Reductions in genetic variation inDrosophila andE. coli caused by selection at linked sites

Selection at linked sites has important consequences for the properties of neutral variation and for tests of the predictions of the neutral theory of molecular evolution. We review the theory of the effect of adaptive gene substitutions on neutral variability at linked sites (hitchhiking or selective sweeps) and discuss theoretical results on the effect of selection against deleterious alleles on variation at linked sites (background selection). InDrosophila melanogaster there is a clear relation between the frequency of recombination in a given region of the chromosome and the amount of natural variability in that region. Attempts to predict this relation have given rise to models of selective sweeps and background selection. We describe possible methods of discriminating between these models, and also discuss the probable strong influence of selective sweeps on variation in largely nonrecombining genomes, with particular reference toEscherichia coll. Finally we present some unresolved questions and possible directions for future research.     

Inferences of Demography and Selection in an African Population of Drosophila melanogaster

It remains a central problem in population genetics to infer the past action of natural selection, and these inferences pose a challenge because demographic events will also substantially affect patterns of polymorphism and divergence. Thus it is imperative to explicitly model the underlying demographic history of the population whenever making inferences about natural selection. In light of the considerable interest in adaptation in African populations of Drosophila melanogaster, which are considered ancestral to the species, we generated a large polymorphism data set representing 2.1 Mb from each of 20 individuals from a Ugandan population of D. melanogaster. In contrast to previous inferences of a simple population expansion in eastern Africa, our demographic modeling of this ancestral population reveals a strong signature of a population bottleneck followed by population expansion, which has significant implications for future demographic modeling of derived populations of this species. Taking this more complex underlying demographic history into account, we also estimate a mean X-linked region-wide rate of adaptation of 6 × 10⁻¹¹/site/generation and a mean selection coefficient of beneficial mutations of 0.0009. These inferences regarding the rate and strength of selection are largely consistent with most other estimates from D. melanogaster and indicate a relatively high rate of adaptation driven by weakly beneficial mutations.     

Genomic Evidence of Rapid and Stable Adaptive Oscillations over Seasonal Time Scales in Drosophila

In many species, genomic data have revealed pervasive adaptive evolution indicated by the fixation of beneficial alleles. However, when selection pressures are highly variable along a species'' range or through time adaptive alleles may persist at intermediate frequencies for long periods. So called “balanced polymorphisms” have long been understood to be an important component of standing genetic variation, yet direct evidence of the strength of balancing selection and the stability and prevalence of balanced polymorphisms has remained elusive. We hypothesized that environmental fluctuations among seasons in a North American orchard would impose temporally variable selection on Drosophila melanogaster that would drive repeatable adaptive oscillations at balanced polymorphisms. We identified hundreds of polymorphisms whose frequency oscillates among seasons and argue that these loci are subject to strong, temporally variable selection. We show that these polymorphisms respond to acute and persistent changes in climate and are associated in predictable ways with seasonally variable phenotypes. In addition, our results suggest that adaptively oscillating polymorphisms are likely millions of years old, with some possibly predating the divergence between D. melanogaster and D. simulans. Taken together, our results are consistent with a model of balancing selection wherein rapid temporal fluctuations in climate over generational time promotes adaptive genetic diversity at loci underlying polygenic variation in fitness related phenotypes.     

Pervasive adaptive protein evolution apparent in diversity patterns around amino acid substitutions in Drosophila simulans

In Drosophila, multiple lines of evidence converge in suggesting that beneficial substitutions to the genome may be common. All suffer from confounding factors, however, such that the interpretation of the evidence-in particular, conclusions about the rate and strength of beneficial substitutions-remains tentative. Here, we use genome-wide polymorphism data in D. simulans and sequenced genomes of its close relatives to construct a readily interpretable characterization of the effects of positive selection: the shape of average neutral diversity around amino acid substitutions. As expected under recurrent selective sweeps, we find a trough in diversity levels around amino acid but not around synonymous substitutions, a distinctive pattern that is not expected under alternative models. This characterization is richer than previous approaches, which relied on limited summaries of the data (e.g., the slope of a scatter plot), and relates to underlying selection parameters in a straightforward way, allowing us to make more reliable inferences about the prevalence and strength of adaptation. Specifically, we develop a coalescent-based model for the shape of the entire curve and use it to infer adaptive parameters by maximum likelihood. Our inference suggests that ～13% of amino acid substitutions cause selective sweeps. Interestingly, it reveals two classes of beneficial fixations: a minority (approximately 3%) that appears to have had large selective effects and accounts for most of the reduction in diversity, and the remaining 10%, which seem to have had very weak selective effects. These estimates therefore help to reconcile the apparent conflict among previously published estimates of the strength of selection. More generally, our findings provide unequivocal evidence for strongly beneficial substitutions in Drosophila and illustrate how the rapidly accumulating genome-wide data can be leveraged to address enduring questions about the genetic basis of adaptation.     

Genomic effects of nucleotide substitutions in Drosophila simulans

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

Multi-locus Analysis of Genomic Time Series Data from Experimental Evolution

Genomic time series data generated by evolve-and-resequence (E&R) experiments offer a powerful window into the mechanisms that drive evolution. However, standard population genetic inference procedures do not account for sampling serially over time, and new methods are needed to make full use of modern experimental evolution data. To address this problem, we develop a Gaussian process approximation to the multi-locus Wright-Fisher process with selection over a time course of tens of generations. The mean and covariance structure of the Gaussian process are obtained by computing the corresponding moments in discrete-time Wright-Fisher models conditioned on the presence of a linked selected site. This enables our method to account for the effects of linkage and selection, both along the genome and across sampled time points, in an approximate but principled manner. We first use simulated data to demonstrate the power of our method to correctly detect, locate and estimate the fitness of a selected allele from among several linked sites. We study how this power changes for different values of selection strength, initial haplotypic diversity, population size, sampling frequency, experimental duration, number of replicates, and sequencing coverage depth. In addition to providing quantitative estimates of selection parameters from experimental evolution data, our model can be used by practitioners to design E&R experiments with requisite power. We also explore how our likelihood-based approach can be used to infer other model parameters, including effective population size and recombination rate. Then, we apply our method to analyze genome-wide data from a real E&R experiment designed to study the adaptation of D. melanogaster to a new laboratory environment with alternating cold and hot temperatures.     

Evidence of the accumulation of allele-specific non-synonymous substitutions in the young region of recombination suppression within the mating-type chromosomes of Neurospora tetrasperma

Currently, little is known about the origin and early evolution of sex chromosomes. This is largely due to the fact that ancient non-recombining sex chromosomes are highly degenerated, and thus provide little information about the early genomic events in their evolution. The Neurospora tetrasperma mating-type (mat) chromosomes contain a young (<6 Mya) and large region (>6.6 Mb) of suppressed recombination, thereby providing a model system to study early stages of sex chromosome evolution. Here, we examined alleles of 207 genes located on the N. tetrasperma mat a and mat A chromosomes to test for signs of genomic alterations at the protein level in the young region of recombination suppression. We report that the N. tetrasperma mat a and mat A chromosomes have each independently accumulated allele-specific non-synonymous codon substitutions in a time-dependent, and gene-specific manner in the recombinationally suppressed region. In addition, examination of the ratio (ω) of non-synonymous substitutions (dN) to synonymous substitutions (dS) using maximum likelihood analyses, indicates that such changes are associated with relaxed purifying selection, a finding consistent with genomic degeneration. We also reveal that sex specific biases in mutation rates or selection pressures are not necessary for genomic alterations in sex chromosomes, and that recombination suppression in itself is sufficient to explain these results. The present findings extend our current understanding of genomic events associated within the young region of recombination suppression in these fungal sex-regulating chromosomes.     

Courtship Song Does Not Increase the Rate of Adaptation to a Thermally Stressful Environment in a Drosophila melanogaster Laboratory Population

Courtship song in D. melanogaster contributes substantially to male mating success through female selection. We used experimental evolution to test whether this display trait is maintained through adaptive female selection because it indicates heritable male quality for thermal stress tolerance. We used non-displaying, outbred populations of D. melanogaster (nub¹) mutants and measured their rate of adaptation to a new, thermally stressful environment, relative to wild-type control populations that retained courtship song. This design retains sexually selected conflict in both treatments. Thermal stress should select across genomes for newly beneficial alleles, increasing the available genetic and phenotypic variation and, therefore, the magnitude of female benefit derived from courtship song. Following introduction to the thermally stressful environment, net reproductive rate decreased 50% over four generations, and then increased 19% over the following 16 generations. There were no differences between the treatments. Possible explanations for these results are discussed.     

Selective sweeps in the presence of interference among partially linked loci

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

Genetic draft and quasi-neutrality in large facultatively sexual populations

Large populations may contain numerous simultaneously segregating polymorphisms subject to natural selection. Since selection acts on individuals whose fitness depends on many loci, different loci affect each other’s dynamics. This leads to stochastic fluctuations of allele frequencies above and beyond genetic drift—an effect known as genetic draft. Since recombination disrupts associations between alleles, draft is strong when recombination is rare. Here, we study a facultatively outcrossing population in a regime where the frequency of outcrossing and recombination, r, is small compared to the characteristic scale of fitness differences σ. In this regime, fit genotypes expand clonally, leading to large fluctuations in the number of recombinant offspring genotypes. The power law tail in the distribution of the latter makes it impossible to capture the dynamics of draft by an effective neutral model. Instead, we find that the fixation time of a neutral allele increases only slowly with the population size but depends sensitively on the ratio r/σ. The efficacy of selection is reduced dramatically and alleles behave “quasi-neutrally” even for Ns≫1, provided that |s| < s_c, where s_c depends strongly on r/σ, but only weakly on population size N. In addition, the anomalous fluctuations due to draft change the spectrum of (quasi)-neutral alleles from f(ν) ∼ ν⁻¹, corresponding to drift, to ∼ ν⁻². Finally, draft accelerates the rate of two-step adaptations through deleterious intermediates.THE genetic diversity of a population is determined by mutation, selection, recombination, and genetic drift, i.e., the stochasticity inherent in reproduction. Understanding how genetic diversity depends on these elements of evolutionary dynamics is central to population genetics, since it allows us to make inferences about the past history and to predict how rapidly populations can adapt.Population genetic inference focuses on the diversity at putatively neutral sites and assumes that the history of these sites is described by the neutral “coalescent” (Kingman 1982). Coalescent theory models the genealogy of asexual organisms or nonrecombining segments of a genome by positing that lineages merge at random, backward in time, due to common ancestry. Under this assumption, the mean time to the most recent common ancestor, T_C, of the extant N individuals, is 2N generations. The coalescence timescale is very important, since the genetic diversity of the population is given by the number of mutations that occur in all lineages descending from the most recent common ancestor of the population. Genetic diversity is therefore controlled by T_C and hence, under the assumption of neutral evolution, proportional to N. [Coalescent theory has been extended to weak selection (Krone and Neuhauser 1997) and recombination (Hudson 1983; Griffiths and Marjoram 1996).]However, the prediction that neutral genetic diversity is proportional to N is at odds with observations: Population sizes of different organisms differ by many orders of magnitude, while genetic variation among organisms is fairly constant (Lewontin 1974). To resolve this “paradox of variation”, Maynard Smith and Haigh (1974) suggested that selection acting on linked loci might reduce diversity at a neutral locus. Rapid fixation of a novel mutation at a linked locus will perturb the allele frequencies. These perturbations can bring alleles to fixation and, more generally, reduce the coalescence time and hence the average genetic diversity (Kaplan et al. 1989; Barton 1998; Gillespie 2001). Such “hitchhiking” of neutral alleles on linked selected loci will dominate over genetic drift in large populations. Since hitchhiking leads to larger perturbations for more closely linked loci, one expects genetic variation to correlate with the recombination rate, as is indeed observed in Drosophila (Begun and Aquadro 1992; Stephan and Mitchell 1992; Andolfatto and Przeworski 2001; Sella et al. 2009).A related effect was described earlier by Hill and Robertson (1966), who studied the reduction in the fixation probability of a novel beneficial mutation because of selection acting at a linked locus. This effect is commonly known as Hill–Robertson interference (Felsenstein 1974). Hitchhiking and Hill–Robertson interference are different aspects of the same phenomenon, one focusing on the effects of linked selection on genetic diversity and the other on the efficacy of selection. While hitchhiking and Hill–Robertson effects are primarily associated with positive selection for novel alleles, purifying selection against deleterious mutations also affects genetic diversity. The elimination of (neutral) alleles linked deleterious mutations is known as background selection. The lower the recombination rates are, the larger is the target for linked deleterious mutations, resulting in stronger background selection (Charlesworth et al. 1993; Hudson and Kaplan 1995; Nordborg et al. 1996).Most models used to study Hill–Robertson and hitchhiking effects between positively selected mutations consider only two loci. Deleterious mutations, however, are expected to be much more frequent, and background selection models typically consider many mutations with small deleterious effects. A systematic study of the effect of interference between many weakly selected sites in a mutation/selection/drift equilibrium was presented by McVean and Charlesworth (2000), who used computer simulations of a model of codon bias evolution. They showed that linkage-dependent interference between a large number of weakly selected sites has substantial effects on genetic diversity, fixation probability of mutations, and the degree of adaptation measured as the frequency of preferred codons. This and subsequent computational studies reinforced the understanding that the Hill–Roberson effect reduces the effectiveness of selection and made clear that a quantitative understanding of Hill–Robertson effects in multilocus systems requires an analysis that goes beyond two-locus models (Comeron and Kreitman 2002; Seger et al. 2010); see Comeron et al. (2008) for a recent review.It is common to interpret the effect of linked selection in terms of increased variance in offspring number. In this interpretation, linked selection can be thought of as a stochastic force analogous to genetic drift and is often referred to as genetic draft—a term coined by Gillespie (2000). Following Hill and Robertson (1966) and Felsenstein (1974), the increased variance in offspring number is often captured by a reduction in the “effective population” size, N_e, in a neutral model (which means enhanced drift and accelerated coalescence). It has, however, been noted that a rescaled neutral model does not consistently explain all observables (Charlesworth et al. 1993; Braverman et al. 1995; Fay and Wu 2000; McVean and Charlesworth 2000; Barton and Etheridge 2004; Seger et al. 2010) and that different effective population sizes need to be defined depending on the question and timescale of interest (Ewens 2004; Karasov et al. 2010). Furthermore, the dependence of N_e on the actual population size and other relevant parameters is not understood (Wiehe and Stephan 1993; Gillespie 2000; Lynch 2007).Here, we provide analytic results on the effect of draft in a stochastic multilocus evolution model. Instead of a mutation/selection equilibrium considered in McVean and Charlesworth (2000), our focus here is a continuously adapting and facultatively sexual population, like human immunodeficiency virus (HIV) in coevolution with the host’s immune system. Our model and its relation to the biology of HIV are described in more detail below. The scope of the model, however, extends beyond HIV and is equally applicable to scenarios where background selection is dominant. Many important and well-studied organisms such as influenza, yeast, and plants are facultatively sexual. Rice, for example, is a partly selfing species and strong selection has acted during its domestication (Caicedo et al. 2007). While dominance effects can render the selfing of diploid organisms more complicated than facultatively sexual propagation of haploid organisms (Charlesworth et al. 1991; Kelly and Williamson 2000), our analysis still provides a null model on top of which dominance effects can be investigated.Using computer simulations of an adapting population, we first demonstrate how quantities such as the coalescence time, the fixation probability of beneficial or deleterious mutations, and the allele frequency spectra depend on the rate of outcrossing relative to selection. We also show that our in silico observations cannot be described by a neutral model with a reduced effective population size. This is because single genotypes can, through clonal expansion, give rise to a wildly fluctuating number of recombinant genotypes. The distribution is so broad that its variance diverges, which in turn makes an effectively neutral diffusion limit impossible. To provide an analytic understanding of the simulation results, we use a branching process model that allows us to study the stochastic dynamics of novel mutations (neutral, beneficial, and deleterious) as they spread through the population. We calculate fixation probabilities and the typical time to fixation, T_fix (and more generally, the probability of attaining n copies after time T), for a new mutant allele, making explicit the dependence on the rate of recombination, fitness variance, and the population size. An important consequence of genetic draft is a qualitatively different frequency spectrum of rare alleles, which we also calculate analytically. Finally, we show that empirical HIV allele frequency spectra are in agreement with our theoretical prediction, confirming the relevance of our model to the dynamics of HIV adaptation.     

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.     

Coalescence with Background and Balancing Selection in Systems with Bi- and Uniparental Reproduction: Contrasting Partial Asexuality and Selfing

Uniparental reproduction in diploids, via asexual reproduction or selfing, reduces the independence with which separate loci are transmitted across generations. This is expected to increase the extent to which a neutral marker is affected by selection elsewhere in the genome. Such effects have previously been quantified in coalescent models involving selfing. Here we examine the effects of background selection and balancing selection in diploids capable of both sexual and asexual reproduction (i.e., partial asexuality). We find that the effect of background selection on reducing coalescent time (and effective population size) can be orders of magnitude greater when rates of sex are low than when sex is common. This is because asexuality enhances the effects of background selection through both a recombination effect and a segregation effect. We show that there are several reasons that the strength of background selection differs between systems with partial asexuality and those with comparable levels of uniparental reproduction via selfing. Expectations for reductions in N_e via background selection have been verified using stochastic simulations. In contrast to background selection, balancing selection increases the coalescence time for a linked neutral site. With partial asexuality, the effect of balancing selection is somewhat dependent upon the mode of selection (e.g., heterozygote advantage vs. negative frequency-dependent selection) in a manner that does not apply to selfing. This is because the frequency of heterozygotes, which are required for recombination onto alternative genetic backgrounds, is more dependent on the pattern of selection with partial asexuality than with selfing.     

A microsatellite-based analysis for the detection of selection on BTA1 and BTA20 in northern Eurasian cattle (Bos taurus) populations

Background

Microsatellites surrounding functionally important candidate genes or quantitative trait loci have received attention as proxy measures of polymorphism level at the candidate loci themselves. In cattle, selection for economically important traits is a long-term strategy and it has been reported that microsatellites are linked to these important loci.

Methods

We have investigated the variation of seven microsatellites on BTA1 (Bos taurus autosome 1) and 16 on BTA20, using bovine populations of typical production types and horn status in northern Eurasia. Genetic variability of these loci and linkage disequilibrium among these loci were compared with those of 28 microsatellites on other bovine chromosomes. Four different tests were applied to detect molecular signatures of selection.

Results

No marked difference in locus variability was found between microsatellites on BTA1, BTA20 and the other chromosomes in terms of different diversity indices. Average D'' values of pairwise syntenic markers (0.32 and 0.28 across BTA 1 and BTA20 respectively) were significantly (P < 0.05) higher than for non-syntenic markers (0.15). The Ewens-Watterson test, the Beaumont and Nichol''s modified frequentist test and the Bayesian F_ST-test indicated elevated or decreased genetic differentiation, at SOD1 and AGLA17 markers respectively, deviating significantly (P < 0.05) from neutral expectations. Furthermore, lnRV, lnRH and lnRθ'' statistics were used for the pairwise population comparison tests and were significantly less variable in one population relative to the other, providing additional evidence of selection signatures for two of the 51 loci. Moreover, the three Finnish native populations showed evidence of subpopulation divergence at SOD1 and AGLA17. Our data also indicate significant intergenic linkage disequilibrium around the candidate loci and suggest that hitchhiking selection has played a role in shaping the pattern of observed linkage disequilibrium.

Conclusion

Hitchhiking due to tight linkage with alleles at candidate genes, e.g. the POLL gene, is a possible explanation for this pattern. The potential impact of selective breeding by man on cattle populations is discussed in the context of selection effects. Our results also suggest that a practical approach to detect loci under selection is to simultaneously apply multiple neutrality tests based on different assumptions and estimations.     

Tempo of Degeneration Across Independently Evolved Nonrecombining Regions

Recombination is beneficial over the long term, allowing more effective selection. Despite long-term advantages of recombination, local recombination suppression can evolve and lead to genomic degeneration, in particular on sex chromosomes. Here, we investigated the tempo of degeneration in nonrecombining regions, that is, the function curve for the accumulation of deleterious mutations over time, leveraging on 22 independent events of recombination suppression identified on mating-type chromosomes of anther-smut fungi, including newly identified ones. Using previously available and newly generated high-quality genome assemblies of alternative mating types of 13 Microbotryum species, we estimated degeneration levels in terms of accumulation of nonoptimal codons and nonsynonymous substitutions in nonrecombining regions. We found a reduced frequency of optimal codons in the nonrecombining regions compared with autosomes, that was not due to less frequent GC-biased gene conversion or lower ancestral expression levels compared with recombining regions. The frequency of optimal codons rapidly decreased following recombination suppression and reached an asymptote after ca. 3 Ma. The strength of purifying selection remained virtually constant at d_N/d_S = 0.55, that is, at an intermediate level between purifying selection and neutral evolution. Accordingly, nonsynonymous differences between mating-type chromosomes increased linearly with stratum age, at a rate of 0.015 per My. We thus develop a method for disentangling effects of reduced selection efficacy from GC-biased gene conversion in the evolution of codon usage and we quantify the tempo of degeneration in nonrecombining regions, which is important for our knowledge on genomic evolution and on the maintenance of regions without recombination.     

The Molecular Clock of Neutral Evolution Can Be Accelerated or Slowed by Asymmetric Spatial Structure

Over time, a population acquires neutral genetic substitutions as a consequence of random drift. A famous result in population genetics asserts that the rate, K, at which these substitutions accumulate in the population coincides with the mutation rate, u, at which they arise in individuals: K = u. This identity enables genetic sequence data to be used as a “molecular clock” to estimate the timing of evolutionary events. While the molecular clock is known to be perturbed by selection, it is thought that K = u holds very generally for neutral evolution. Here we show that asymmetric spatial population structure can alter the molecular clock rate for neutral mutations, leading to either K<u or K>u. Our results apply to a general class of haploid, asexually reproducing, spatially structured populations. Deviations from K = u occur because mutations arise unequally at different sites and have different probabilities of fixation depending on where they arise. If birth rates are uniform across sites, then K ≤ u. In general, K can take any value between 0 and Nu. Our model can be applied to a variety of population structures. In one example, we investigate the accumulation of genetic mutations in the small intestine. In another application, we analyze over 900 Twitter networks to study the effect of network topology on the fixation of neutral innovations in social evolution.     

The classical hitchhiking model with continuous mutational pressure and purifying selection

Detecting selective sweeps driven by strong positive selection and localizing the targets of selection in the genome play a major role in modern population genetics and genomics. Most of these analyses are based on the classical model of genetic hitchhiking proposed by Maynard Smith and Haigh (1974, Genetical Research, 23, 23). Here, we consider extensions of the classical two‐locus model. Introducing mutation at the strongly selected site, we analyze the conditions under which soft sweeps may arise. We identify a new parameter (the ratio of the beneficial mutation rate to the selection coefficient) that characterizes the occurrence of multiple‐origin soft sweeps. Furthermore, we quantify the hitchhiking effect when the polymorphism at the linked locus is not neutral but maintained in a mutation‐selection balance. In this case, we find a smaller relative reduction of heterozygosity at the linked site than for a neutral polymorphism. In our analysis, we use a semi‐deterministic approach; i.e., we analyze the frequency process of the beneficial allele in an infinitely large population when its frequency is above a certain threshold; however, for very small frequencies in the initial phase after the onset of selection we rely on diffusion theory.     

Odorant receptor (Or) genes: polymorphism and divergence in the D. melanogaster and D. pseudoobscura lineages

Background

In insects, like in most invertebrates, olfaction is the principal sensory modality, which provides animals with essential information for survival and reproduction. Odorant receptors are involved in this response, mediating interactions between an individual and its environment, as well as between individuals of the same or different species. The adaptive importance of odorant receptors renders them good candidates for having their variation shaped by natural selection.

Methodology/Principal Findings

We analyzed nucleotide variation in a subset of eight Or genes located on the 3L chromosomal arm of Drosophila melanogaster in a derived population of this species and also in a population of Drosophila pseudoobscura. Some heterogeneity in the silent polymorphism to divergence ratio was detected in the D. melanogaster/D. simulans comparison, with a single gene (Or67b) contributing ∼37% to the test statistic. However, no other signals of a very recent selective event were detected at this gene. In contrast, at the speciation timescale, the MK test uncovered the footprint of positive selection driving the evolution of two of the encoded proteins in both D. melanogaster —OR65c and OR67a —and D. pseudoobscura —OR65b1 and OR67c.

Conclusions

The powerful polymorphism/divergence approach provided evidence for adaptive evolution at a rather high proportion of the Or genes studied after relatively recent speciation events. It did not provide, however, clear evidence for very recent selective events in either D. melanogaster or D. pseudoobscura.     

Deep Learning for Population Genetic Inference

Given genomic variation data from multiple individuals, computing the likelihood of complex population genetic models is often infeasible. To circumvent this problem, we introduce a novel likelihood-free inference framework by applying deep learning, a powerful modern technique in machine learning. Deep learning makes use of multilayer neural networks to learn a feature-based function from the input (e.g., hundreds of correlated summary statistics of data) to the output (e.g., population genetic parameters of interest). We demonstrate that deep learning can be effectively employed for population genetic inference and learning informative features of data. As a concrete application, we focus on the challenging problem of jointly inferring natural selection and demography (in the form of a population size change history). Our method is able to separate the global nature of demography from the local nature of selection, without sequential steps for these two factors. Studying demography and selection jointly is motivated by Drosophila, where pervasive selection confounds demographic analysis. We apply our method to 197 African Drosophila melanogaster genomes from Zambia to infer both their overall demography, and regions of their genome under selection. We find many regions of the genome that have experienced hard sweeps, and fewer under selection on standing variation (soft sweep) or balancing selection. Interestingly, we find that soft sweeps and balancing selection occur more frequently closer to the centromere of each chromosome. In addition, our demographic inference suggests that previously estimated bottlenecks for African Drosophila melanogaster are too extreme.