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

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

Genomic changes under rapid evolution: selection for parasitoid resistance

In this study, we characterize changes in the genome during a swift evolutionary adaptation, by combining experimental selection with high-throughput sequencing. We imposed strong experimental selection on an ecologically relevant trait, parasitoid resistance in Drosophila melanogaster against Asobara tabida. Replicated selection lines rapidly evolved towards enhanced immunity. Larval survival after parasitization increased twofold after just five generations of selection. Whole-genome sequencing revealed that the fast and strong selection response in innate immunity produced multiple, highly localized genomic changes. We identified narrow genomic regions carrying a significant signature of selection, which were present across all chromosomes and covered in total less than 5% of the whole D. melanogaster genome. We identified segregating sites with highly significant changes in frequency between control and selection lines that fell within these narrow ‘selected regions’. These segregating sites were associated with 42 genes that constitute possible targets of selection. A region on chromosome 2R was highly enriched in significant segregating sites and may be of major effect on parasitoid defence. The high genetic variability and small linkage blocks in our base population are likely responsible for allowing this complex trait to evolve without causing widespread erosive effects in the genome, even under such a fast and strong selective regime.     

General Triallelic Frequency Spectrum Under Demographic Models with Variable Population Size

It is becoming routine to obtain data sets on DNA sequence variation across several thousands of chromosomes, providing unprecedented opportunity to infer the underlying biological and demographic forces. Such data make it vital to study summary statistics that offer enough compression to be tractable, while preserving a great deal of information. One well-studied summary is the site frequency spectrum—the empirical distribution, across segregating sites, of the sample frequency of the derived allele. However, most previous theoretical work has assumed that each site has experienced at most one mutation event in its genealogical history, which becomes less tenable for very large sample sizes. In this work we obtain, in closed form, the predicted frequency spectrum of a site that has experienced at most two mutation events, under very general assumptions about the distribution of branch lengths in the underlying coalescent tree. Among other applications, we obtain the frequency spectrum of a triallelic site in a model of historically varying population size. We demonstrate the utility of our formulas in two settings: First, we show that triallelic sites are more sensitive to the parameters of a population that has experienced historical growth, suggesting that they will have use if they can be incorporated into demographic inference. Second, we investigate a recently proposed alternative mechanism of mutation in which the two derived alleles of a triallelic site are created simultaneously within a single individual, and we develop a test to determine whether it is responsible for the excess of triallelic sites in the human genome.     

Studying models of balancing selection using phase-type theory

Balancing selection (BLS) is the evolutionary force that maintains high levels of genetic variability in many important genes. To further our understanding of its evolutionary significance, we analyze models with BLS acting on a biallelic locus: an equilibrium model with long-term BLS, a model with long-term BLS and recent changes in population size, and a model of recent BLS. Using phase-type theory, a mathematical tool for analyzing continuous time Markov chains with an absorbing state, we examine how BLS affects polymorphism patterns in linked neutral regions, as summarized by nucleotide diversity, the expected number of segregating sites, the site frequency spectrum, and the level of linkage disequilibrium (LD). Long-term BLS affects polymorphism patterns in a relatively small genomic neighborhood, and such selection targets are easier to detect when the equilibrium frequencies of the selected variants are close to 50%, or when there has been a population size reduction. For a new mutation subject to BLS, its initial increase in frequency in the population causes linked neutral regions to have reduced diversity, an excess of both high and low frequency derived variants, and elevated LD with the selected locus. These patterns are similar to those produced by selective sweeps, but the effects of recent BLS are weaker. Nonetheless, compared to selective sweeps, nonequilibrium polymorphism and LD patterns persist for a much longer period under recent BLS, which may increase the chance of detecting such selection targets. An R package for analyzing these models, among others (e.g., isolation with migration), is available.     

The Effect of Change in Population Size on DNA Polymorphism

The expected number of segregating sites and the expectation of the average number of nucleotide differences among DNA sequences randomly sampled from a population, which is not in equilibrium, have been developed. The results obtained indicate that, in the case where the population size has changed drastically, the number of segregating sites is influenced by the size of the current population more strongly than is the average number of nucleotide differences, while the average number of nucleotide differences is affected by the size of the original population more severely than is the number of segregating sites. The results also indicate that the average number of nucleotide differences is affected by a population bottleneck more strongly than is the number of segregating sites.     

The Effect of Deleterious Mutations on Neutral Molecular Variation

Selection against deleterious alleles maintained by mutation may cause a reduction in the amount of genetic variability at linked neutral sites. This is because a new neutral variant can only remain in a large population for a long period of time if it is maintained in gametes that are free of deleterious alleles, and hence are not destined for rapid elimination from the population by selection. Approximate formulas are derived for the reduction below classical neutral values resulting from such background selection against deleterious mutations, for the mean times to fixation and loss of new mutations, nucleotide site diversity, and number of segregating sites. These formulas apply to random-mating populations with no genetic recombination, and to populations reproducing exclusively asexually or by self-fertilization. For a given selection regime and mating system, the reduction is an exponential function of the total mutation rate to deleterious mutations for the section of the genome involved. Simulations show that the effect decreases rapidly with increasing recombination frequency or rate of outcrossing. The mean time to loss of new neutral mutations and the total number of segregating neutral sites are less sensitive to background selection than the other statistics, unless the population size is of the order of a hundred thousand or more. The stationary distribution of allele frequencies at the neutral sites is correspondingly skewed in favor of rare alleles, compared with the classical neutral result. Observed reductions in molecular variation in low recombination genomic regions of sufficiently large size, for instance in the centromere-proximal regions of Drosophila autosomes or in highly selfing plant populations, may be partly due to background selection against deleterious mutations.     

Population Growth Inflates the Per-Individual Number of Deleterious Mutations and Reduces Their Mean Effect

This study addresses the question of how purifying selection operates during recent rapid population growth such as has been experienced by human populations. This is not a straightforward problem because the human population is not at equilibrium: population genetics predicts that, on the one hand, the efficacy of natural selection increases as population size increases, eliminating ever more weakly deleterious variants; on the other hand, a larger number of deleterious mutations will be introduced into the population and will be more likely to increase in their number of copies as the population grows. To understand how patterns of human genetic variation have been shaped by the interaction of natural selection and population growth, we examined the trajectories of mutations with varying selection coefficients, using computer simulations. We observed that while population growth dramatically increases the number of deleterious segregating sites in the population, it only mildly increases the number carried by each individual. Our simulations also show an increased efficacy of natural selection, reflected in a higher fraction of deleterious mutations eliminated at each generation and a more efficient elimination of the most deleterious ones. As a consequence, while each individual carries a larger number of deleterious alleles than expected in the absence of growth, the average selection coefficient of each segregating allele is less deleterious. Combined, our results suggest that the genetic risk of complex diseases in growing populations might be distributed across a larger number of more weakly deleterious rare variants.     

Inferring the demographic history and rate of adaptive substitution in Drosophila

An important goal of population genetics is to determine the forces that have shaped the pattern of genetic variation in natural populations. We developed a maximum likelihood method that allows us to infer demographic changes and detect recent positive selection (selective sweeps) in populations of varying size from DNA polymorphism data. Applying this approach to single nucleotide polymorphism data at more than 250 noncoding loci on the X chromosome of Drosophila melanogaster from an (ancestral) African population and a (derived) European, we found that the African population expanded about 60,000 y ago and that the European population split off from the African lineage about 15,800 y ago, thereby suffering a severe population size bottleneck. We estimated that about 160 beneficial mutations (with selection coefficients s between 0.05% and 0.5%) were fixed in the euchromatic portion of the X in the African population since population size expansion, and about 60 mutations (with s around 0.5%) in the diverging European lineage.     

Studying Patterns of Recent Evolution at Synonymous Sites and Intronic Sites in Drosophila melanogaster

Most previous studies of the evolution of codon usage bias (CUB) and intronic GC content (iGC) in Drosophila melanogaster were based on between-species comparisons, reflecting long-term evolutionary events. However, a complete picture of the evolution of CUB and iGC cannot be drawn without knowledge of their more recent evolutionary history. Here, we used a polymorphism dataset collected from Zimbabwe to study patterns of the recent evolution of CUB and iGC. Analyzing coding and intronic data jointly with a model which can simultaneously estimate selection, mutational, and demographic parameters, we have found that: (1) natural selection is probably acting on synonymous codons; (2) a constant population size model seems to be sufficient to explain most of the observed synonymous polymorphism patterns; (3) GC is favored over AT in introns. In agreement with the long-term evolutionary patterns, ongoing selection acting on X-linked synonymous codons is stronger than that acting on autosomal codons. The selective differences between preferred and unpreferred codons tend to be greater than the differences between GC and AT in introns, suggesting that natural selection, not just biased gene conversion, may have influenced the evolution of CUB. Interestingly, evidence for non-equilibrium evolution comes exclusively from the intronic data. However, three different models, an equilibrium model with two classes of selected sites and two non-equilibrium models with changes in either population size or mutational parameters, fit the intronic data equally well. These results show that using inadequate selection (or demographic) models can result in incorrect estimates of demographic (or selection) parameters.     

The Interaction between Selection,Demography and Selfing and How It Affects Population Viability

Population extinction due to the accumulation of deleterious mutations has only been considered to occur at small population sizes, large sexual populations being expected to efficiently purge these mutations. However, little is known about how the mutation load generated by segregating mutations affects population size and, eventually, population extinction. We propose a simple analytical model that takes into account both the demographic and genetic evolution of populations, linking population size, density dependence, the mutation load, and self-fertilisation. Analytical predictions were found to be relatively good predictors of population size and probability of population viability when verified using an explicit individual based stochastic model. We show that initially large populations do not always reach mutation-selection balance and can go extinct due to the accumulation of segregating deleterious mutations. Population survival depends not only on the relative fitness and demographic stochasticity, but also on the interaction between the two. When deleterious mutations are recessive, self-fertilisation affects viability non-monotonically and genomic cold-spots could favour the viability of outcrossing populations.     

The number of segregating sites in expanding human populations, with implications for estimates of demographic parameters

The frequency distribution of pairwise differences between sequences of mtDNA has recently been used to estimate the size of human populations before and after a hypothetical episode of rapid population growth and the time at which the population grew. To test the internal consistency of this method, we used three different sets of human mtDNA data and the corresponding demographic parameters estimated from the distribution of pairwise differences to determine by simulation the expected number of segregating sites, S, and its empirical distribution. The results indicate that the observed values of S are significantly lower than expected in two of three cases under the assumption of the infinite-sites model. Further simulations in which mutations were allowed to occur more than once at the same site and in which there was variation in mutation rate among sites show that the expected number of segregating sites can be much lower than under the infinite-site assumption. Nevertheless, the observed value of S is still significantly different from the value expected under the expansion hypothesis in two of three cases.      

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.     

Soft Selective Sweeps in Complex Demographic Scenarios

Adaptation from de novo mutation can produce so-called soft selective sweeps, where adaptive alleles of independent mutational origin sweep through the population at the same time. Population genetic theory predicts that such soft sweeps should be likely if the product of the population size and the mutation rate toward the adaptive allele is sufficiently large, such that multiple adaptive mutations can establish before one has reached fixation; however, it remains unclear how demographic processes affect the probability of observing soft sweeps. Here we extend the theory of soft selective sweeps to realistic demographic scenarios that allow for changes in population size over time. We first show that population bottlenecks can lead to the removal of all but one adaptive lineage from an initially soft selective sweep. The parameter regime under which such “hardening” of soft selective sweeps is likely is determined by a simple heuristic condition. We further develop a generalized analytical framework, based on an extension of the coalescent process, for calculating the probability of soft sweeps under arbitrary demographic scenarios. Two important limits emerge within this analytical framework: In the limit where population-size fluctuations are fast compared to the duration of the sweep, the likelihood of soft sweeps is determined by the harmonic mean of the variance effective population size estimated over the duration of the sweep; in the opposing slow fluctuation limit, the likelihood of soft sweeps is determined by the instantaneous variance effective population size at the onset of the sweep. We show that as a consequence of this finding the probability of observing soft sweeps becomes a function of the strength of selection. Specifically, in species with sharply fluctuating population size, strong selection is more likely to produce soft sweeps than weak selection. Our results highlight the importance of accurate demographic estimates over short evolutionary timescales for understanding the population genetics of adaptation from de novo mutation.     

Selection on laying date is connected to breeding density in the pied flycatcher

Timing of reproduction and clutch size are important determinants of breeding success, especially in seasonal environments. Several recent bird population studies have shown changes in breeding time and in natural selection on it. These changes have often been linked with climate change, but few studies have investigated how the traits or natural selection are actually connected with climatic factors. Furthermore, the effect of population density on selection has been rarely considered, despite the potential importance of density in demographic processes. We studied variation in natural selection on laying date and on clutch size in relation to measures of spring phenology and population density in a long-term study of pied flycatchers in SW Finland. The phenological stage of the environment at mean egg-laying did not affect the direction of selection on either laying date or on clutch size. There was, however, stronger selection for earlier laying date when the breeding density of the population was high, suggesting that early breeding is not necessarily beneficial as such, but that its importance is emphasized when high population density increases competition. In addition, early breeding was favoured when the pre-breeding period was cool, which may indicate an increased advantage for the fittest individuals in harsher conditions. In the middle of the twentieth century, there was selection for large clutch size, which subsequently ceased, along with an overall decrease in recruit production. Our results indicate that attention should be paid to demographic factors such as breeding density when studying natural selection and temporal changes in it.     

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.     

When did the human population size start increasing?

We analyze the frequency spectra of all available human nuclear sequence data sets by using a model of constant population size followed by exponential growth. Parameters of growth (more extreme than or) comparable to what has been suggested from mtDNA data can be rejected for 6 out of the 10 largest data sets. When the data are separated into African and non-African samples, a constant size no-growth model can be rejected for 4 out of 8 non-African samples. Long-term growth (i.e., starting 50-100 kya) can be rejected for 2 out of 8 African samples and 5 out of 8 non-African ones. Under more complex demographic models, including a bottleneck or population subdivision, more of the data are compatible with long-term growth. One problem with the data used here is that a subset of loci may reflect the action of natural selection as well as of demography. It remains possible that the correct demographic model is one of constant population size followed by long-term growth but that at several loci the demographic signature has been obscured by balancing or diversifying selection. However, it is not clear that the data at these loci are consistent with a simple model of balancing selection; more complicated selective alternatives cannot be tested unless they are made explicit. An alternative explanation is that population size growth is more recent (e.g., upper Paleolithic) and that some of the loci have experienced recent directional selection. Given the available data, the latter hypothesis seems more likely.     

Analytical results on the neutral non-equilibrium allele frequency spectrum based on diffusion theory

The allele frequency spectrum has attracted considerable interest for the simultaneous inference of the demographic and adaptive history of populations. In a recent study, Evans et al. (2007) developed a forward diffusion equation describing the allele frequency spectrum, when the population is subject to size changes, selection and mutation. From the diffusion equation, the authors derived a system of ordinary differential equations (ODEs) for the moments in a Wright–Fisher diffusion with varying population size and constant selection. Here, we present an explicit solution for this system of ODEs with variable population size, but without selection, and apply this result to derive the expected spectrum of a sample for time-varying population size. We use this forward-in-time-solution of the allele frequency spectrum to obtain the backward-in-time-solution previously derived via coalescent theory by Griffiths and Tavaré (1998). Finally, we discuss the applicability of the theoretical results to the analysis of nucleotide polymorphism data.     

Effective population size and evolutionary dynamics in outbred laboratory populations of Drosophila

Census population size, sex-ratio and female reproductive success were monitored in 10 laboratory populations of Drosophila melanogaster selected for different ages of reproduction. With this demographic information, we estimated eigenvalue, variance and probability of allele loss effective population sizes. We conclude that estimates of effective size based on gene-frequency change at a few loci are biased downwards. We analysed the relative roles of selection and genetic drift in maintaining genetic variation in laboratory populations of Drosophila. We suggest that rare, favourable genetic variants in our laboratory populations have a high chance of being lost if their fitness effect is weak, e.g. 1% or less. However, if the fitness effect of this variation is 10% or greater, these rare variants are likely to increase to high frequency. The demographic information developed in this study suggests that some of our laboratory populations harbour more genetic variation than expected. One explanation for this finding is that part of the genetic variation in these outbred laboratory Drosophila populations may be maintained by some form of balancing selection. We suggest that, unlike bacteria, medium-term adaptation of laboratory populations of fruit flies is not primarily driven by new mutations, but rather by changes in the frequency of preexisting alleles.     

Genetic variation and selection of MHC class I loci differ in two congeneric frogs

Major histocompatibility complex (MHC) genes encode proteins in the acquired immune response pathway that often show distinctive selection-driven patterns in wild vertebrate populations. We examined genetic variation and signatures of selection in the MHC class I alpha 1 (A1)- and alpha 2 (A2)-domain encoding exons of two frog congeners [Agalychnis callidryas (n?=?20) and A. lemur (n?=?20)] from a single locality in Panama. We also investigated how historical demographic processes may have impacted MHC genetic diversity by analyzing a neutral mitochondrial marker. We found that both MHC domains were highly variable in both species, with both species likely expressing three loci. Our analyses revealed different signatures of selection between the two species, most notably that the A. callidryas A2 domain had experienced positive selection while the A2 domain of A. lemur had not. Diversifying selection acted on the same number of A1 and A2 allelic lineages, but on a higher percentage of A1 sites compared to A2 sites. Neutrality tests of mitochondrial haplotypes predominately indicated that the two species were at genetic equilibrium when the samples were collected. In addition, two historical tests of demography indicated both species have had relatively stable population sizes over the past 100,000 years; thus large population size changes are unlikely to have greatly influenced MHC diversity in either species during this time period. In conclusion, our results suggest that the impact of selection on MHC diversity varied between these two closely related species, likely due to a combination of distinct ecological conditions and past pathogenic pressures.     

The Evolution of Selfing Is Accompanied by Reduced Efficacy of Selection and Purging of Deleterious Mutations

The transition from outcrossing to selfing is predicted to reduce the genome-wide efficacy of selection because of the lower effective population size (N_e) that accompanies this change in mating system. However, strongly recessive deleterious mutations exposed in the homozygous backgrounds of selfers should be under strong purifying selection. Here, we examine estimates of the distribution of fitness effects (DFE) and changes in the magnitude of effective selection coefficients (N_es) acting on mutations during the transition from outcrossing to selfing. Using forward simulations, we investigated the ability of a DFE inference approach to detect the joint influence of mating system and the dominance of deleterious mutations on selection efficacy. We investigated predictions from our simulations in the annual plant Eichhornia paniculata, in which selfing has evolved from outcrossing on multiple occasions. We used range-wide sampling to generate population genomic datasets and identified nonsynonymous and synonymous polymorphisms segregating in outcrossing and selfing populations. We found that the transition to selfing was accompanied by a change in the DFE, with a larger fraction of effectively neutral sites (N_es < 1), a result consistent with the effects of reduced N_e in selfers. Moreover, an increased proportion of sites in selfers were under strong purifying selection (N_es > 100), and simulations suggest that this is due to the exposure of recessive deleterious mutations. We conclude that the transition to selfing has been accompanied by the genome-wide influences of reduced N_e and strong purifying selection against deleterious recessive mutations, an example of purging at the molecular level.