A field theoretic approach to non-equilibrium population genetics in the strong selection regime.

Natural populations are virtually never observed in equilibrium, yet equilibrium approximations comprise the majority of our understanding of population genetics. Using standard tools from statistical physics, a formalism is presented that re-expresses the stochastic equations describing allelic evolution as a partition functional over all possible allelic trajectories ('paths') governed by selection, mutation, and drift. A perturbative field theory is developed for strong additive selection, relevant to disease variation, that facilitates the straightforward computation of closed-form approximations for time-dependent moments of the allele frequency distribution across a wide range of non-equilibrium scenarios; examples are presented for constant population size, exponential growth, bottlenecks, and oscillatory size, all of which align well to simulations and break down just above the drift barrier. Equilibration times are computed and, even for static population size, generically extend beyond the order 1/s timescale associated with exponential frequency decay. Though the mutation load is largely robust to variable population size, perturbative drift-based corrections to the deterministic trajectory are readily computed. Under strong selection, the variance of a new mutation's frequency (related to homozygosity) is dominated by drift-driven dynamics and a transient increase in variance often occurs prior to equilibrating. The excess kurtosis over skew squared is roughly constant (i.e., independent of selection, provided 2Ns ≳ 5) for static population size, and thus potentially sensitive to deviation from equilibrium. These insights highlight the value of such closed-form approximations, naturally generated from Feynman diagrams in a perturbative field theory, which can simply and accurately capture the parameter dependences describing a variety of non-equilibrium population genetic phenomena of interest.

Overcoming constraints on the detection of recessive selection in human genes from population frequency data.

The identification of genes that evolve under recessive natural selection is a long-standing goal of population genetics research that has important applications to the discovery of genes associated with disease. We found that commonly used methods to evaluate selective constraint at the gene level are highly sensitive to genes under heterozygous selection but ubiquitously fail to detect recessively evolving genes. Additionally, more sophisticated likelihood-based methods designed to detect recessivity similarly lack power for a human gene of realistic length from current population sample sizes. However, extensive simulations suggested that recessive genes may be detectable in aggregate. Here, we offer a method informed by population genetics simulations designed to detect recessive purifying selection in gene sets. Applying this to empirical gene sets produced significant enrichments for strong recessive selection in genes previously inferred to be under recessive selection in a consanguineous cohort and in genes involved in autosomal recessive monogenic disorders.

Purifying selection on noncoding deletions of human regulatory loci detected using their cellular pleiotropy.

Genomic deletions provide a powerful loss-of-function model in noncoding regions to assess the role of purifying selection on genetic variation. Regulatory element function is characterized by nonuniform tissue and cell type activity, necessarily linking the study of fitness consequences from regulatory variants to their corresponding cellular activity. We generated a callset of deletions from genomes in the Alzheimer's Disease Neuroimaging Initiative (ADNI) and used deletions from The 1000 Genomes Project Consortium (1000GP) in order to examine whether purifying selection preserves noncoding sites of chromatin accessibility marked by DNase I hypersensitivity (DHS), histone modification (enhancer, transcribed, Polycomb-repressed, heterochromatin), and chromatin loop anchors. To examine this in a cellular activity-aware manner, we developed a statistical method, pleiotropy ratio score (PlyRS), which calculates a correlation-adjusted count of "cellular pleiotropy" for each noncoding base pair by analyzing shared regulatory annotations across tissues and cell types. By comparing real deletion PlyRS values to simulations in a length-matched framework and by using genomic covariates in analyses, we found that purifying selection acts to preserve both DHS and enhancer noncoding sites. However, we did not find evidence of purifying selection for noncoding transcribed, Polycomb-repressed, or heterochromatin sites beyond that of the noncoding background. Additionally, we found evidence that purifying selection is acting on chromatin loop integrity by preserving colocalized CTCF binding sites. At regions of DHS, enhancer, and CTCF within chromatin loop anchors, we found evidence that both sites of activity specific to a particular tissue or cell type and sites of cellularly pleiotropic activity are preserved by selection.

Probing the aggregated effects of purifying selection per individual on 1,380 medical phenotypes in the UK Biobank.

Understanding the relationship between natural selection and phenotypic variation has been a long-standing challenge in human population genetics. With the emergence of biobank-scale datasets, along with new statistical metrics to approximate strength of purifying selection at the variant level, it is now possible to correlate a proxy of individual relative fitness with a range of medical phenotypes. We calculated a per-individual deleterious load score by summing the total number of derived alleles per individual after incorporating a weight that approximates strength of purifying selection. We assessed four methods for the weight, including GERP, phyloP, CADD, and fitcons. By quantitatively tracking each of these scores with the site frequency spectrum, we identified phyloP as the most appropriate weight. The phyloP-weighted load score was then calculated across 15,129,142 variants in 335,161 individuals from the UK Biobank and tested for association on 1,380 medical phenotypes. After accounting for multiple test correction, we observed a strong association of the load score amongst coding sites only on 27 traits including body mass, adiposity and metabolic rate. We further observed that the association signals were driven by common variants (derived allele frequency > 5%) with high phyloP score (phyloP > 2). Finally, through permutation analyses, we showed that the load score amongst coding sites had an excess of nominally significant associations on many medical phenotypes. These results suggest a broad impact of deleterious load on medical phenotypes and highlight the deleterious load score as a tool to disentangle the complex relationship between natural selection and medical phenotypes.

Applicability of the Mutation-Selection Balance Model to Population Genetics of Heterozygous Protein-Truncating Variants in Humans.

The fate of alleles in the human population is believed to be highly affected by the stochastic force of genetic drift. Estimation of the strength of natural selection in humans generally necessitates a careful modeling of drift including complex effects of the population history and structure. Protein-truncating variants (PTVs) are expected to evolve under strong purifying selection and to have a relatively high per-gene mutation rate. Thus, it is appealing to model the population genetics of PTVs under a simple deterministic mutation-selection balance, as has been proposed earlier (Cassa et al. 2017). Here, we investigated the limits of this approximation using both computer simulations and data-driven approaches. Our simulations rely on a model of demographic history estimated from 33,370 individual exomes of the Non-Finnish European subset of the ExAC data set (Lek et al. 2016). Additionally, we compared the African and European subset of the ExAC study and analyzed de novo PTVs. We show that the mutation-selection balance model is applicable to the majority of human genes, but not to genes under the weakest selection.

Quantification of frequency-dependent genetic architectures in 25 UK Biobank traits reveals action of negative selection.

Understanding the role of rare variants is important in elucidating the genetic basis of human disease. Negative selection can cause rare variants to have larger per-allele effect sizes than common variants. Here, we develop a method to estimate the minor allele frequency (MAF) dependence of SNP effect sizes. We use a model in which per-allele effect sizes have variance proportional to [p(1 - p)]α, where p is the MAF and negative values of α imply larger effect sizes for rare variants. We estimate α for 25 UK Biobank diseases and complex traits. All traits produce negative α estimates, with best-fit mean of -0.38 (s.e. 0.02) across traits. Despite larger rare variant effect sizes, rare variants (MAF < 1%) explain less than 10% of total SNP-heritability for most traits analyzed. Using evolutionary modeling and forward simulations, we validate the α model of MAF-dependent trait effects and assess plausible values of relevant evolutionary parameters.

Estimating the selective effects of heterozygous protein-truncating variants from human exome data.

The evolutionary cost of gene loss is a central question in genetics and has been investigated in model organisms and human cell lines. In humans, tolerance of the loss of one or both functional copies of a gene is related to the gene's causal role in disease. However, estimates of the selection and dominance coefficients in humans have been elusive. Here we analyze exome sequence data from 60,706 individuals to make genome-wide estimates of selection against heterozygous loss of gene function. Using this distribution of selection coefficients for heterozygous protein-truncating variants (PTVs), we provide corresponding Bayesian estimates for individual genes. We find that genes under the strongest selection are enriched in embryonic lethal mouse knockouts, Mendelian disease-associated genes, and regulators of transcription. Screening by essentiality, we find a large set of genes under strong selection that are likely to have crucial functions but have not yet been thoroughly characterized.

Dominance of Deleterious Alleles Controls the Response to a Population Bottleneck.

Population bottlenecks followed by re-expansions have been common throughout history of many populations. The response of alleles under selection to such demographic perturbations has been a subject of great interest in population genetics. On the basis of theoretical analysis and computer simulations, we suggest that this response qualitatively depends on dominance. The number of dominant or additive deleterious alleles per haploid genome is expected to be slightly increased following the bottleneck and re-expansion. In contrast, the number of completely or partially recessive alleles should be sharply reduced. Changes of population size expose differences between recessive and additive selection, potentially providing insight into the prevalence of dominance in natural populations. Specifically, we use a simple statistic, [Formula: see text], where xi represents the derived allele frequency, to compare the number of mutations in different populations, and detail its functional dependence on the strength of selection and the intensity of the population bottleneck. We also provide empirical evidence showing that gene sets associated with autosomal recessive disease in humans may have a BR indicative of recessive selection. Together, these theoretical predictions and empirical observations show that complex demographic history may facilitate rather than impede inference of parameters of natural selection.

Dynamic mutation-selection balance as an evolutionary attractor.

The vast majority of mutations are deleterious and are eliminated by purifying selection. Yet in finite asexual populations, purifying selection cannot completely prevent the accumulation of deleterious mutations due to Muller's ratchet: once lost by stochastic drift, the most-fit class of genotypes is lost forever. If deleterious mutations are weakly selected, Muller's ratchet can lead to a rapid degradation of population fitness. Evidently, the long-term stability of an asexual population requires an influx of beneficial mutations that continuously compensate for the accumulation of the weakly deleterious ones. Hence any stable evolutionary state of a population in a static environment must involve a dynamic mutation-selection balance, where accumulation of deleterious mutations is on average offset by the influx of beneficial mutations. We argue that such a state can exist for any population size N and mutation rate U and calculate the fraction of beneficial mutations, ε, that maintains the balanced state. We find that a surprisingly low ε suffices to achieve stability, even in small populations in the face of high mutation rates and weak selection, maintaining a well-adapted population in spite of Muller's ratchet. This may explain the maintenance of mitochondria and other asexual genomes.

Distribution of fixed beneficial mutations and the rate of adaptation in asexual populations.

When large asexual populations adapt, competition between simultaneously segregating mutations slows the rate of adaptation and restricts the set of mutations that eventually fix. This phenomenon of interference arises from competition between mutations of different strengths as well as competition between mutations that arise on different fitness backgrounds. Previous work has explored each of these effects in isolation, but the way they combine to influence the dynamics of adaptation remains largely unknown. Here, we describe a theoretical model to treat both aspects of interference in large populations. We calculate the rate of adaptation and the distribution of fixed mutational effects accumulated by the population. We focus particular attention on the case when the effects of beneficial mutations are exponentially distributed, as well as on a more general class of exponential-like distributions. In both cases, we show that the rate of adaptation and the influence of genetic background on the fixation of new mutants is equivalent to an effective model with a single selection coefficient and rescaled mutation rate, and we explicitly calculate these effective parameters. We find that the effective selection coefficient exactly coincides with the most common fixed mutational effect. This equivalence leads to an intuitive picture of the relative importance of different types of interference effects, which can shift dramatically as a function of the population size, mutation rate, and the underlying distribution of fitness effects.