The Effects of Background and Interference Selection on Patterns of Genetic Variation in Subdivided Populations

It is well known that most new mutations that affect fitness exert deleterious effects and that natural populations are often composed of subpopulations (demes) connected by gene flow. To gain a better understanding of the joint effects of purifying selection and population structure, we focus on a scenario where an ancestral population splits into multiple demes and study neutral diversity patterns in regions linked to selected sites. In the background selection regime of strong selection, we first derive analytic equations for pairwise coalescent times and F_ST as a function of time after the ancestral population splits into two demes and then construct a flexible coalescent simulator that can generate samples under complex models such as those involving multiple demes or nonconservative migration. We have carried out extensive forward simulations to show that the new methods can accurately predict diversity patterns both in the nonequilibrium phase following the split of the ancestral population and in the equilibrium between mutation, migration, drift, and selection. In the interference selection regime of many tightly linked selected sites, forward simulations provide evidence that neutral diversity patterns obtained from both the nonequilibrium and equilibrium phases may be virtually indistinguishable for models that have identical variance in fitness, but are nonetheless different with respect to the number of selected sites and the strength of purifying selection. This equivalence in neutral diversity patterns suggests that data collected from subdivided populations may have limited power for differentiating among the selective pressures to which closely linked selected sites are subject.     

The structure of allelic diversity in the presence of purifying selection

In the absence of selection, the structure of equilibrium allelic diversity is described by the elegant sampling formula of Ewens. This formula has helped to shape our expectations of empirical patterns of molecular variation. Along with coalescent theory, it provides statistical techniques for rejecting the null model of neutrality. However, we still do not fully understand the statistics of the allelic diversity expected in the presence of natural selection. Earlier work has described the effects of strongly deleterious mutations linked to many neutral sites, and allelic variation in models where offspring fitness is unrelated to parental fitness, but it has proven difficult to understand allelic diversity in the presence of purifying selection at many linked sites. Here, we study the population genetics of infinitely many perfectly linked sites, some neutral and some deleterious. Our approach is based on studying the lineage structure within each class of individuals of similar fitness in the deleterious mutation-selection balance. Consistent with previous observations, we find that for moderate and weak selection pressures, the patterns of allelic diversity cannot be described by a neutral model for any choice of the effective population site. We compute precisely how purifying selection at many linked sites distorts the patterns of allelic diversity, by developing expressions for the likelihood of any configuration of allelic types in a sample analogous to the Ewens sampling formula.     

Stabilizing Selection,Purifying Selection,and Mutational Bias in Finite Populations

Genomic traits such as codon usage and the lengths of noncoding sequences may be subject to stabilizing selection rather than purifying selection. Mutations affecting these traits are often biased in one direction. To investigate the potential role of stabilizing selection on genomic traits, the effects of mutational bias on the equilibrium value of a trait under stabilizing selection in a finite population were investigated, using two different mutational models. Numerical results were generated using a matrix method for calculating the probability distribution of variant frequencies at sites affecting the trait, as well as by Monte Carlo simulations. Analytical approximations were also derived, which provided useful insights into the numerical results. A novel conclusion is that the scaled intensity of selection acting on individual variants is nearly independent of the effective population size over a wide range of parameter space and is strongly determined by the logarithm of the mutational bias parameter. This is true even when there is a very small departure of the mean from the optimum, as is usually the case. This implies that studies of the frequency spectra of DNA sequence variants may be unable to distinguish between stabilizing and purifying selection. A similar investigation of purifying selection against deleterious mutations was also carried out. Contrary to previous suggestions, the scaled intensity of purifying selection with synergistic fitness effects is sensitive to population size, which is inconsistent with the general lack of sensitivity of codon usage to effective population size.     

EVOLUTION IN FLUCTUATING ENVIRONMENTS: DECOMPOSING SELECTION INTO ADDITIVE COMPONENTS OF THE ROBERTSON–PRICE EQUATION

We analyze the stochastic components of the Robertson–Price equation for the evolution of quantitative characters that enables decomposition of the selection differential into components due to demographic and environmental stochasticity. We show how these two types of stochasticity affect the evolution of multivariate quantitative characters by defining demographic and environmental variances as components of individual fitness. The exact covariance formula for selection is decomposed into three components, the deterministic mean value, as well as stochastic demographic and environmental components. We show that demographic and environmental stochasticity generate random genetic drift and fluctuating selection, respectively. This provides a common theoretical framework for linking ecological and evolutionary processes. Demographic stochasticity can cause random variation in selection differentials independent of fluctuating selection caused by environmental variation. We use this model of selection to illustrate that the effect on the expected selection differential of random variation in individual fitness is dependent on population size, and that the strength of fluctuating selection is affected by how environmental variation affects the covariance in Malthusian fitness between individuals with different phenotypes. Thus, our approach enables us to partition out the effects of fluctuating selection from the effects of selection due to random variation in individual fitness caused by demographic stochasticity.     

Impact of demography on linked selection in two outcrossing Brassicaceae species

Genetic diversity is shaped by mutation, genetic drift, gene flow, recombination, and selection. The dynamics and interactions of these forces shape genetic diversity across different parts of the genome, between populations and species. Here, we have studied the effects of linked selection on nucleotide diversity in outcrossing populations of two Brassicaceae species, Arabidopsis lyrata and Capsella grandiflora, with contrasting demographic history. In agreement with previous estimates, we found evidence for a modest population size expansion thousands of generations ago, as well as efficient purifying selection in C. grandiflora. In contrast, the A. lyrata population exhibited evidence for very recent strong population size decline and weaker efficacy of purifying selection. Using multiple regression analyses with recombination rate and other genomic covariates as explanatory variables, we can explain 47% of the variance in neutral diversity in the C. grandiflora population, while in the A. lyrata population, only 11% of the variance was explained by the model. Recombination rate had a significant positive effect on neutral diversity in both species, suggesting that selection at linked sites has an effect on patterns of neutral variation. In line with this finding, we also found reduced neutral diversity in the vicinity of genes in the C. grandiflora population. However, in A. lyrata no such reduction in diversity was evident, a finding that is consistent with expectations of the impact of a recent bottleneck on patterns of neutral diversity near genes. This study thus empirically demonstrates how differences in demographic history modulate the impact of selection at linked sites in natural populations.     

Joint inference of the distribution of fitness effects of deleterious mutations and population demography based on nucleotide polymorphism frequencies

The distribution of fitness effects of new mutations (DFE) is important for addressing several questions in genetics, including the nature of quantitative variation and the evolutionary fate of small populations. Properties of the DFE can be inferred by comparing the distributions of the frequencies of segregating nucleotide polymorphisms at selected and neutral sites in a population sample, but demographic changes alter the spectrum of allele frequencies at both neutral and selected sites, so can bias estimates of the DFE if not accounted for. We have developed a maximum-likelihood approach, based on the expected allele-frequency distribution generated by transition matrix methods, to estimate parameters of the DFE while simultaneously estimating parameters of a demographic model that allows a population size change at some time in the past. We tested the method using simulations and found that it accurately recovers simulated parameter values, even if the simulated demography differs substantially from that assumed in our analysis. We use our method to estimate parameters of the DFE for amino acid-changing mutations in humans and Drosophila melanogaster. For a model of unconditionally deleterious mutations, with effects sampled from a gamma distribution, the mean estimate for the distribution shape parameter is approximately 0.2 for human populations, which implies that the DFE is strongly leptokurtic. For Drosophila populations, we estimate that the shape parameter is approximately 0.35. Differences in the shape of the distribution and the mean selection coefficient between humans and Drosophila result in significantly more strongly deleterious mutations in Drosophila than in humans, and, conversely, nearly neutral mutations are significantly less frequent.     

Genealogies and weak purifying selection

The assumption that selection alters the genealogical tree of a sample of alleles from a population relative to the neutral expectation underlies several "tests of neutrality." Two recent papers have studied the effect of purifying selection; their suggestive but incomplete results indicate that, in the single site case, the shape of a gene genealogy for a locus may differ only from the neutral expectation. We verify this finding for weak selection using the "ancestral selection graph." We consider a wider range of models, including both a four-allele single-site model and an infinite-sites model. Our results confirm the previous claim for the symmetric-mutation single site model. We emphasize, however, that a neutral-seeming genealogy is consistent with detectable effects of selection on the distribution of allele frequences within the sample. With selection operating, the information about a sample cannot be reduced to the genealogy. As a result, a distinction needs to be made between the selected sites themselves, for which the genealogy offers insufficient information, and linked neutral variation. This distinction seems to have been overlooked in previous papers, yet it has significant implications for the interpretation of data on DNA sequence variation. In particular, it predicts that under purifying selection, the frequency spectrum of neutral mutations will not reflect the skew toward rare polymorphisms at replacement sites even if there is no recombination between them. We caution, however, that the effect of weak selection on the genealogy is specific to the model; a (more realistic) model of multiple linked sites could lead to a more distorted genealogy than is observed for a single site.     

The genealogy of a sequence subject to purifying selection at multiple sites

We investigate the effect of purifying selection at multiple sites on both the shape of the genealogy and the distribution of mutations on the tree. We find that the primary effect of purifying selection on a genealogy is to shift the distribution of mutations on the tree, whereas the shape of the tree remains largely unchanged. This result is relevant to the large number of coalescent estimation procedures, which generally assume neutrality for segregating polymorphisms--applying these estimators to evolutionarily constrained sequences could lead to a significant degree of bias. We also estimate the statistical power of several neutrality tests in detecting weak to moderate purifying selection and find that the power is quite good for some parameter combinations. This result contrasts with previous studies, which predicted low statistical power because of the minor effect that weak purifying selection has on the shape of a genealogy. Finally, we investigate the effect of Hill-Robertson interference among linked deleterious mutations on patterns of molecular variation. We find that dependence among selected loci can substantially reduce the efficacy of even fairly strong purifying selection.     

Natural selection at linked sites in humans

Theoretical and empirical work indicates that patterns of neutral polymorphism can be affected by linked, selected mutations. Under background selection, deleterious mutations removed from a population by purifying selection cause a reduction in linked neutral diversity. Under genetic hitchhiking, the rise in frequency and fixation of beneficial mutations also reduces the level of linked neutral polymorphism. Here we review the evidence that levels of neutral polymorphism in humans are affected by selection at linked sites. We then discuss four approaches for distinguishing between background selection and genetic hitchhiking based on (i) the relationship between polymorphism level and recombination rate for neutral loci with high mutation rates, (ii) relative levels of variation on the X chromosome and the autosomes, (iii) the frequency distribution of neutral polymorphisms, and (iv) population-specific patterns of genetic variation. Although the evidence for selection at linked sites in humans is clear, current methods and data do not allow us to clearly assess the relative importance of background selection and genetic hitchhiking in humans. These results contrast with those obtained for Drosophila, where the signals of positive selection are stronger.     

Linked selection,demography and the evolution of correlated genomic landscapes in birds and beyond

Selection has a deep impact on the distribution of genetic diversity and population differentiation along the genome (the genomic landscapes of diversity and differentiation), reducing diversity and elevating differentiation not only at the sites it targets, but also at linked neutral sites. Fuelled by the high‐throughput sequencing revolution, these genomic footprints of selection have been extensively exploited over the past decade with the aim to identify genomic regions involved in adaptation and speciation. However, while this research has shown that the genomic landscapes of diversity and differentiation are usually highly heterogeneous, it has also led to the increasing realization that this heterogeneity may evolve under processes other than adaptation or speciation. In particular, instead of being an effect of selective sweeps or barriers to gene flow, accentuated differentiation can evolve by any process reducing genetic diversity locally within the genome (Charlesworth, 1998 ), including purifying selection at linked sites (background selection). In particular, in genomic regions where recombination is infrequent, accentuated differentiation can evolve as a by‐product of diversity reductions unrelated to adaptation or speciation (Cruickshank & Hahn, 2014 ; Nachman & Payseur, 2012 ; Noor & Bennett, 2009 ). In such genomic regions, linkage extends over physically larger genome stretches, and selection affects a particularly high number of linked neutral sites. Even though the effects of selection on linked neutral diversity (linked selection) within populations are well documented (Cutter & Payseur, 2013 ), recent observations of diversity and differentiation landscapes that are highly correlated even among independent lineages suggest that the effects of long‐term linked selection may have a deeper impact on the evolution of the genomic landscapes of diversity and differentiation than previously anticipated. The study on Saxicola stonechats by Van Doren et al. ( 2017 ) reported in the current issue of Molecular Ecology lines in with a rapidly expanding body of evidence in this direction. Correlations of genomic landscapes extending from within stonechats to comparisons with Ficedula flycatchers add to recent insights into the timescales across which the effects of linked selection persist. Absent and inverted correlations of genomic landscapes in comparisons involving an island taxon, on the other hand, provide important empirical clues about the role of demographic constraints in the evolution of the genomic landscapes of diversity and differentiation.     

Evolution of the segregation ratio: modification of gene conversion and meiotic drive

We compare the evolutionary pressures that direct the modification of gene conversion and meiotic drive at loci subject to purifying and overdominant viability selection. Gene conversion differs from meiotic drive in that modifers do not affect their own segregation ratios, even when linked to the viability locus. Segregation distortion generates gametic level disequilibria between alleles at the viability locus and modifiers of gene conversion and meiotic drive: enhancers of segregation distortion become positively associated with driven alleles. Suppression of gene conversion evolves if the driven allele is marginally disadvantageous (overdominant viability selection), and higher rates evolve if the driven alleles are relatively advantageous (purifying viability selection). Gametic disequilibria permit enhancers of meiotic drive that are linked to the driven locus to promote their own segregation. We attribute the failure of genetic modifiers of gene conversion and meiotic drive to maximinize mean fitness to the generation of such associations.     

The effects of deleterious mutations on evolution at linked sites

The process of evolution at a given site in the genome can be influenced by the action of selection at other sites, especially when these are closely linked to it. Such selection reduces the effective population size experienced by the site in question (the Hill-Robertson effect), reducing the level of variability and the efficacy of selection. In particular, deleterious variants are continually being produced by mutation and then eliminated by selection at sites throughout the genome. The resulting reduction in variability at linked neutral or nearly neutral sites can be predicted from the theory of background selection, which assumes that deleterious mutations have such large effects that their behavior in the population is effectively deterministic. More weakly selected mutations can accumulate by Muller's ratchet after a shutdown of recombination, as in an evolving Y chromosome. Many functionally significant sites are probably so weakly selected that Hill-Robertson interference undermines the effective strength of selection upon them, when recombination is rare or absent. This leads to large departures from deterministic equilibrium and smaller effects on linked neutral sites than under background selection or Muller's ratchet. Evidence is discussed that is consistent with the action of these processes in shaping genome-wide patterns of variation and evolution.     

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.     

Habitat selection and the value of information in heterogenous landscapes

Despite the wide usage of the term information in evolutionary ecology, there is no general treatise between fitness (i.e. density‐dependent population growth) and selection of the environment sensu lato. Here we 1) initiate the building of a quantitative framework with which to examine the relationship between information use in spatially heterogeneous landscapes and density‐dependent population growth, and 2) illustrate its utility by applying the framework to an existing model of breeding habitat selection. We begin by linking information, as a process of narrowing choice, to population growth/fitness. Second, we define a measure of a population's penalty of ignorance based on the Kullback–Leibler index that combines the contributions of resource selection (i.e. biased use of breeding sites) and density‐dependent depletion. Third, we quantify the extent to which environmental heterogeneity (i.e. mean and variance within a landscape) constrains sustainable population growth of unbiased agents. We call this the heterogeneity‐based fitness deficit, and combine this with population simulations to quantify the independent contribution of information‐use strategies to the total population growth rate. We further capitalize on this example to highlight the interactive effects of information between ecological scales when fear affects individual fitness through phenotypic plasticity. Informed breeding habitat selection moderates the demographic cost of fear commensurate with density‐dependent information use. Thus, future work should attempt to differentiate between phenotypic plasticity (i.e. acute fear) and demographic responses (i.e. chronic changes in population size). We conclude with a broader discussion of information in alternative contexts, and explore some evolutionary considerations for information use. We note how competition among individuals may constrain the information state among individuals, and the implications of this constraint under environmental change.     

The Strength of Selection against Neanderthal Introgression

Hybridization between humans and Neanderthals has resulted in a low level of Neanderthal ancestry scattered across the genomes of many modern-day humans. After hybridization, on average, selection appears to have removed Neanderthal alleles from the human population. Quantifying the strength and causes of this selection against Neanderthal ancestry is key to understanding our relationship to Neanderthals and, more broadly, how populations remain distinct after secondary contact. Here, we develop a novel method for estimating the genome-wide average strength of selection and the density of selected sites using estimates of Neanderthal allele frequency along the genomes of modern-day humans. We confirm that East Asians had somewhat higher initial levels of Neanderthal ancestry than Europeans even after accounting for selection. We find that the bulk of purifying selection against Neanderthal ancestry is best understood as acting on many weakly deleterious alleles. We propose that the majority of these alleles were effectively neutral—and segregating at high frequency—in Neanderthals, but became selected against after entering human populations of much larger effective size. While individually of small effect, these alleles potentially imposed a heavy genetic load on the early-generation human–Neanderthal hybrids. This work suggests that differences in effective population size may play a far more important role in shaping levels of introgression than previously thought.     

Density dependence, lifespan and the evolutionary dynamics of longevity

Longevity is a life-history trait that is shaped by natural selection. Evolution will shape mortality trajectories and lifespans, but until now the evolutionary analysis of longevity is based principally on a density-independent (Euler-Lotka) framework. The effects of density dependence on the evolution of lifespan and mortality remain largely unexplored. We investigate the influence of different population demographies on the evolution of longevity, and show how these can be linked to adaptive radiations. We present a range of models to explore the intraspecific and interspecific density effects on longevity and, consequently, diversification. We show how the magnitude, type, and timing of mutation can also affect fitness, invasion and diversification. We argue that fitness of alternative strategies under a range of different demographic structures leads to flat, as opposed to rugged, landscapes and that these flat fitness surfaces are important in the evolution of lifespan and senescence.     

Duplication and population dynamics shape historic patterns of selection and genetic variation at the major histocompatibility complex in rodents

Genetic variation at the major histocompatibility complex (MHC) is vitally important for wildlife populations to respond to pathogen threats. As natural populations can fluctuate greatly in size, a key issue concerns how population cycles and bottlenecks that could reduce genetic diversity will influence MHC genes. Using 454 sequencing, we characterized genetic diversity at the DRB Class II locus in montane voles (Microtus montanus), a North American rodent that regularly undergoes high‐amplitude fluctuations in population size. We tested for evidence of historic balancing selection, recombination, and gene duplication to identify mechanisms maintaining allelic diversity. Counter to our expectations, we found strong evidence of purifying selection acting on the DRB locus in montane voles. We speculate that the interplay between population fluctuations and gene duplication might be responsible for the weak evidence of historic balancing selection and strong evidence of purifying selection detected. To further explore this idea, we conducted a phylogenetically controlled comparative analysis across 16 rodent species with varying demographic histories and MHC duplication events (based on the maximum number of alleles detected per individual). On the basis of phylogenetic generalized linear model‐averaging, we found evidence that the estimated number of duplicated loci was positively related to allelic diversity and, surprisingly, to the strength of purifying selection at the DRB locus. Our analyses also revealed that species that had undergone population bottlenecks had lower allelic richness than stable species. This study highlights the need to consider demographic history and genetic structure alongside patterns of natural selection to understand resulting patterns of genetic variation at the MHC.     

Background selection and population differentiation

A general analytical formula is derived, which predicts the effects of background selection on population differentiation at a neutral locus as a result of its linkage with selected loci of deleterious mutations. The theory is based on the assumptions of random mating, multiplicative fitness, and weak selection in hermaphrodite plants in the island model of population structure. The analytical results show that Fst at the neutral locus increases as a result of the effects of background selection, regardless of the dependence or independence among linked background selective loci. The increment in Fst is closely related to the magnitude of linkage disequilibria between the neutral locus and selected loci, and can be estimated by the ratio of Fst with background selection to Fst without background selection minus one. The steady-state linkage disequilibrium between a neutral locus and a selected locus in subpopulations, primarily attained by gene flow, decreases with the recombination rate, and can be enhanced when there are dependence among linked selected loci. Monte Carlo computer simulations with two- and three-locus models show that the analytical formulae perform well under general conditions. Application of the present theory may aid in analyzing the genome-wide mapping of the effect of background selection in terms of Fst.     

Natural selection for earlier male arrival to breeding grounds through direct and indirect effects in a migratory songbird

For migratory birds, the earlier arrival of males to breeding grounds is often expected to have fitness benefits. However, the selection differential on male arrival time has rarely been decomposed into the direct effect of male arrival and potential indirect effects through female traits. We measured the directional selection differential on male arrival time in the pied flycatcher (Ficedula hypoleuca) using data from 6 years and annual number of fledglings as the fitness proxy. Using structural equation modeling, we were able to take into account the temporal structure of the breeding cycle and the hierarchy between the examined traits. We found directional selection differentials for earlier male arrival date and earlier female laying date, as well as strong selection differential for larger clutch size. These selection differentials were due to direct selection only as indirect selection for these traits was nonsignificant. When decomposing the direct selection for earlier male arrival into direct and indirect effects, we discovered that it was almost exclusively due to the direct effect of male arrival date on fitness and not due to its indirect effects via female traits. In other words, we showed for the first time that there is a direct effect of male arrival date on fitness while accounting for those effects that are mediated by effects of the social partner. Our study thus indicates that natural selection directly favored earlier male arrival in this flycatcher population.