Joint Prediction of the Effective Population Size and the Rate of Fixation of Deleterious Mutations

Background Selection From Unlinked Sites Causes Nonindependent Evolution of Deleterious Mutations

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

A quantitative genetic model of background selection in humans

Across the human genome, there are large-scale fluctuations in genetic diversity caused by the indirect effects of selection. This "linked selection signal" reflects the impact of selection according to the physical placement of functional regions and recombination rates along chromosomes. Previous work has shown that purifying selection acting against the steady influx of new deleterious mutations at functional portions of the genome shapes patterns of genomic variation. To date, statistical efforts to estimate purifying selection parameters from linked selection models have relied on classic Background Selection theory, which is only applicable when new mutations are so deleterious that they cannot fix in the population. Here, we develop a statistical method based on a quantitative genetics view of linked selection, that models how polygenic additive fitness variance distributed along the genome increases the rate of stochastic allele frequency change. By jointly predicting the equilibrium fitness variance and substitution rate due to both strong and weakly deleterious mutations, we estimate the distribution of fitness effects (DFE) and mutation rate across three geographically distinct human samples. While our model can accommodate weaker selection, we find evidence of strong selection operating similarly across all human samples. Although our quantitative genetic model of linked selection fits better than previous models, substitution rates of the most constrained sites disagree with observed divergence levels. We find that a model incorporating selective interference better predicts observed divergence in conserved regions, but overall our results suggest uncertainty remains about the processes generating fitness variation in humans.

An empirical test of the estimation of historical effective population size using Drosophila melanogaster

The availability of a large number of high-density markers (SNPs) allows the estimation of historical effective population size (Ne ) from linkage disequilibrium between loci. A recent refinement of methods to estimate historical Ne from the recent past has been shown to be rather accurate with simulation data. The method has also been applied to real data for numerous species. However, the simulation data cannot encompass all the complexities of real genomes, and the performance of any estimation method with real data is always uncertain, as the true demography of the populations is not known. Here, we carried out an experimental design with Drosophila melanogaster to test the method with real data following a known demographic history. We used a population maintained in the laboratory with a constant census size of about 2800 individuals and subjected the population to a drastic decline to a size of 100 individuals. After a few generations, the population was expanded back to the previous size and after a few further generations again expanded to twice the initial size. Estimates of historical Ne were obtained with the software GONE both for autosomal and X chromosomes from samples of 17 individuals sequenced for the whole genome. Estimates of the historical effective size were able to infer the patterns of changes that occurred in the populations showing generally good performance of the method. We discuss the limitations of the method and the application of the software carried out so far.

What is N e, anyway?

Few doubt that effective population size (Ne) is one of the most important parameters in evolutionary biology, but how many can say they really understand the concept? Ne is the evolutionary analogue of the number of individuals (or adults) in the population, N. Whereas ecological consequences of population size depend on N, evolutionary consequences (rates of loss of genetic diversity and increase in inbreeding; relative effectiveness of selection) depend on Ne. Formal definitions typically relate effective size to a key population genetic parameter, such as loss of heterozygosity or variance in allele frequency. However, for practical application to real populations, it is more useful to define Ne in terms of three demographic parameters: number of potential parents (adult N), and mean and variance in offspring number. Defined this way, Ne determines the rate of random genetic drift across the entire genome in the offspring generation. Other evolutionary forces (mutation, migration, selection)—together with factors such as variation in recombination rate—can also affect genetic variation, and this leads to heterogeneity across the genome in observed rates of genetic change. For some, it has been convenient to interpret this heterogeneity in terms of heterogeneity in Ne, but unfortunately this has muddled the concepts of genetic drift and effective population size. A commonly-repeated misconception is that Ne is the number of parents that actually contribute genes to the next generation (NP). In reality, NP can be smaller or larger than Ne, and the NP/Ne ratio depends on the sex ratio, the mean and variance in offspring number, and whether inbreeding or variance Ne is of interest.

The estimates of effective population size based on linkage disequilibrium are virtually unaffected by natural selection

The effective population size (Ne) is a key parameter to quantify the magnitude of genetic drift and inbreeding, with important implications in human evolution. The increasing availability of high-density genetic markers allows the estimation of historical changes in Ne across time using measures of genome diversity or linkage disequilibrium between markers. Directional selection is expected to reduce diversity and Ne, and this reduction is modulated by the heterogeneity of the genome in terms of recombination rate. Here we investigate by computer simulations the consequences of selection (both positive and negative) and recombination rate heterogeneity in the estimation of historical Ne. We also investigate the relationship between diversity parameters and Ne across the different regions of the genome using human marker data. We show that the estimates of historical Ne obtained from linkage disequilibrium between markers (NeLD) are virtually unaffected by selection. In contrast, those estimates obtained by coalescence mutation-recombination-based methods can be strongly affected by it, which could have important consequences for the estimation of human demography. The simulation results are supported by the analysis of human data. The estimates of NeLD obtained for particular genomic regions do not correlate, or they do it very weakly, with recombination rate, nucleotide diversity, proportion of polymorphic sites, background selection statistic, minor allele frequency of SNPs, loss of function and missense variants and gene density. This suggests that NeLD measures mainly reflect demographic changes in population size across generations.

Highly pleiotropic variants of human traits are enriched in genomic regions with strong background selection

Recent studies have shown the ubiquity of pleiotropy for variants affecting human complex traits. These studies also show that rare variants tend to be less pleiotropic than common ones, suggesting that purifying natural selection acts against highly pleiotropic variants of large effect. Here, we investigate the mean frequency, effect size and recombination rate associated with pleiotropic variants, and focus particularly on whether highly pleiotropic variants are enriched in regions with putative strong background selection. We evaluate variants for 41 human traits using data from the NHGRI-EBI GWAS Catalog, as well as data from other three studies. Our results show that variants involving a higher degree of pleiotropy tend to be more common, have larger mean effect sizes, and contribute more to heritability than variants with a lower degree of pleiotropy. This is consistent with the fact that variants of large effect and frequency are more likely detected by GWAS. Using data from four different studies, we also show that more pleiotropic variants are enriched in genome regions with stronger background selection than less pleiotropic variants, suggesting that highly pleiotropic variants are subjected to strong purifying selection. From the above results, we hypothesized that a number of highly pleiotropic variants of low effect/frequency may pass undetected by GWAS.

The Temporal Dynamics of Background Selection in Nonequilibrium Populations

Neutral genetic diversity across the genome is determined by the complex interplay of mutation, demographic history, and natural selection. While the direct action of natural selection is limited to functional loci across the genome, its impact can have effects on nearby neutral loci due to genetic linkage. These effects of selection at linked sites, referred to as genetic hitchhiking and background selection (BGS), are pervasive across natural populations. However, only recently has there been a focus on the joint consequences of demography and selection at linked sites, and some empirical studies have come to apparently contradictory conclusions as to their combined effects. To understand the relationship between demography and selection at linked sites, we conducted an extensive forward simulation study of BGS under a range of demographic models. We found that the relative levels of diversity in BGS and neutral regions vary over time and that the initial dynamics after a population size change are often in the opposite direction of the long-term expected trajectory. Our detailed observations of the temporal dynamics of neutral diversity in the context of selection at linked sites in nonequilibrium populations provide new intuition about why patterns of diversity under BGS vary through time in natural populations and help reconcile previously contradictory observations. Most notably, our results highlight that classical models of BGS are poorly suited for predicting diversity in nonequilibrium populations.

Background selection as null hypothesis in population genomics: insights and challenges from Drosophila studies

The consequences of selection at linked sites are multiple and widespread across the genomes of most species. Here, I first review the main concepts behind models of selection and linkage in recombining genomes, present the difficulty in parametrizing these models simply as a reduction in effective population size (N_e) and discuss the predicted impact of recombination rates on levels of diversity across genomes. Arguments are then put forward in favour of using a model of selection and linkage with neutral and deleterious mutations (i.e. the background selection model, BGS) as a sensible null hypothesis for investigating the presence of other forms of selection, such as balancing or positive. I also describe and compare two studies that have generated high-resolution landscapes of the predicted consequences of selection at linked sites in Drosophila melanogaster. Both studies show that BGS can explain a very large fraction of the observed variation in diversity across the whole genome, thus supporting its use as null model. Finally, I identify and discuss a number of caveats and challenges in studies of genetic hitchhiking that have been often overlooked, with several of them sharing a potential bias towards overestimating the evidence supporting recent selective sweeps to the detriment of a BGS explanation. One potential source of bias is the analysis of non-equilibrium populations: it is precisely because models of selection and linkage predict variation in N_e across chromosomes that demographic dynamics are not expected to be equivalent chromosome- or genome-wide. Other challenges include the use of incomplete genome annotations, the assumption of temporally stable recombination landscapes, the presence of genes under balancing selection and the consequences of ignoring non-crossover (gene conversion) recombination events.

This article is part of the themed issue ‘Evolutionary causes and consequences of recombination rate variation in sexual organisms’.