Site Frequency Spectrum Research Articles

Accuracy of Demographic Inferences from the Site Frequency Spectrum: The Case of the Yoruba Population

Some methods for demographic inference based on the observed genetic diversity of current populations rely on the use of summary statistics such as the Site Frequency Spectrum (SFS). Demographic models can be either model-constrained with numerous parameters, such as growth rates, timing of demographic events, and migration rates, or model-flexible, with an unbounded collection of piecewise constant sizes. It is still debated whether demographic histories can be accurately inferred based on the SFS. Here, we illustrate this theoretical issue on an example of demographic inference for an African population. The SFS of the Yoruba population (data from the 1000 Genomes Project) is fit to a simple model of population growth described with a single parameter (e.g., founding time). We infer a time to the most recent common ancestor of 1.7million years (MY) for this population. However, we show that the Yoruba SFS is not informative enough to discriminate between several different models of growth. We also show that for such simple demographies, the fit of one-parameter models outperforms the stairway plot, a recently developed model-flexible method. The use of this method on simulated data suggests that it is biased by the noise intrinsically present in the data.

Inference of the Distribution of Selection Coefficients for New Nonsynonymous Mutations Using Large Samples.

The distribution of fitness effects (DFE) has considerable importance in population genetics. To date, estimates of the DFE come from studies using a small number of individuals. Thus, estimates of the proportion of moderately to strongly deleterious new mutations may be unreliable because such variants are unlikely to be segregating in the data. Additionally, the true functional form of the DFE is unknown, and estimates of the DFE differ significantly between studies. Here we present a flexible and computationally tractable method, called Fit∂a∂i, to estimate the DFE of new mutations using the site frequency spectrum from a large number of individuals. We apply our approach to the frequency spectrum of 1300 Europeans from the Exome Sequencing Project ESP6400 data set, 1298 Danes from the LuCamp data set, and 432 Europeans from the 1000 Genomes Project to estimate the DFE of deleterious nonsynonymous mutations. We infer significantly fewer (0.38–0.84 fold) strongly deleterious mutations with selection coefficient |s| > 0.01 and more (1.24–1.43 fold) weakly deleterious mutations with selection coefficient |s| < 0.001 compared to previous estimates. Furthermore, a DFE that is a mixture distribution of a point mass at neutrality plus a gamma distribution fits better than a gamma distribution in two of the three data sets. Our results suggest that nearly neutral forces play a larger role in human evolution than previously thought.

Identifying signatures of positive selection in pigmentation genes in two South Asian populations.

Skin pigmentation is a polygenic trait showing wide phenotypic variations among global populations. While numerous pigmentation genes have been identified to be under positive selection among European and East populations, genes contributing to phenotypic variation in skin pigmentation within and among South Asian populations are still poorly understood. The present study uses data from the Phase 3 of the 1000 genomes project focusing on two South Asian populations-GIH (Gujarati Indian from Houston, Texas) and ITU (Indian Telugu from UK), so as to decode the genetic architecture involved in adaptation to ultraviolet radiation in South Asian populations. Statistical tests included were (1) tests to identify deviations of the Site Frequency Spectrum (SFS) from neutral expectations (Tajima's D, Fay and Wu's H and Fu and Li's D* and F*), (2) tests focused on the identification of high-frequency haplotypes with extended linkage disequilibrium (iHS and Rsb), and (3) tests based on genetic differentiation between populations (LSBL). Twenty-two pigmentation genes fall in the top 1% for at least one statistic in the GIH population, 5 of which (LYST, OCA2, SLC24A5, SLC45A2, and TYR) have been previously associated with normal variation in skin, hair, or eye color. In comparison, 17 genes fall in the top 1% for at least one statistic in the ITU population. Twelve loci which are identified as outliers in the ITU scan were also identified in the GIH population. These results suggest that selection may have affected these loci broadly across the region.

LINE Insertion Polymorphisms are Abundant but at Low Frequencies across Populations of Anolis carolinensis.

Vertebrate genomes differ considerably in size and structure. Among the features that show the most variation is the abundance of Long Interspersed Nuclear Elements (LINEs). Mammalian genomes contain 100,000s LINEs that belong to a single clade, L1, and in most species a single family is usually active at a time. In contrast, non-mammalian vertebrates (fish, amphibians and reptiles) contain multiple active families, belonging to several clades, but each of them is represented by a small number of recently inserted copies. It is unclear why vertebrate genomes harbor such drastic differences in LINE composition. To address this issue, we conducted whole genome resequencing to investigate the population genomics of LINEs across 13 genomes of the lizard Anolis carolinensis sampled from two geographically and genetically distinct populations in the Eastern Florida and the Gulf Atlantic regions of the United States. We used the Mobile Element Locator Tool to identify and genotype polymorphic insertions from five major clades of LINEs (CR1, L1, L2, RTE and R4) and the 41 subfamilies that constitute them. Across these groups we found large variation in the frequency of polymorphic insertions and the observed length distributions of these insertions, suggesting these groups vary in their activity and how frequently they successfully generate full-length, potentially active copies. Though we found an abundance of polymorphic insertions (over 45,000) most of these were observed at low frequencies and typically appeared as singletons. Site frequency spectra for most LINEs showed a significant shift toward low frequency alleles compared to the spectra observed for total genomic single nucleotide polymorphisms. Using Tajima’s D, FST and the mean number of pairwise differences in LINE insertion polymorphisms, we found evidence that negative selection is acting on LINE families in a length-dependent manner, its effects being stronger in the larger Eastern Florida population. Our results suggest that a large effective population size and negative selection limit the expansion of polymorphic LINE insertions across these populations and that the probability of LINE polymorphisms reaching fixation is extremely low.

Partitioning the heritability of coronary artery disease highlights the importance of immune-mediated processes and epigenetic sites associated with transcriptional activity.

With the availability of genome-wide genotype data from GWAS studies, it is now possible to compute the genetic relatedness among individuals and estimate its contribution (SNP-based heritability) to phenotypic variance using Mixed-Linear-Models (MLMs). The estimated heritability can be partitioned according to biological features to gain insight into the genetic architecture of a disease. Here, we aimed to examine the genetic structure of coronary artery disease (CAD). We investigated the genetic structure of CAD using 3,163,082 autosomal genome-wide SNPs (MAF ≥ 0.01) and MLMs in a sample of genetically 'unrelated' 4535 cases and 2977 controls. We find that genome-wide SNPs explain 22% of liability to CAD (55% of narrow-sense heritability) and sex-differences in CAD is not due to common SNPs on autosomal chromosomes. Heritability was proportionally distributed across the allele frequency spectrum and notably enriched among genic SNPs. We identified a number of modules that are significantly associated with CAD including: Dendritic cells stimulation; Basigin interactions; and a Cancer module. Of note, genes involved in inflammation account for one-fifth of SNP-based heritability. Heritability-enrichment analysis showed significant enrichment in epigenetic sites associated with transcriptionally activity; namely, enhancers, H3K9ac/H3K27ac/H3K4me1/H3K4me3 histone modifications, and Fetal DNase I hypersensitivity sites whereas heritability was highly depleted in transcriptionally repressed regions. More individual SNP associations will be detected for CAD as sample size increases. The identified modules provide further biological insight for CAD and highlight the importance of immune-mediated processes in CAD pathogenesis. Finally, we showed that genetic liability to CAD is mainly attributed to epigenetic sites associated with transcriptional activity which encourage the design of custom sequencing/genotyping panels based on transcriptionally active regions.

History, geography and host use shape genomewide patterns of genetic variation in the redheaded pine sawfly (Neodiprion lecontei).

Divergent host use has long been suspected to drive population differentiation and speciation in plant-feeding insects. Evaluating the contribution of divergent host use to genetic differentiation can be difficult, however, as dispersal limitation and population structure may also influence patterns of genetic variation. In this study, we use double-digest restriction-associated DNA (ddRAD) sequencing to test the hypothesis that divergent host use contributes to genetic differentiation among populations of the redheaded pine sawfly (Neodiprion lecontei), a widespread pest that uses multiple Pinus hosts throughout its range in eastern North America. Because this species has a broad range and specializes on host plants known to have migrated extensively during the Pleistocene, we first assess overall genetic structure using model-based and model-free clustering methods and identify three geographically distinct genetic clusters. Next, using a composite-likelihood approach based on the site frequency spectrum and a novel strategy for maximizing the utility of linked RAD markers, we infer the population topology and date divergence to the Pleistocene. Based on existing knowledge of Pinus refugia, estimated demographic parameters and patterns of diversity among sawfly populations, we propose a Pleistocene divergence scenario for N.lecontei. Finally, using Mantel and partial Mantel tests, we identify a significant relationship between genetic distance and geography in all clusters, and between genetic distance and host use in two of three clusters. Overall, our results indicate that Pleistocene isolation, dispersal limitation and ecological divergence all contribute to genomewide differentiation in this species and support the hypothesis that host use is a common driver of population divergence in host-specialized insects.

A Model of Compound Heterozygous, Loss-of-Function Alleles Is Broadly Consistent with Observations from Complex-Disease GWAS Datasets.

The genetic component of complex disease risk in humans remains largely unexplained. A corollary is that the allelic spectrum of genetic variants contributing to complex disease risk is unknown. Theoretical models that relate population genetic processes to the maintenance of genetic variation for quantitative traits may suggest profitable avenues for future experimental design. Here we use forward simulation to model a genomic region evolving under a balance between recurrent deleterious mutation and Gaussian stabilizing selection. We consider multiple genetic and demographic models, and several different methods for identifying genomic regions harboring variants associated with complex disease risk. We demonstrate that the model of gene action, relating genotype to phenotype, has a qualitative effect on several relevant aspects of the population genetic architecture of a complex trait. In particular, the genetic model impacts genetic variance component partitioning across the allele frequency spectrum and the power of statistical tests. Models with partial recessivity closely match the minor allele frequency distribution of significant hits from empirical genome-wide association studies without requiring homozygous effect sizes to be small. We highlight a particular gene-based model of incomplete recessivity that is appealing from first principles. Under that model, deleterious mutations in a genomic region partially fail to complement one another. This model of gene-based recessivity predicts the empirically observed inconsistency between twin and SNP based estimated of dominance heritability. Furthermore, this model predicts considerable levels of unexplained variance associated with intralocus epistasis. Our results suggest a need for improved statistical tools for region based genetic association and heritability estimation.

The Genetic Architecture of Major Depressive Disorder in Han Chinese Women

Despite the moderate, well-demonstrated heritability of major depressive disorder (MDD), there has been limited success in identifying replicable genetic risk loci, suggesting a complex genetic architecture. Research is needed to quantify the relative contribution of classes of genetic variation across the genome to inform future genetic studies of MDD. To apply aggregate genetic risk methods to clarify the genetic architecture of MDD by estimating and partitioning heritability by chromosome, minor allele frequency, and functional annotations and to test for enrichment of rare deleterious variants. The CONVERGE (China, Oxford, and Virginia Commonwealth University Experimental Research on Genetic Epidemiology) study collected data on 5278 patients with recurrent MDD from 58 provincial mental health centers and psychiatric departments of general medical hospitals in 45 cities and 23 provinces of China. Screened controls (n = 5196) were recruited from a range of locations, including general hospitals and local community centers. Data were collected from August 1, 2008, to October 31, 2012. Genetic risk for liability to recurrent MDD was partitioned using sparse whole-genome sequencing. In aggregate, common single-nucleotide polymorphisms (SNPs) explained between 20% and 29% of the variance in MDD risk, and the heritability in MDD explained by each chromosome was proportional to its length (r = 0.680; P = .0003), supporting a common polygenic etiology. Partitioning heritability by minor allele frequency indicated that the variance explained was distributed across the allelic frequency spectrum, although relatively common SNPs accounted for a disproportionate fraction of risk. Partitioning by genic annotation indicated a greater contribution of SNPs in protein-coding regions and within 3'-UTR regions of genes. Enrichment of SNPs associated with DNase I-hypersensitive sites was also found in many tissue types, including brain tissue. Examining burden scores from singleton exonic SNPs predicted to be deleterious indicated that cases had significantly more mutations than controls (odds ratio, 1.009; 95% CI, 1.003-1.014; P = .003), including those occurring in genes expressed in the brain (odds ratio, 1.011; 95% CI, 1.003-1.018; P = .004) and within nuclear-encoded genes with mitochondrial gene products (odds ratio, 1.075; 95% CI, 1.018-1.135; P = .009). Results support a complex etiology for MDD and highlight the value of analyzing components of heritability to clarify genetic architecture.

Resetting the bar: Statistical significance in whole-genome sequencing-based association studies of global populations.

Genome-wide association studies (GWAS) of common disease have been hugely successful in implicating loci that modify disease risk. The bulk of these associations have proven robust and reproducible, in part due to community adoption of statistical criteria for claiming significant genotype-phenotype associations. As the cost of sequencing continues to drop, assembling large samples in global populations is becoming increasingly feasible. Sequencing studies interrogate not only common variants, as was true for genotyping-based GWAS, but variation across the full allele frequency spectrum, yielding many more (independent) statistical tests. We sought to empirically determine genome-wide significance thresholds for various analysis scenarios. Using whole-genome sequence data, we simulated sequencing-based disease studies of varying sample size and ancestry. We determined that future sequencing efforts in >2,000 samples of European, Asian, or admixed ancestry should set genome-wide significance at approximately P = 5 × 10-9 , and studies of African samples should apply a more stringent genome-wide significance threshold of P = 1 × 10-9 . Adoption of a revised multiple test correction will be crucial in avoiding irreproducible claims of association.

Mutation Rate Variation is a Primary Determinant of the Distribution of Allele Frequencies in Humans.

The site frequency spectrum (SFS) has long been used to study demographic history and natural selection. Here, we extend this summary by examining the SFS conditional on the alleles found at the same site in other species. We refer to this extension as the “phylogenetically-conditioned SFS” or cSFS. Using recent large-sample data from the Exome Aggregation Consortium (ExAC), combined with primate genome sequences, we find that human variants that occurred independently in closely related primate lineages are at higher frequencies in humans than variants with parallel substitutions in more distant primates. We show that this effect is largely due to sites with elevated mutation rates causing significant departures from the widely-used infinite sites mutation model. Our analysis also suggests substantial variation in mutation rates even among mutations involving the same nucleotide changes. In summary, we show that variable mutation rates are key determinants of the SFS in humans.

Fisher–Wright model with deterministic seed bank and selection

Seed banks are common characteristics to many plant species, which allow storage of genetic diversity in the soil as dormant seeds for various periods of time. We investigate an above-ground population following a Fisher–Wright model with selection coupled with a deterministic seed bank assuming the length of the seed bank is kept constant and the number of seeds is large. To assess the combined impact of seed banks and selection on genetic diversity, we derive a general diffusion model. The applied techniques outline a path of approximating a stochastic delay differential equation by an appropriately rescaled stochastic differential equation. We compute the equilibrium solution of the site-frequency spectrum and derive the times to fixation of an allele with and without selection. Finally, it is demonstrated that seed banks enhance the effect of selection onto the site-frequency spectrum while slowing down the time until the mutation–selection equilibrium is reached.

Methylome evolution in plants.

Despite major progress in dissecting the molecular pathways that control DNA methylation patterns in plants, little is known about the mechanisms that shape plant methylomes over evolutionary time. Drawing on recent intra- and interspecific epigenomic studies, we show that methylome evolution over long timescales is largely a byproduct of genomic changes. By contrast, methylome evolution over short timescales appears to be driven mainly by spontaneous epimutational events. We argue that novel methods based on analyses of the methylation site frequency spectrum (mSFS) of natural populations can provide deeper insights into the evolutionary forces that act at each timescale.Electronic supplementary materialThe online version of this article (doi:10.1186/s13059-016-1127-5) contains supplementary material, which is available to authorized users.

Bioinformatic processing of RAD‐seq data dramatically impacts downstream population genetic inference

Summary Restriction site‐associated DNA sequencing (RAD‐seq) provides high‐resolution population genomic data at low cost, and has become an important component in ecological and evolutionary studies. As with all high‐throughput technologies, analytic strategies require critical validation to ensure precise and unbiased interpretation. To test the impact of bioinformatic data processing on downstream population genetic inferences, we analysed mammalian RAD‐seq data (&gt;100 individuals) with 312 combinations of methodology (de novo vs. mapping to references of increasing divergence) and filtering criteria (missing data, HWE, FIS, coverage, mapping and genotype quality). In an effort to identify commonalities and biases in all pipelines, we computed summary statistics (nr. loci, nr. SNP, π, Hetobs, FIS, FST, Ne and m) and compared the results to independent null expectations (isolation‐by‐distance correlation, expected transition‐to‐transversion ratio Ts/Tv and Mendelian mismatch rates of known parent–offspring trios). We observed large differences between reference‐based and de novo approaches, the former generally calling more SNPs and reducing FIS and Ts/Tv. Data completion levels showed little impact on most summary statistics, and FST estimates were robust across all pipelines. The site frequency spectrum was highly sensitive to the chosen approach as reflected in large variance of parameter estimates across demographic scenarios (single‐population bottlenecks and isolation‐with‐migration model). Null expectations were best met by reference‐based approaches, although contingent on the specific criteria. We recommend that RAD‐seq studies employ reference‐based approaches to a closely related genome, and due to the high stochasticity associated with the pipeline advocate the use of multiple pipelines to ensure robust population genetic and demographic inferences.

Genomic epidemiology of Lineage 4 Mycobacterium tuberculosis subpopulations in New York City and New Jersey, 1999-2009.

BackgroundWhole genome sequencing (WGS) has rapidly become an important research tool in tuberculosis epidemiology and is likely to replace many existing methods in public health microbiology in the near future. WGS-based methods may be particularly useful in areas with less diverse Mycobacterium tuberculosis populations, such as New York City, where conventional genotyping is often uninformative and field epidemiology often difficult. This study applies four candidate strategies for WGS-based identification of emerging M. tuberculosis subpopulations, employing both phylogenomic and population genetics methods.Results M. tuberculosis subpopulations in New York City and New Jersey can be distinguished via phylogenomic reconstruction, evidence of demographic expansion and subpopulation-specific signatures of selection, and by determination of subgroup-defining nucleotide substitutions. These methods identified known historical outbreak clusters and previously unidentified subpopulations within relatively monomorphic M. tuberculosis endemic clone groups. Neutrality statistics based on the site frequency spectrum were less useful for identifying M. tuberculosis subpopulations, likely due to the low levels of informative genetic variation in recently diverged isolate groups. In addition, we observed that isolates from New York City endemic clone groups have acquired multiple non-synonymous SNPs in virulence- and growth-associated pathways, and relatively few mutations in drug resistance-associated genes, suggesting that overall pathoadaptive fitness, rather than the acquisition of drug resistance mutations, has played a central role in the evolutionary history and epidemiology of M. tuberculosis subpopulations in New York City.ConclusionsOur results demonstrate that some but not all WGS-based methods are useful for detection of emerging M. tuberculosis clone groups, and support the use of phylogenomic reconstruction in routine tuberculosis laboratory surveillance, particularly in areas with relatively less diverse M. tuberculosis populations. Our study also supports the use of wider-reaching phylogenomic and population genomic methods in tuberculosis public health practice, which can support tuberculosis control activities by identifying genetic polymorphisms contributing to epidemiological success in local M. tuberculosis populations and possibly explain why certain isolate groups are apparently more successful in specific host populations.Electronic supplementary materialThe online version of this article (doi:10.1186/s12864-016-3298-6) contains supplementary material, which is available to authorized users.

On the performance of tests for the detection of signatures of selection: a case study with the Spanish autochthonous beef cattle populations.

Background Procedures for the detection of signatures of selection can be classified according to the source of information they use to reject the null hypothesis of absence of selection. Three main groups of tests can be identified that are based on: (1) the analysis of the site frequency spectrum, (2) the study of the extension of the linkage disequilibrium across the length of the haplotypes that surround the polymorphism, and (3) the differentiation among populations. The aim of this study was to compare the performance of a subset of these procedures by using a dataset on seven Spanish autochthonous beef cattle populations.ResultsAnalysis of the correlations between the logarithms of the statistics that were obtained by 11 tests for detecting signatures of selection at each single nucleotide polymorphism confirmed that they can be clustered into the three main groups mentioned above. A factor analysis summarized the results of the 11 tests into three canonical axes that were each associated with one of the three groups. Moreover, the signatures of selection identified with the first and second groups of tests were shared across populations, whereas those with the third group were more breed-specific. Nevertheless, an enrichment analysis identified the metabolic pathways that were associated with each group; they coincided with canonical axes and were related to immune response, muscle development, protein biosynthesis, skin and pigmentation, glucose metabolism, fat metabolism, embryogenesis and morphology, heart and uterine metabolism, regulation of the hypothalamic–pituitary–thyroid axis, hormonal, cellular cycle, cell signaling and extracellular receptors.ConclusionsWe show that the results of the procedures used to identify signals of selection differed substantially between the three groups of tests. However, they can be classified using a factor analysis. Moreover, each canonical factor that coincided with a group of tests identified different signals of selection, which could be attributed to processes of selection that occurred at different evolutionary times. Nevertheless, the metabolic pathways that were associated with each group of tests were similar, which suggests that the selection events that occurred during the evolutionary history of the populations probably affected the same group of traits.Electronic supplementary materialThe online version of this article (doi:10.1186/s12711-016-0258-1) contains supplementary material, which is available to authorized users.

Genomic Epidemiology of Lineage 4 Mycobacterium tuberculosis Subpopulations in New York City and New Jersey, 1999–2009

Whole genome sequencing (WGS) has rapidly become an important research tool in tuberculosis epidemiology and is likely to replace many existing methods in public health microbiology in the near future. WGS-based methods may be particularly useful in areas with less diverse Mycobacterium tuberculosis populations, such as New York City, where conventional genotyping is often uninformative and field epidemiology often difficult. This study applies four candidate strategies for WGS-based identification of emerging M. tuberculosis subpopulations, employing both phylogenomic and population genetics methods. M. tuberculosis subpopulations in New York City and New Jersey can be distinguished via phylogenomic reconstruction, evidence of demographic expansion and subpopulation-specific signatures of selection, and by determination of subgroup-defining nucleotide substitutions. These methods identified known historical outbreak clusters and previously unidentified subpopulations within relatively monomorphic M. tuberculosis endemic clone groups. Neutrality statistics based on the site frequency spectrum were less useful for identifying M. tuberculosis subpopulations, likely due to the low levels of informative genetic variation in recently diverged isolate groups. In addition, we observed that isolates from New York City endemic clone groups have acquired multiple non-synonymous SNPs in virulence- and growth-associated pathways, and relatively few mutations in drug resistance-associated genes, suggesting that overall pathoadaptive fitness, rather than the acquisition of drug resistance mutations, has played a central role in the evolutionary history and epidemiology of M. tuberculosis subpopulations in New York City. Our results demonstrate that some but not all WGS-based methods are useful for detection of emerging M. tuberculosis clone groups, and support the use of phylogenomic reconstruction in routine tuberculosis laboratory surveillance, particularly in areas with relatively less diverse M. tuberculosis populations. Our study also supports the use of wider-reaching phylogenomic and population genomic methods in tuberculosis public health practice, which can support tuberculosis control activities by identifying genetic polymorphisms contributing to epidemiological success in local M. tuberculosis populations and possibly explain why certain isolate groups are apparently more successful in specific host populations.

Evolutionary processes and cellular functions underlying divergence in Alexandrium minutum.

Understanding divergence in the highly dispersive and seemingly homogeneous pelagic environment for organisms living as free drifters in the water column remains a challenge. Here, we analysed the transcriptome-wide mRNA sequences, as well as the morphology of 18 strains of Alexandrium minutum, a dinoflagellate responsible for harmful algal blooms worldwide, to investigate the functional bases of a divergence event. Analysis of the joint site frequency spectrum (JSFS) pointed towards an ancestral divergence in complete isolations followed by a secondary contact resulting in gene flow between the two diverging groups, but heterogeneous across sites. The sites displaying fixed SNPs were associated with a highly restricted gene flow and a strong overrepresentation of nonsynonymous polymorphism, suggesting the importance of selective pressures as drivers of the divergence. The most divergent transcripts were homologs to genes involved in calcium/potassium fluxes across the membrane, calcium transduction signal and saxitoxin production. The implication of these results in terms of ecological divergence and build-up of reproductive isolation is discussed. Dinoflagellates are especially difficult to study in the field at the ecological level due to their small size and the dynamic nature of their natural environment, but also at the genomic level due to their huge and complex genome and the absence of closely related model organism. This study illustrates the possibility to identify the traits of primary importance in ecology and evolution starting from high-throughput sequencing data, even for such organisms.

Adaptive evolution and segregating load contribute to the genomic landscape of divergence in two tree species connected by episodic gene flow.

Speciation often involves repeated episodes of genetic contact between divergent populations before reproductive isolation (RI) is complete. Whole-genome sequencing (WGS) holds great promise for unravelling the genomic bases of speciation. We have studied two ecologically divergent, hybridizing species of the 'model tree' genus Populus (poplars, aspens, cottonwoods), Populus alba and P.tremula, using >8.6million single nucleotide polymorphisms (SNPs) from WGS of population pools. We used the genomic data to (i) scan these species' genomes for regions of elevated and reduced divergence, (ii) assess key aspects of their joint demographic history based on genomewide site frequency spectra (SFS) and (iii) infer the potential roles of adaptive and deleterious coding mutations in shaping the genomic landscape of divergence. We identified numerous small, unevenly distributed genome regions without fixed polymorphisms despite high overall genomic differentiation. The joint SFS was best explained by ancient and repeated gene flow and allowed pinpointing candidate interspecific migrant tracts. The direction of selection (DoS) differed between genes in putative migrant tracts and the remainder of the genome, thus indicating the potential roles of adaptive divergence and segregating deleterious mutations on the evolution and breakdown of RI. Genes affected by positive selection during divergence were enriched for several functionally interesting groups, including well-known candidate 'speciation genes' involved in plant innate immunity. Our results suggest that adaptive divergence affects RI in these hybridizing species mainly through intrinsic and demographic processes. Integrating genomic with molecular data holds great promise for revealing the effects of particular genetic pathways on speciation.

An approximate stationary solution for multi-allele neutral diffusion with low mutation rates

We address the problem of determining the stationary distribution of the multi-allelic, neutral-evolution Wright–Fisher model in the diffusion limit. A full solution to this problem for an arbitrary K×K mutation rate matrix involves solving for the stationary solution of a forward Kolmogorov equation over a (K−1)-dimensional simplex, and remains intractable. In most practical situations mutations rates are slow on the scale of the diffusion limit and the solution is heavily concentrated on the corners and edges of the simplex. In this paper we present a practical approximate solution for slow mutation rates in the form of a set of line densities along the edges of the simplex. The method of solution relies on parameterising the general non-reversible rate matrix as the sum of a reversible part and a set of (K−1)(K−2)/2 independent terms corresponding to fluxes of probability along closed paths around faces of the simplex. The solution is potentially a first step in estimating non-reversible evolutionary rate matrices from observed allele frequency spectra.

Refining the Use of Linkage Disequilibrium as a Robust Signature of Selective Sweeps.

During a selective sweep, characteristic patterns of linkage disequilibrium can arise in the genomic region surrounding a selected locus. These have been used to infer past selective sweeps. However, the recombination rate is known to vary substantially along the genome for many species. We here investigate the effectiveness of current (Kelly's [Formula: see text] and [Formula: see text]) and novel statistics at inferring hard selective sweeps based on linkage disequilibrium distortions under different conditions, including a human-realistic demographic model and recombination rate variation. When the recombination rate is constant, Kelly's [Formula: see text] offers high power, but is outperformed by a novel statistic that we test, which we call [Formula: see text] We also find this statistic to be effective at detecting sweeps from standing variation. When recombination rate fluctuations are included, there is a considerable reduction in power for all linkage disequilibrium-based statistics. However, this can largely be reversed by appropriately controlling for expected linkage disequilibrium using a genetic map. To further test these different methods, we perform selection scans on well-characterized HapMap data, finding that all three statistics-[Formula: see text] Kelly's [Formula: see text] and [Formula: see text]-are able to replicate signals at regions previously identified as selection candidates based on population differentiation or the site frequency spectrum. While [Formula: see text] replicates most candidates when recombination map data are not available, the [Formula: see text] and [Formula: see text] statistics are more successful when recombination rate variation is controlled for. Given both this and their higher power in simulations of selective sweeps, these statistics are preferred when information on local recombination rate variation is available.