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

Hill-Robertson interference may bias the inference of fitness effects of new mutations in highly selfing species

The accurate estimation of the distribution of fitness effects (DFE) of new mutations is critical for population genetic inference but remains a challenging task. While various methods have been developed for DFE inference using the site frequency spectrum of putatively neutral and selected sites, their applicability in species with diverse life history traits and complex demographic scenarios is not well understood. Selfing is common among eukaryotic species and can lead to decreased effective recombination rates, increasing the effects of selection at linked sites, including interference between selected alleles. We employ forward simulations to investigate the limitations of current DFE estimation approaches in the presence of selfing and other model violations, such as linkage, departures from semidominance, population structure, and uneven sampling. We find that distortions of the site frequency spectrum due to Hill-Robertson interference in highly selfing populations lead to mis-inference of the deleterious DFE of new mutations. Specifically, when inferring the distribution of selection coefficients, there is an overestimation of nearly neutral and strongly deleterious mutations and an underestimation of mildly deleterious mutations when interference between selected alleles is pervasive. In addition, the presence of cryptic population structure with low rates of migration and uneven sampling across subpopulations leads to the false inference of a deleterious DFE skewed towards effectively neutral/mildly deleterious mutations. Finally, the proportion of adaptive substitutions estimated at high rates of selfing is substantially overestimated. Our observations apply broadly to species and genomic regions with little/no recombination and where interference might be pervasive.

The fitness consequences of genetic divergence between polymorphic gene arrangements

Inversions restrict recombination when heterozygous with standard arrangements, but often have few noticeable phenotypic effects. Nevertheless, there are several examples of inversions that can be maintained polymorphic by strong selection under laboratory conditions. A long-standing model for the source of such selection is divergence between arrangements with respect to recessive or partially recessive deleterious mutations, resulting in a selective advantage to heterokaryotypic individuals over homokaryotypes. This paper uses a combination of analytical and numerical methods to investigate this model, for the simple case of an autosomal inversion with multiple independent nucleotide sites subject to mildly deleterious mutations. A complete lack of recombination in heterokaryotypes is assumed, as well as constancy of the frequency of the inversion over space and time. It is shown that a significantly higher mutational load will develop for the less frequent arrangement. A selective advantage to heterokaryotypes is only expected when the two alternative arrangements are nearly equal in frequency, so that their mutational loads are very similar in size. The effects of some Drosophila pseudoobscura polymorphic inversions on fitness traits seem to be too large to be explained by this process, although it may contribute to some of the observed effects. Several population genomic statistics can provide evidence for signatures of a reduced efficacy of selection associated with the rarer of two arrangements, but there is currently little published data that are relevant to the theoretical predictions.

Background Selection From Unlinked Sites Causes Nonindependent Evolution of Deleterious Mutations

Background selection describes the reduction in neutral diversity caused by selection against deleterious alleles at other loci. It is typically assumed that the purging of deleterious alleles affects linked neutral variants, and indeed simulations typically only treat a genomic window. However, background selection at unlinked loci also depresses neutral diversity. In agreement with previous analytical approximations, in our simulations of a human-like genome with a realistically high genome-wide deleterious mutation rate, the effects of unlinked background selection exceed those of linked background selection. Background selection reduces neutral genetic diversity by a factor that is independent of census population size. Outside of genic regions, the strength of background selection increases with the mean selection coefficient, contradicting the linked theory but in agreement with the unlinked theory. Neutral diversity within genic regions is fairly independent of the strength of selection. Deleterious genetic load among haploid individuals is underdispersed, indicating nonindependent evolution of deleterious mutations. Empirical evidence for underdispersion was previously interpreted as evidence for global epistasis, but we recover it from a non-epistatic model.

The Effects of Mutation and Recombination Rate Heterogeneity on the Inference of Demography and the Distribution of Fitness Effects

Disentangling the effects of demography and selection has remained a focal point of population genetic analysis. Knowledge about mutation and recombination is essential in this endeavor; however, despite clear evidence that both mutation and recombination rates vary across genomes, it is common practice to model both rates as fixed. In this study, we quantify how this unaccounted for rate heterogeneity may impact inference using common approaches for inferring selection (DFE-alpha, Grapes, and polyDFE) and/or demography (fastsimcoal2 and δaδi). We demonstrate that, if not properly modeled, this heterogeneity can increase uncertainty in the estimation of demographic and selective parameters and in some scenarios may result in mis-leading inference. These results highlight the importance of quantifying the fundamental evolutionary parameters of mutation and recombination before utilizing population genomic data to quantify the effects of genetic drift (i.e. as modulated by demographic history) and selection; or, at the least, that the effects of uncertainty in these parameters can and should be directly modeled in downstream inference.

Pan-genome analysis highlights the role of structural variation in the evolution and environmental adaptation of Asian honeybees

The Asian honeybee, Apis cerana, is an ecologically and economically important pollinator. Mapping its genetic variation is key to understanding population-level health, histories and potential capacities to respond to environmental changes. However, most efforts to date were focused on single nucleotide polymorphisms (SNPs) based on a single reference genome, thereby ignoring larger scale genomic variation. We employed long-read sequencing technologies to generate a chromosome-scale reference genome for the ancestral group of A. cerana. Integrating this with 525 resequencing data sets, we constructed the first pan-genome of A. cerana, encompassing almost the entire gene content. We found that 31.32% of genes in the pan-genome were variably present across populations, providing a broad gene pool for environmental adaptation. We identified and characterized structural variations (SVs) and found that they were not closely linked with SNP distributions; however, the formation of SVs was closely associated with transposable elements. Furthermore, phylogenetic analysis using SVs revealed a novel A. cerana ecological group not recoverable from the SNP data. Performing environmental association analysis identified a total of 44 SVs likely to be associated with environmental adaptation. Verification and analysis of one of these, a 330 bp deletion in the Atpalpha gene, indicated that this SV may promote the cold adaptation of A. cerana by altering gene expression. Taken together, our study demonstrates the feasibility and utility of applying pan-genome approaches to map and explore genetic feature variations of honeybee populations, and in particular to examine the role of SVs in the evolution and environmental adaptation of A. cerana.

Evolution of a plant sex chromosome driven by expanding pericentromeric recombination suppression

Recombination suppression around sex-determining gene(s) is a key step in evolution of sex chromosomes, but it is not well understood how it evolves. Recently evolved sex-linked regions offer an opportunity to understand the mechanisms of recombination cessation. This paper analyses such a region on Silene latifolia (Caryophyllaceae) sex chromosomes, where recombination was suppressed in the last 120 thousand years ("stratum 3"). Locating the boundaries of the stratum 3 in S. latifolia genome sequence revealed that this region is far larger than assumed previously-it is about 14 Mb long and includes 202 annotated genes. A gradient of X:Y divergence detected in the stratum 3, with divergence increasing proximally, indicates gradual recombination cessation, possibly caused by expansion of pericentromeric recombination suppression (PRS) into the pseudoautosomal region. Expansion of PRS was also the likely cause for the formation of the older stratum 2 on S. latifolia sex chromosomes. The role of PRS in sex chromosome evolution has been underappreciated, but it may be a significant factor, especially in the species with large chromosomes where PRS is often extensive.

Pericentromeric recombination suppression and the 'large X effect' in plants

X chromosome was reported to be a major contributor to isolation between closely related species-the 'large X' effect (LXE). The causes of LXE are not clear, but the leading theory is that it is caused by recessive species incompatibilities exposed in the phenotype due to the hemizygosity of X-linked genes in the heterogametic sex. However, the LXE was also reported in species with relatively recently evolved sex chromosomes where Y chromosome is not completely degenerate and X-linked genes are not hemizygous, such as the plant Silene latifolia. Recent genome sequencing and detailed genetic mapping in this species revealed a massive (> 330 Mb) non- or rarely-recombining pericentromeric region on the X chromosome (Xpr) that comprises ~ 90% of the chromosome and over 13% of the entire genome. If any of the Xpr genes are involved in species incompatibilities, this would oppose interspecific gene flow for other genes tightly linked in the Xpr. Here we test the hypothesis that the previously reported LXE in S. latifolia is caused by the lack of recombination on most of the X chromosome. Based on genome-wide analysis of DNA polymorphism and gene expression in S. latifolia and its close cross-compatible relative S. dioica, we report that the rarely-recombining regions represent a significant barrier for interspecific gene flow. We found little evidence for any additional factors contributing to the LXE, suggesting that extensive pericentromeric recombination suppression on the X-chromosome is the major if not the only cause of the LXE in S. latifolia and S. dioica.

Evaluating power to detect recurrent selective sweeps under increasingly realistic evolutionary null models

The detection of selective sweeps from population genomic data often relies on the premise that the beneficial mutations in question have fixed very near the sampling time. As it has been previously shown that the power to detect a selective sweep is strongly dependent on the time since fixation as well as the strength of selection, it is naturally the case that strong, recent sweeps leave the strongest signatures. However, the biological reality is that beneficial mutations enter populations at a rate, one that partially determines the mean wait time between sweep events and hence their age distribution. An important question thus remains about the power to detect recurrent selective sweeps when they are modeled by a realistic mutation rate and as part of a realistic distribution of fitness effects, as opposed to a single, recent, isolated event on a purely neutral background as is more commonly modeled. Here we use forward-in-time simulations to study the performance of commonly used sweep statistics, within the context of more realistic evolutionary baseline models incorporating purifying and background selection, population size change, and mutation and recombination rate heterogeneity. Results demonstrate the important interplay of these processes, necessitating caution when interpreting selection scans; specifically, false-positive rates are in excess of true-positive across much of the evaluated parameter space, and selective sweeps are often undetectable unless the strength of selection is exceptionally strong.

The divergence of mean phenotypes under persistent directional selection

Numerous organismal traits, particularly at the cellular level, are likely to be under persistent directional selection across phylogenetic lineages. Unless all mutations affecting such traits have large enough effects to be efficiently selected in all species, gradients in mean phenotypes are expected to arise as a consequence of differences in the power of random genetic drift, which varies by approximately five orders of magnitude across the Tree of Life. Prior theoretical work examining the conditions under which such gradients can arise focused on the simple situation in which all genomic sites affecting the trait have identical and constant mutational effects. Here, we extend this theory to incorporate the more biologically realistic situation in which mutational effects on a trait differ among nucleotide sites. Pursuit of such modifications leads to the development of semi-analytic expressions for the ways in which selective interference arises via linkage effects in single-effects models, which then extend to more complex scenarios. The theory developed clarifies the conditions under which mutations of different selective effects mutually interfere with each others' fixation and shows how variance in effects among sites can substantially modify and extend the expected scaling relationships between mean phenotypes and effective population sizes.

Evaluating power to detect recurrent selective sweeps under increasingly realistic evolutionary null models

The detection of selective sweeps from population genomic data often relies on the premise that the beneficial mutations in question have fixed very near the sampling time. As it has been previously shown that the power to detect a selective sweep is strongly dependent on the time since fixation as well as the strength of selection, it is naturally the case that strong, recent sweeps leave the strongest signatures. However, the biological reality is that beneficial mutations enter populations at a rate, one that partially determines the mean wait time between sweep events and hence their age distribution. An important question thus remains about the power to detect recurrent selective sweeps when they are modelled by a realistic mutation rate and as part of a realistic distribution of fitness effects (DFE), as opposed to a single, recent, isolated event on a purely neutral background as is more commonly modelled. Here we use forward-in-time simulations to study the performance of commonly used sweep statistics, within the context of more realistic evolutionary baseline models incorporating purifying and background selection, population size change, and mutation and recombination rate heterogeneity. Results demonstrate the important interplay of these processes, necessitating caution when interpreting selection scans; specifically, false positive rates are in excess of true positive across much of the evaluated parameter space, and selective sweeps are often undetectable unless the strength of selection is exceptionally strong.

Teaser Text

Outlier-based genomic scans have proven a popular approach for identifying loci that have potentially experienced recent positive selection. However, it has previously been shown that an evolutionarily appropriate baseline model that incorporates non-equilibrium population histories, purifying and background selection, and variation in mutation and recombination rates is necessary to reduce often extreme false positive rates when performing genomic scans. Here we evaluate the power to detect recurrent selective sweeps using common SFS-based and haplotype-based methods under these increasingly realistic models. We find that while these appropriate evolutionary baselines are essential to reduce false positive rates, the power to accurately detect recurrent selective sweeps is generally low across much of the biologically relevant parameter space.

A butterfly pan-genome reveals that a large amount of structural variation underlies the evolution of chromatin accessibility

Despite insertions and deletions being the most common structural variants (SVs) found across genomes, not much is known about how much these SVs vary within populations and between closely related species, nor their significance in evolution. To address these questions, we characterized the evolution of indel SVs using genome assemblies of three closely related Heliconius butterfly species. Over the relatively short evolutionary timescales investigated, up to 18.0% of the genome was composed of indels between two haplotypes of an individual Heliconius charithonia butterfly and up to 62.7% included lineage-specific SVs between the genomes of the most distant species (11 Mya). Lineage-specific sequences were mostly characterized as transposable elements (TEs) inserted at random throughout the genome and their overall distribution was similarly affected by linked selection as single nucleotide substitutions. Using chromatin accessibility profiles (i.e., ATAC-seq) of head tissue in caterpillars to identify sequences with potential cis-regulatory function, we found that out of the 31,066 identified differences in chromatin accessibility between species, 30.4% were within lineage-specific SVs and 9.4% were characterized as TE insertions. These TE insertions were localized closer to gene transcription start sites than expected at random and were enriched for sites with significant resemblance to several transcription factor binding sites with known function in neuron development in Drosophila We also identified 24 TE insertions with head-specific chromatin accessibility. Our results show high rates of structural genome evolution that were previously overlooked in comparative genomic studies and suggest a high potential for structural variation to serve as raw material for adaptive evolution.

impMKT: the imputed McDonald and Kreitman test, a straightforward correction that significantly increases the evidence of positive selection of the McDonald and Kreitman test at the gene level

The McDonald and Kreitman test is one of the most powerful and widely used methods to detect and quantify recurrent natural selection in DNA sequence data. One of its main limitations is the underestimation of positive selection due to the presence of slightly deleterious variants segregating at low frequencies. Although several approaches have been developed to overcome this limitation, most of them work on gene pooled analyses. Here, we present the imputed McDonald and Kreitman test (impMKT), a new straightforward approach for the detection of positive selection and other selection components of the distribution of fitness effects at the gene level. We compare imputed McDonald and Kreitman test with other widely used McDonald and Kreitman test approaches considering both simulated and empirical data. By applying imputed McDonald and Kreitman test to humans and Drosophila data at the gene level, we substantially increase the statistical evidence of positive selection with respect to previous approaches (e.g. by 50% and 157% compared with the McDonald and Kreitman test in Drosophila and humans, respectively). Finally, we review the minimum number of genes required to obtain a reliable estimation of the proportion of adaptive substitution (α) in gene pooled analyses by using the imputed McDonald and Kreitman test compared with other McDonald and Kreitman test implementations. Because of its simplicity and increased power to detect recurrent positive selection on genes, we propose the imputed McDonald and Kreitman test as the first straightforward approach for testing specific evolutionary hypotheses at the gene level. The software implementation and population genomics data are available at the web-server imkt.uab.cat.

Estimating the rates of crossover and gene conversion from individual genomes

Recombination can occur either as a result of crossover or gene conversion events. Population genetic methods for inferring the rate of recombination from patterns of linkage disequilibrium generally assume a simple model of recombination that only involves crossover events and ignore gene conversion. However, distinguishing the 2 processes is not only necessary for a complete description of recombination, but also essential for understanding the evolutionary consequences of inversions and other genomic partitions in which crossover (but not gene conversion) is reduced. We present heRho, a simple composite likelihood scheme for coestimating the rate of crossover and gene conversion from individual diploid genomes. The method is based on analytic results for the distance-dependent probability of heterozygous and homozygous states at 2 loci. We apply heRho to simulations and data from the house mouse Mus musculus castaneus, a well-studied model. Our analyses show (1) that the rates of crossover and gene conversion can be accurately coestimated at the level of individual chromosomes and (2) that previous estimates of the population scaled rate of recombination ρ=4Ner under a pure crossover model are likely biased.

Mutation accumulation opposes polymorphism: supergenes and the curious case of balanced lethals

Supergenes offer spectacular examples of long-term balancing selection in nature, but their origin and maintenance remain a mystery. Reduced recombination between arrangements, a critical aspect of many supergenes, protects adaptive multi-trait phenotypes but can lead to mutation accumulation. Mutation accumulation can stabilize the system through the emergence of associative overdominance (AOD), destabilize the system, or lead to new evolutionary outcomes. One outcome is the formation of maladaptive balanced lethal systems, where only heterozygotes remain viable and reproduce. We investigated the conditions under which these different outcomes occur, assuming a scenario of introgression after divergence. We found that AOD aided the invasion of a new supergene arrangement and the establishment of a polymorphism. However, this polymorphism was easily destabilized by further mutation accumulation, which was often asymmetric, disrupting the quasi-equilibrium state. Mechanisms that accelerated degeneration tended to amplify asymmetric mutation accumulation between the supergene arrangements and vice-versa. As the evolution of balanced lethal systems requires symmetric degeneration of both arrangements, this leaves only restricted conditions for their evolution, namely small population sizes and low rates of gene conversion. The dichotomy between the persistence of polymorphism and degeneration of supergene arrangements likely underlies the rarity of balanced lethal systems in nature. This article is part of the theme issue 'Genomic architecture of supergenes: causes and evolutionary consequences'.

How Can We Resolve Lewontin's Paradox?

We discuss the genetic, demographic, and selective forces that are likely to be at play in restricting observed levels of DNA sequence variation in natural populations to a much smaller range of values than would be expected from the distribution of census population sizes alone-Lewontin's Paradox. While several processes that have previously been strongly emphasized must be involved, including the effects of direct selection and genetic hitchhiking, it seems unlikely that they are sufficient to explain this observation without contributions from other factors. We highlight a potentially important role for the less-appreciated contribution of population size change; specifically, the likelihood that many species and populations may be quite far from reaching the relatively high equilibrium diversity values that would be expected given their current census sizes.

The effects of weak selection on neutral diversity at linked sites

The effects of selection on variability at linked sites have an important influence on levels and patterns of within-population variation across the genome. Most theoretical models of these effects have assumed that selection is sufficiently strong that allele frequency changes at the loci concerned are largely deterministic. These models have led to the conclusion that directional selection for selectively favorable mutations, or against recurrent deleterious mutations, reduces nucleotide site diversity at linked neutral sites. Recent work has shown, however, that fixations of weakly selected mutations, accompanied by significant stochastic changes in allele frequencies, can sometimes cause higher diversity at linked sites when compared with the effects of fixations of neutral mutations. This study extends this work by deriving approximate expressions for the mean conditional times to fixation and loss of mutations subject to selection, and analyzing the conditions under which selection increases rather than reduces these times. Simulations are used to examine the relations between diversity at a neutral site and the fixation and loss times of mutations at a linked site that is subject to selection. It is shown that the long-term level of neutral diversity can be increased over the purely neutral value by recurrent fixations and losses of linked, weakly selected dominant or partially dominant favorable mutations, or linked recessive or partially recessive deleterious mutations. The results are used to examine the conditions under which associative overdominance, as opposed to background selection, is likely to operate.

Recommendations for improving statistical inference in population genomics

The field of population genomics has grown rapidly in response to the recent advent of affordable, large-scale sequencing technologies. As opposed to the situation during the majority of the 20th century, in which the development of theoretical and statistical population genetic insights outpaced the generation of data to which they could be applied, genomic data are now being produced at a far greater rate than they can be meaningfully analyzed and interpreted. With this wealth of data has come a tendency to focus on fitting specific (and often rather idiosyncratic) models to data, at the expense of a careful exploration of the range of possible underlying evolutionary processes. For example, the approach of directly investigating models of adaptive evolution in each newly sequenced population or species often neglects the fact that a thorough characterization of ubiquitous nonadaptive processes is a prerequisite for accurate inference. We here describe the perils of these tendencies, present our consensus views on current best practices in population genomic data analysis, and highlight areas of statistical inference and theory that are in need of further attention. Thereby, we argue for the importance of defining a biologically relevant baseline model tuned to the details of each new analysis, of skepticism and scrutiny in interpreting model fitting results, and of carefully defining addressable hypotheses and underlying uncertainties.

Chromosome size affects sequence divergence between species through the interplay of recombination and selection

The structure of the genome shapes the distribution of genetic diversity and sequence divergence. To investigate how the relationship between chromosome size and recombination rate affects sequence divergence between species, we combined empirical analyses and evolutionary simulations. We estimated pairwise sequence divergence among 15 species from three different mammalian clades-Peromyscus rodents, Mus mice, and great apes-from chromosome-level genome assemblies. We found a strong significant negative correlation between chromosome size and sequence divergence in all species comparisons within the Peromyscus and great apes clades but not the Mus clade, suggesting that the dramatic chromosomal rearrangements among Mus species may have masked the ancestral genomic landscape of divergence in many comparisons. Our evolutionary simulations showed that the main factor determining differences in divergence among chromosomes of different sizes is the interplay of recombination rate and selection, with greater variation in larger populations than in smaller ones. In ancestral populations, shorter chromosomes harbor greater nucleotide diversity. As ancestral populations diverge, diversity present at the onset of the split contributes to greater sequence divergence in shorter chromosomes among daughter species. The combination of empirical data and evolutionary simulations revealed that chromosomal rearrangements, demography, and divergence times may also affect the relationship between chromosome size and divergence, thus deepening our understanding of the role of genome structure in the evolution of species divergence.

Population-genomic analysis identifies a low rate of global adaptive fixation in the proteins of the cyclical parthenogen Daphnia magna

Daphnia are well-established ecological and evolutionary models, and the interaction between D. magna and its microparasites is widely considered a paragon of the host-parasite coevolutionary process. Like other well-studied arthropods such as Drosophila melanogaster and Anopheles gambiae, D. magna is a small, widespread, and abundant species that is therefore expected to display a large long-term population size and high rates of adaptive protein evolution. However, unlike these other species, D. magna is cyclically asexual and lives in a highly structured environment (ponds and lakes) with moderate levels of dispersal, both of which are predicted to impact upon long-term effective population size and adaptive protein evolution. To investigate patterns of adaptive protein fixation, we produced the complete coding genomes of 36 D. magna clones sampled from across the European range (Western Palaearctic), along with draft sequences for the close relatives D. similis and D. lumholtzi, used as outgroups. We analyzed genome-wide patterns of adaptive fixation, with a particular focus on genes that have an a priori expectation of high rates, such as those likely to mediate immune responses, RNA interference against viruses and transposable elements, and those with a strongly male-biased expression pattern. We find that, as expected, D. magna displays high levels of diversity and that this is highly structured among populations. However, compared with Drosophila, we find that D. magna proteins appear to have a high proportion of weakly deleterious variants and do not show evidence of pervasive adaptive fixation across its entire range. This is true of the genome as a whole, and also of putative ‘arms race’ genes that often show elevated levels of adaptive substitution in other species. In addition to the likely impact of extensive, and previously documented, local adaptation, we speculate that these findings may reflect reduced efficacy of selection associated with cyclical asexual reproduction.

Revisiting the notion of deleterious sweeps

It has previously been shown that, conditional on its fixation, the time to fixation of a semi-dominant deleterious autosomal mutation in a randomly mating population is the same as that of an advantageous mutation. This result implies that deleterious mutations could generate selective sweep-like effects. Although their fixation probabilities greatly differ, the much larger input of deleterious relative to beneficial mutations suggests that this phenomenon could be important. We here examine how the fixation of mildly deleterious mutations affects levels and patterns of polymorphism at linked sites-both in the presence and absence of interference amongst deleterious mutations-and how this class of sites may contribute to divergence between-populations and species. We find that, while deleterious fixations are unlikely to represent a significant proportion of outliers in polymorphism-based genomic scans within populations, minor shifts in the frequencies of deleterious mutations can influence the proportions of private variants and the value of FST after a recent population split. As sites subject to deleterious mutations are necessarily found in functional genomic regions, interpretations in terms of recurrent positive selection may require reconsideration.

Effects of Selection at Linked Sites on Patterns of Genetic Variability

Patterns of variation and evolution at a given site in a genome can be strongly influenced by the effects of selection at genetically linked sites. In particular, the recombination rates of genomic regions correlate with their amount of within-population genetic variability, the degree to which the frequency distributions of DNA sequence variants differ from their neutral expectations, and the levels of adaptation of their functional components. We review the major population genetic processes that are thought to lead to these patterns, focusing on their effects on patterns of variability: selective sweeps, background selection, associative overdominance, and Hill–Robertson interference among deleterious mutations. We emphasize the difficulties in distinguishing among the footprints of these processes and disentangling them from the effects of purely demographic factors such as population size changes. We also discuss how interactions between selective and demographic processes can significantly affect patterns of variability within genomes.

Chromosome Fusion Affects Genetic Diversity and Evolutionary Turnover of Functional Loci but Consistently Depends on Chromosome Size

Major changes in chromosome number and structure are linked to a series of evolutionary phenomena, including intrinsic barriers to gene flow or suppression of recombination due to chromosomal rearrangements. However, chromosome rearrangements can also affect the fundamental dynamics of molecular evolution within populations by changing relationships between linked loci and altering rates of recombination. Here, we build chromosome-level assembly Eueides isabella and, together with a recent chromosome-level assembly of Dryas iulia, examine the evolutionary consequences of multiple chromosome fusions in Heliconius butterflies. These assemblies pinpoint fusion points on 10 of the 20 autosomal chromosomes and reveal striking differences in the characteristics of fused and unfused chromosomes. The ten smallest autosomes in D. iulia and E. isabella, which have each fused to a longer chromosome in Heliconius, have higher repeat and GC content, and longer introns than predicted by their chromosome length. When fused, these characteristics change to become more in line with chromosome length. The fusions also led to reduced diversity, which likely reflects increased background selection and selection against introgression between diverging populations, following a reduction in per-base recombination rate. We further show that chromosome size and fusion impact turnover rates of functional loci at a macroevolutionary scale. Together these results provide further evidence that chromosome fusion in Heliconius likely had dramatic effects on population level processes shaping rates of neutral and adaptive divergence. These effects may have impacted patterns of diversification in Heliconius, a classic example of an adaptive radiation.

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.

A Fine-Scale Genetic Map for Vervet Monkeys

Despite its important biological role, the evolution of recombination rates remains relatively poorly characterized. This owes, in part, to the lack of high-quality genomic resources to address this question across diverse species. Humans and our closest evolutionary relatives, anthropoid apes, have remained a major focus of large-scale sequencing efforts, and thus recombination rate variation has been comparatively well studied in this group-with earlier work revealing a conservation at the broad- but not the fine-scale. However, in order to better understand the nature of this variation, and the time scales on which substantial modifications occur, it is necessary to take a broader phylogenetic perspective. I here present the first fine-scale genetic map for vervet monkeys based on whole-genome population genetic data from ten individuals and perform a series of comparative analyses with the great apes. The results reveal a number of striking features. First, owing to strong positive correlations with diversity and weak negative correlations with divergence, analyses suggest a dominant role for purifying and background selection in shaping patterns of variation in this species. Second, results support a generally reduced broad-scale recombination rate compared with the great apes, as well as a narrower fraction of the genome in which the majority of recombination events are observed to occur. Taken together, this data set highlights the great necessity of future research to identify genomic features and quantify evolutionary processes that are driving these rate changes across primates.

The Impact of Purifying and Background Selection on the Inference of Population History: Problems and Prospects

Current procedures for inferring population history generally assume complete neutrality—that is, they neglect both direct selection and the effects of selection on linked sites. We here examine how the presence of direct purifying selection and background selection may bias demographic inference by evaluating two commonly-used methods (MSMC and fastsimcoal2), specifically studying how the underlying shape of the distribution of fitness effects and the fraction of directly selected sites interact with demographic parameter estimation. The results show that, even after masking functional genomic regions, background selection may cause the mis-inference of population growth under models of both constant population size and decline. This effect is amplified as the strength of purifying selection and the density of directly selected sites increases, as indicated by the distortion of the site frequency spectrum and levels of nucleotide diversity at linked neutral sites. We also show how simulated changes in background selection effects caused by population size changes can be predicted analytically. We propose a potential method for correcting for the mis-inference of population growth caused by selection. By treating the distribution of fitness effect as a nuisance parameter and averaging across all potential realizations, we demonstrate that even directly selected sites can be used to infer demographic histories with reasonable accuracy.

The impact of purifying and background selection on the inference of population history: problems and prospects

Current procedures for inferring population history generally assume complete neutrality - that is, they neglect both direct selection and the effects of selection on linked sites. We here examine how the presence of direct purifying selection and background selection may bias demographic inference by evaluating two commonly-used methods (MSMC and fastsimcoal2), specifically studying how the underlying shape of the distribution of fitness effects (DFE) and the fraction of directly selected sites interact with demographic parameter estimation. The results show that, even after masking functional genomic regions, background selection may cause the mis-inference of population growth under models of both constant population size and decline. This effect is amplified as the strength of purifying selection and the density of directly selected sites increases, as indicated by the distortion of the site frequency spectrum and levels of nucleotide diversity at linked neutral sites. We also show how simulated changes in background selection effects caused by population size changes can be predicted analytically. We propose a potential method for correcting for the mis-inference of population growth caused by selection. By treating the DFE as a nuisance parameter and averaging across all potential realizations, we demonstrate that even directly selected sites can be used to infer demographic histories with reasonable accuracy.

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.

Inferring Parameters of the Distribution of Fitness Effects of New Mutations When Beneficial Mutations Are Strongly Advantageous and Rare

Characterizing the distribution of fitness effects (DFE) for new mutations is central in evolutionary genetics. Analysis of molecular data under the McDonald-Kreitman test has suggested that adaptive substitutions make a substantial contribution to between-species divergence. Methods have been proposed to estimate the parameters of the distribution of fitness effects for positively selected mutations from the unfolded site frequency spectrum (uSFS). Such methods perform well when beneficial mutations are mildly selected and frequent. However, when beneficial mutations are strongly selected and rare, they may make little contribution to standing variation and will thus be difficult to detect from the uSFS. In this study, I analyze uSFS data from simulated populations subject to advantageous mutations with effects on fitness ranging from mildly to strongly beneficial. As expected, frequent, mildly beneficial mutations contribute substantially to standing genetic variation and parameters are accurately recovered from the uSFS. However, when advantageous mutations are strongly selected and rare, there are very few segregating in populations at any one time. Fitting the uSFS in such cases leads to underestimates of the strength of positive selection and may lead researchers to false conclusions regarding the relative contribution adaptive mutations make to molecular evolution. Fortunately, the parameters for the distribution of fitness effects for harmful mutations are estimated with high accuracy and precision. The results from this study suggest that the parameters of positively selected mutations obtained by analysis of the uSFS should be treated with caution and that variability at linked sites should be used in conjunction with standing variability to estimate parameters of the distribution of fitness effects in the future.

Toward an Evolutionarily Appropriate Null Model: Jointly Inferring Demography and Purifying Selection

The question of the relative evolutionary roles of adaptive and nonadaptive processes has been a central debate in population genetics for nearly a century. While advances have been made in the theoretical development of the underlying models, and statistical methods for estimating their parameters from large-scale genomic data, a framework for an appropriate null model remains elusive. A model incorporating evolutionary processes known to be in constant operation, genetic drift (as modulated by the demographic history of the population) and purifying selection, is lacking. Without such a null model, the role of adaptive processes in shaping within- and between-population variation may not be accurately assessed. Here, we investigate how population size changes and the strength of purifying selection affect patterns of variation at "neutral" sites near functional genomic components. We propose a novel statistical framework for jointly inferring the contribution of the relevant selective and demographic parameters. By means of extensive performance analyses, we quantify the utility of the approach, identify the most important statistics for parameter estimation, and compare the results with existing methods. Finally, we reanalyze genome-wide population-level data from a Zambian population of Drosophila melanogaster, and find that it has experienced a much slower rate of population growth than was inferred when the effects of purifying selection were neglected. Our approach represents an appropriate null model, against which the effects of positive selection can be assessed.

From Drift to Draft: How Much Do Beneficial Mutations Actually Contribute to Predictions of Ohta's Slightly Deleterious Model of Molecular Evolution?

Since its inception in 1973, the slightly deleterious model of molecular evolution, also known as the nearly neutral theory of molecular evolution, remains a central model to explain the main patterns of DNA polymorphism in natural populations. This is not to say that the quantitative fit to data are perfect. A recent study used polymorphism data from Drosophila melanogaster to test whether, as predicted by the nearly neutral theory, the proportion of effectively neutral mutations depends on the effective population size (Ne ). It showed that a nearly neutral model simply scaling with Ne variation across the genome could not alone explain the data, but that consideration of linked positive selection improves the fit between observations and predictions. In the present article, we extended the work in two main directions. First, we confirmed the observed pattern on a set of 59 species, including high-quality genomic data from 11 animal and plant species with different mating systems and effective population sizes, hence a priori different levels of linked selection. Second, for the 11 species with high-quality genomic data we also estimated the full distribution of fitness effects (DFE) of mutations, and not solely the DFE of deleterious mutations. Both Ne and beneficial mutations contributed to the relationship between the proportion of effectively neutral mutations and local Ne across the genome. In conclusion, the predictions of the slightly deleterious model of molecular evolution hold well for species with small Ne , but for species with large Ne , the fit is improved by incorporating linked positive selection to the model.

How Long Does It Take to Fix a Favorable Mutation, and Why Should We Care?

The time taken for a selectively favorable allele to spread through a single population was investigated early in the history of population genetics. The resulting formulas are based on deterministic dynamics, leading to inaccuracies at allele frequencies close to 0 or 1. To remedy this problem, the properties of the stochastic phases at either end point of allele frequency need to be analyzed. This article uses a heuristic approach to determining the expected times spent in the stochastic and deterministic phases of allele frequency trajectories, for a model of weak selection at a single locus that is valid for inbreeding populations and for autosomal and sex-linked inheritance. The net fixation time is surprisingly insensitive to the level of dominance of a favorable mutation, even with random mating. Approximate expressions for the variance of the net fixation time are also obtained, which imply that there can be substantial stochastic effects even in very large populations. The accuracy of the approximations was evaluated by comparisons with computer simulations. The results reveal some areas that need further investigation if a full understanding of selective sweeps is to be obtained, notably the possibility that fixations of slightly deleterious mutations may be affecting variability at closely linked sites.

Selective Sweeps Under Dominance and Inbreeding

A major research goal in evolutionary genetics is to uncover loci experiencing positive selection. One approach involves finding 'selective sweeps' patterns, which can either be 'hard sweeps' formed by de novo mutation, or 'soft sweeps' arising from recurrent mutation or existing standing variation. Existing theory generally assumes outcrossing populations, and it is unclear how dominance affects soft sweeps. We consider how arbitrary dominance and inbreeding via self-fertilization affect hard and soft sweep signatures. With increased self-fertilization, they are maintained over longer map distances due to reduced effective recombination and faster beneficial allele fixation times. Dominance can affect sweep patterns in outcrossers if the derived variant originates from either a single novel allele, or from recurrent mutation. These models highlight the challenges in distinguishing hard and soft sweeps, and propose methods to differentiate between scenarios.

Patterns of Genetic Variability in Genomic Regions with Low Rates of Recombination

The amount of DNA sequence variability in a genomic region is often positively correlated with its rate of crossing over (CO) [1-3]. This pattern is caused by selection acting on linked sites, which reduces genetic variability and biases the frequency distribution of segregating variants toward more rare variants than are expected without selection (skew). These effects may involve the spread of beneficial mutations (selective sweeps [SSWs]), the elimination of deleterious mutations (background selection [BGS]), or both, and are expected to be stronger with lower CO rates [1-3]. However, in a recent study of human populations, the skew was reduced in the lowest CO regions compared with regions with somewhat higher CO rates [4]. A low skew in very low CO regions, compared with theoretical predictions, is seen in the population genomic studies of Drosophila simulans described here and in other Drosophila species. Here, we propose an explanation for lower than expected skew in low CO regions, and validate it using computer simulations; explanations for higher skew with higher CO rates, as in D. simulans, will be explored elsewhere. Partially recessive, linked deleterious mutations can increase neutral variability when the product of the effective population size (N_e) and the selection coefficient against homozygous carriers of mutations (s) is ≤1, i.e., there is associative overdominance (AOD) rather than BGS [5]. AOD can operate in low CO regions, producing a lower skew than in its absence. This opens up a new perspective on how selection affects patterns of variability at linked sites.

Evolutionary Modeling in SLiM 3 for Beginners

The SLiM forward genetic simulation framework has proved to be a powerful and flexible tool for population genetic modeling. However, as a complex piece of software with many features that allow simulating a diverse assortment of evolutionary models, its initial learning curve can be difficult. Here we provide a step-by-step demonstration of how to build a simple evolutionary model in SLiM 3, to help new users get started. We will begin with a panmictic neutral model, and build up to a model of the evolution of a polygenic quantitative trait under selection for an environmental phenotypic optimum.