations than genes with low levels of constraint. Overall, background selection and selective sweeps within a typical gene reduce its synonymous diversity to ∼75% of its value in the absence of selection, with larger reductions for genes with high K_A Gene conversion has a major effect on the estimates of the parameters of positive selection, such that the estimated strength of selection on favorable mutations is greatly reduced if it is ignored.

Determining the Effect of Natural Selection on Linked Neutral Divergence across Species

A major goal in evolutionary biology is to understand how natural selection has shaped patterns of genetic variation across genomes. Studies in a variety of species have shown that neutral genetic diversity (intra-species differences) has been reduced at sites linked to those under direct selection. However, the effect of linked selection on neutral sequence divergence (inter-species differences) remains ambiguous. While empirical studies have reported correlations between divergence and recombination, which is interpreted as evidence for natural selection reducing linked neutral divergence, theory argues otherwise, especially for species that have diverged long ago. Here we address these outstanding issues by examining whether natural selection can affect divergence between both closely and distantly related species. We show that neutral divergence between closely related species (e.g. human-primate) is negatively correlated with functional content and positively correlated with human recombination rate. We also find that neutral divergence between distantly related species (e.g. human-rodent) is negatively correlated with functional content and positively correlated with estimates of background selection from primates. These patterns persist after accounting for the confounding factors of hypermutable CpG sites, GC content, and biased gene conversion. Coalescent models indicate that even when the contribution of ancestral polymorphism to divergence is small, background selection in the ancestral population can still explain a large proportion of the variance in divergence across the genome, generating the observed correlations. Our findings reveal that, contrary to previous intuition, natural selection can indirectly affect linked neutral divergence between both closely and distantly related species. Though we cannot formally exclude the possibility that the direct effects of purifying selection drive some of these patterns, such a scenario would be possible only if more of the genome is under purifying selection than currently believed. Our work has implications for understanding the evolution of genomes and interpreting patterns of genetic variation.

Genetic variation at neutral sites can be reduced through linkage to nearby selected sites. This pattern has been used to show the widespread effects of natural selection at shaping patterns of genetic diversity across genomes from a variety of species. However, it is not entirely clear whether natural selection has an effect on neutral divergence between species. Here we show that putatively neutral divergence between closely related species (human and chimp) and between distantly related pairs of species (humans and mice) show signatures consistent with having been affected by linkage to selected sites. Further, our theoretical models and simulations show that natural selection indirectly affecting linked neutral sites can generate these patterns. Unless substantially more of the genome is under the direct effects of purifying selection than currently believed, our results argue that natural selection has played an important role in shaping variation in levels of putatively neutral sequence divergence across the genome. Our findings further suggest that divergence-based estimates of neutral mutation rate variation across the genome as well as certain estimators of population history may be confounded by linkage to selected sites.

A Genomic Map of the Effects of Linked Selection in Drosophila

Natural selection at one site shapes patterns of genetic variation at linked sites. Quantifying the effects of "linked selection" on levels of genetic diversity is key to making reliable inference about demography, building a null model in scans for targets of adaptation, and learning about the dynamics of natural selection. Here, we introduce the first method that jointly infers parameters of distinct modes of linked selection, notably background selection and selective sweeps, from genome-wide diversity data, functional annotations and genetic maps. The central idea is to calculate the probability that a neutral site is polymorphic given local annotations, substitution patterns, and recombination rates. Information is then combined across sites and samples using composite likelihood in order to estimate genome-wide parameters of distinct modes of selection. In addition to parameter estimation, this approach yields a map of the expected neutral diversity levels along the genome. To illustrate the utility of our approach, we apply it to genome-wide resequencing data from 125 lines in Drosophila melanogaster and reliably predict diversity levels at the 1Mb scale. Our results corroborate estimates of a high fraction of beneficial substitutions in proteins and untranslated regions (UTR). They allow us to distinguish between the contribution of sweeps and other modes of selection around amino acid substitutions and to uncover evidence for pervasive sweeps in untranslated regions (UTRs). Our inference further suggests a substantial effect of other modes of linked selection and of adaptation in particular. More generally, we demonstrate that linked selection has had a larger effect in reducing diversity levels and increasing their variance in D. melanogaster than previously appreciated.

Para-allopatry in hybridizing fire-bellied toads (Bombina bombina and B. variegata): Inference from transcriptome-wide coalescence analyses

Ancient origins, profound ecological divergence, and extensive hybridization make the fire‐bellied toads Bombina bombina and B. variegata (Anura: Bombinatoridae) an intriguing test case of ecological speciation. Previous modeling has proposed that the narrow Bombina hybrid zones represent strong barriers to neutral introgression. We test this prediction by inferring the rate of gene exchange between pure populations on either side of the intensively studied Kraków transect. We developed a method to extract high confidence sets of orthologous genes from de novo transcriptome assemblies, fitted a range of divergence models to these data and assessed their relative support with analytic likelihood calculations. There was clear evidence for postdivergence gene flow, but, as expected, no perceptible signal of recent introgression via the nearby hybrid zone. The analysis of two additional Bombina taxa (B. v. scabra and B. orientalis) validated our parameter estimates against a larger set of prior expectations. Despite substantial cumulative introgression over millions of years, adaptive divergence of the hybridizing taxa is essentially unaffected by their lack of reproductive isolation. Extended distribution ranges also buffer them against small‐scale environmental perturbations that have been shown to reverse the speciation process in other, more recent ecotypes.

Determinants of genetic diversity

Genetic polymorphism varies among species and within genomes, and has important implications for the evolution and conservation of species. The determinants of this variation have been poorly understood, but population genomic data from a wide range of organisms now make it possible to delineate the underlying evolutionary processes, notably how variation in the effective population size (Ne) governs genetic diversity. Comparative population genomics is on its way to providing a solution to 'Lewontin's paradox' - the discrepancy between the many orders of magnitude of variation in population size and the much narrower distribution of diversity levels. It seems that linked selection plays an important part both in the overall genetic diversity of a species and in the variation in diversity within the genome. Genetic diversity also seems to be predictable from the life history of a species.

A Coalescent Model for a Sweep of a Unique Standing Variant

The use of genetic polymorphism data to understand the dynamics of adaptation and identify the loci that are involved has become a major pursuit of modern evolutionary genetics. In addition to the classical "hard sweep" hitchhiking model, recent research has drawn attention to the fact that the dynamics of adaptation can play out in a variety of different ways and that the specific signatures left behind in population genetic data may depend somewhat strongly on these dynamics. One particular model for which a large number of empirical examples are already known is that in which a single derived mutation arises and drifts to some low frequency before an environmental change causes the allele to become beneficial and sweeps to fixation. Here, we pursue an analytical investigation of this model, bolstered and extended via simulation study. We use coalescent theory to develop an analytical approximation for the effect of a sweep from standing variation on the genealogy at the locus of the selected allele and sites tightly linked to it. We show that the distribution of haplotypes that the selected allele is present on at the time of the environmental change can be approximated by considering recombinant haplotypes as alleles in the infinite-alleles model. We show that this approximation can be leveraged to make accurate predictions regarding patterns of genetic polymorphism following such a sweep. We then use simulations to highlight which sources of haplotypic information are likely to be most useful in distinguishing this model from neutrality, as well as from other sweep models, such as the classic hard sweep and multiple-mutation soft sweeps. We find that in general, adaptation from a unique standing variant will likely be difficult to detect on the basis of genetic polymorphism data from a single population time point alone, and when it can be detected, it will be difficult to distinguish from other varieties of selective sweeps. Samples from multiple populations and/or time points have the potential to ease this difficulty.

The Role of Standing Variation in Geographic Convergent Adaptation

The extent to which populations experiencing shared selective pressures adapt through a shared genetic response is relevant to many questions in evolutionary biology. In this article, we explore how standing genetic variation contributes to convergent genetic responses in a geographically spread population. Geographically limited dispersal slows the spread of each selected allele, hence allowing other alleles to spread before any one comes to dominate the population. When selectively equivalent alleles meet, their progress is substantially slowed, dividing the species range into a random tessellation, which can be well understood by analogy to a Poisson process model of crystallization. In this framework, we derive the geographic scale over which an allele dominates and the proportion of adaptive alleles that arise from standing variation. Finally, we explore how negative pleiotropic effects of alleles can bias the subset of alleles that contribute to the species' adaptive response. We apply the results to the malaria-resistance glucose-6-phosphate dehydrogenase-deficiency alleles, where the large mutational target size makes it a likely candidate for adaptation from deleterious standing variation. Our results suggest that convergent adaptation may be common. Therefore, caution must be exercised when arguing that strongly geographically restricted alleles are the outcome of local adaptation. We close by discussing the implications of these results for ideas of species coherence and the nature of divergence between species.

Inferring Bottlenecks from Genome-Wide Samples of Short Sequence Blocks

The advent of the genomic era has necessitated the development of methods capable of analyzing large volumes of genomic data efficiently. Being able to reliably identify bottlenecks—extreme population size changes of short duration—not only is interesting in the context of speciation and extinction but also matters (as a null model) when inferring selection. Bottlenecks can be detected in polymorphism data via their distorting effect on the shape of the underlying genealogy. Here, we use the generating function of genealogies to derive the probability of mutational configurations in short sequence blocks under a simple bottleneck model. Given a large number of nonrecombining blocks, we can compute maximum-likelihood estimates of the time and strength of the bottleneck. Our method relies on a simple summary of the joint distribution of polymorphic sites. We extend the site frequency spectrum by counting mutations in frequency classes in short sequence blocks. Using linkage information over short distances in this way gives greater power to detect bottlenecks than the site frequency spectrum and potentially opens up a wide range of demographic histories to blockwise inference. Finally, we apply our method to genomic data from a species of pig (Sus cebifrons) endemic to islands in the center and west of the Philippines to estimate whether a bottleneck occurred upon island colonization and compare our scheme to Li and Durbin’s pairwise sequentially Markovian coalescent (PSMC) both for the pig data and using simulations.

Genetic approaches in comparative and evolutionary physiology

Whole animal physiological performance is highly polygenic and highly plastic, and the same is generally true for the many subordinate traits that underlie performance capacities. Quantitative genetics, therefore, provides an appropriate framework for the analysis of physiological phenotypes and can be used to infer the microevolutionary processes that have shaped patterns of trait variation within and among species. In cases where specific genes are known to contribute to variation in physiological traits, analyses of intraspecific polymorphism and interspecific divergence can reveal molecular mechanisms of functional evolution and can provide insights into the possible adaptive significance of observed sequence changes. In this review, we explain how the tools and theory of quantitative genetics, population genetics, and molecular evolution can inform our understanding of mechanism and process in physiological evolution. For example, lab-based studies of polygenic inheritance can be integrated with field-based studies of trait variation and survivorship to measure selection in the wild, thereby providing direct insights into the adaptive significance of physiological variation. Analyses of quantitative genetic variation in selection experiments can be used to probe interrelationships among traits and the genetic basis of physiological trade-offs and constraints. We review approaches for characterizing the genetic architecture of physiological traits, including linkage mapping and association mapping, and systems approaches for dissecting intermediary steps in the chain of causation between genotype and phenotype. We also discuss the promise and limitations of population genomic approaches for inferring adaptation at specific loci. We end by highlighting the role of organismal physiology in the functional synthesis of evolutionary biology.

Tandem Duplications and the Limits of Natural Selection in Drosophila yakuba and Drosophila simulans

Tandem duplications are an essential source of genetic novelty, and their variation in natural populations is expected to influence adaptive walks. Here, we describe evolutionary impacts of recently-derived, segregating tandem duplications in Drosophila yakuba and Drosophila simulans. We observe an excess of duplicated genes involved in defense against pathogens, insecticide resistance, chorion development, cuticular peptides, and lipases or endopeptidases associated with the accessory glands across both species. The observed agreement is greater than expectations on chance alone, suggesting large amounts of convergence across functional categories. We document evidence of widespread selection on the D. simulans X, suggesting adaptation through duplication is common on the X. Despite the evidence for positive selection, duplicates display an excess of low frequency variants consistent with largely detrimental impacts, limiting the variation that can effectively facilitate adaptation. Standing variation for tandem duplications spans less than 25% of the genome in D. yakuba and D. simulans, indicating that evolution will be strictly limited by mutation, even in organisms with large population sizes. Effective whole gene duplication rates are low at 1.17 × 10-9 per gene per generation in D. yakuba and 6.03 × 10-10 per gene per generation in D. simulans, suggesting long wait times for new mutations on the order of thousands of years for the establishment of sweeps. Hence, in cases where adaptation depends on individual tandem duplications, evolution will be severely limited by mutation. We observe low levels of parallel recruitment of the same duplicated gene in different species, suggesting that the span of standing variation will define evolutionary outcomes in spite of convergence across gene ontologies consistent with rapidly evolving phenotypes.

Natural selection constrains neutral diversity across a wide range of species

The neutral theory of molecular evolution predicts that the amount of neutral polymorphisms within a species will increase proportionally with the census population size (Nc). However, this prediction has not been borne out in practice: while the range of Nc spans many orders of magnitude, levels of genetic diversity within species fall in a comparatively narrow range. Although theoretical arguments have invoked the increased efficacy of natural selection in larger populations to explain this discrepancy, few direct empirical tests of this hypothesis have been conducted. In this work, we provide a direct test of this hypothesis using population genomic data from a wide range of taxonomically diverse species. To do this, we relied on the fact that the impact of natural selection on linked neutral diversity depends on the local recombinational environment. In regions of relatively low recombination, selected variants affect more neutral sites through linkage, and the resulting correlation between recombination and polymorphism allows a quantitative assessment of the magnitude of the impact of selection on linked neutral diversity. By comparing whole genome polymorphism data and genetic maps using a coalescent modeling framework, we estimate the degree to which natural selection reduces linked neutral diversity for 40 species of obligately sexual eukaryotes. We then show that the magnitude of the impact of natural selection is positively correlated with Nc, based on body size and species range as proxies for census population size. These results demonstrate that natural selection removes more variation at linked neutral sites in species with large Nc than those with small Nc and provides direct empirical evidence that natural selection constrains levels of neutral genetic diversity across many species. This implies that natural selection may provide an explanation for this longstanding paradox of population genetics.

A neutrality test for detecting selection on DNA methylation using single methylation polymorphism frequency spectrum

Inheritable epigenetic mutations (epimutations) can contribute to transmittable phenotypic variation. Thus, epimutations can be subject to natural selection and impact the fitness and evolution of organisms. Based on the framework of the modified Tajima’s D test for DNA mutations, we developed a neutrality test with the statistic “D^m” to detect selection forces on DNA methylation mutations using single methylation polymorphisms. With computer simulation and empirical data analysis, we compared the D^m test with the original and modified Tajima’s D tests and demonstrated that the D^m test is suitable for detecting selection on epimutations and outperforms original/modified Tajima’s D tests. Due to the higher resetting rate of epimutations, the interpretation of D^m on epimutations and Tajima’s D test on DNA mutations could be different in inferring natural selection. Analyses using simulated and empirical genome-wide polymorphism data suggested that genes under genetic and epigenetic selections behaved differently. We applied the D^m test to recently originated Arabidopsis and human genes, and showed that newly evolved genes contain higher level of rare epialleles, suggesting that epimutation may play a role in origination and evolution of genes and genomes. Overall, we demonstrate the utility of the D^m test to detect whether the loci are under selection regarding DNA methylation. Our analytical metrics and methodology could contribute to our understanding of evolutionary processes of genes and genomes in the field of epigenetics. The Perl script for the “D^m” test is available at http://fanlab.wayne.edu/ (last accessed December 18, 2014).

Sexually antagonistic polymorphism in simultaneous hermaphrodites

In hermaphrodites, pleiotropic genetic trade-offs between female and male reproductive functions can lead to sexually antagonistic (SA) selection, where individual alleles have conflicting fitness effects on each sex function. Although an extensive theory of SA selection exists for dioecious species, these results have not been generalized to hermaphrodites. We develop population genetic models of SA selection in simultaneous hermaphrodites, and evaluate effects of dominance, selection on each sex function, self-fertilization, and population size on the maintenance of polymorphism. Under obligate outcrossing, hermaphrodite model predictions converge exactly with those of dioecious populations. Self-fertilization in hermaphrodites generates three points of divergence with dioecious theory. First, opportunities for stable polymorphism decline sharply and become less sensitive to dominance with increased selfing. Second, selfing introduces an asymmetry in the relative importance of selection through male versus female reproductive functions, expands the parameter space favorable for the evolutionary invasion of female-beneficial alleles, and restricts invasion criteria for male-beneficial alleles. Finally, contrary to models of unconditionally beneficial alleles, selfing decreases genetic hitchhiking effects of invading SA alleles, and should therefore decrease these population genetic signals of SA polymorphisms. We discuss implications of SA selection in hermaphrodites, including its potential role in the evolution of "selfing syndromes."

The effect of linkage on establishment and survival of locally beneficial mutations

We study invasion and survival of weakly beneficial mutations arising in linkage to an established migration-selection polymorphism. Our focus is on a continent-island model of migration, with selection at two biallelic loci for adaptation to the island environment. Combining branching and diffusion processes, we provide the theoretical basis for understanding the evolution of islands of divergence, the genetic architecture of locally adaptive traits, and the importance of so-called "divergence hitchhiking" relative to other mechanisms, such as "genomic hitchhiking", chromosomal inversions, or translocations. We derive approximations to the invasion probability and the extinction time of a de novo mutation. Interestingly, the invasion probability is maximized at a nonzero recombination rate if the focal mutation is sufficiently beneficial. If a proportion of migrants carries a beneficial background allele, the mutation is less likely to become established. Linked selection may increase the survival time by several orders of magnitude. By altering the timescale of stochastic loss, it can therefore affect the dynamics at the focal site to an extent that is of evolutionary importance, especially in small populations. We derive an effective migration rate experienced by the weakly beneficial mutation, which accounts for the reduction in gene flow imposed by linked selection. Using the concept of the effective migration rate, we also quantify the long-term effects on neutral variation embedded in a genome with arbitrarily many sites under selection. Patterns of neutral diversity change qualitatively and quantitatively as the position of the neutral locus is moved along the chromosome. This will be useful for population-genomic inference. Our results strengthen the emerging view that physically linked selection is biologically relevant if linkage is tight or if selection at the background locus is strong.

Robust forward simulations of recurrent hitchhiking

Evolutionary forces shape patterns of genetic diversity within populations and contribute to phenotypic variation. In particular, recurrent positive selection has attracted significant interest in both theoretical and empirical studies. However, most existing theoretical models of recurrent positive selection cannot easily incorporate realistic confounding effects such as interference between selected sites, arbitrary selection schemes, and complicated demographic processes. It is possible to quantify the effects of arbitrarily complex evolutionary models by performing forward population genetic simulations, but forward simulations can be computationally prohibitive for large population sizes (>10⁵). A common approach for overcoming these computational limitations is rescaling of the most computationally expensive parameters, especially population size. Here, we show that ad hoc approaches to parameter rescaling under the recurrent hitchhiking model do not always provide sufficiently accurate dynamics, potentially skewing patterns of diversity in simulated DNA sequences. We derive an extension of the recurrent hitchhiking model that is appropriate for strong selection in small population sizes and use it to develop a method for parameter rescaling that provides the best possible computational performance for a given error tolerance. We perform a detailed theoretical analysis of the robustness of rescaling across the parameter space. Finally, we apply our rescaling algorithms to parameters that were previously inferred for Drosophila and discuss practical considerations such as interference between selected sites.

The effects of linkage on comparative estimators of selection

Background

A major goal of molecular evolution is to determine how natural selection has shaped the evolution of a gene. One approach taken by methods such as K_A/K_S and the McDonald-Kreitman (MK) test is to compare the frequency of non-synonymous and synonymous changes. These methods, however, rely on the assumption that a change in frequency of one mutation will not affect changes in frequency of other mutations.

Results

We demonstrate that linkage between sites can bias measures of selection based on synonymous and non-synonymous changes. Using forward simulation of a Wright-Fisher process, we show that hitch-hiking of deleterious mutations with advantageous mutations can lead to overestimation of the number of adaptive substitutions, while background selection and clonal interference can distort the site frequency spectrum to obscure the signal for positive selection. We present three diagnostics for detecting these effects of linked selection and apply them to the human influenza (H3N2) hemagglutinin gene.

Conclusion

Various forms of linked selection have characteristic effects on MK-type statistics. The extent of background selection, hitch-hiking and clonal interference can be evaluated using the diagnostic statistics presented here. The diagnostics can also be used to determine how well we expect the MK statistics to perform and whether one form of the statistic may be preferable to another.

Statistical properties of the site-frequency spectrum associated with lambda-coalescents

Statistical properties of the site-frequency spectrum associated with Λ-coalescents are our objects of study. In particular, we derive recursions for the expected value, variance, and covariance of the spectrum, extending earlier results of Fu (1995) for the classical Kingman coalescent. Estimating coalescent parameters introduced by certain Λ-coalescents for data sets too large for full-likelihood methods is our focus. The recursions for the expected values we obtain can be used to find the parameter values that give the best fit to the observed frequency spectrum. The expected values are also used to approximate the probability a (derived) mutation arises on a branch subtending a given number of leaves (DNA sequences), allowing us to apply a pseudolikelihood inference to estimate coalescence parameters associated with certain subclasses of Λ-coalescents. The properties of the pseudolikelihood approach are investigated on simulated as well as real mtDNA data sets for the high-fecundity Atlantic cod (Gadus morhua). Our results for two subclasses of Λ-coalescents show that one can distinguish these subclasses from the Kingman coalescent, as well as between the Λ-subclasses, even for a moderate (maybe a few hundred) sample size.