The stationary distribution of allele frequencies when selection acts at unlinked loci

Exact simulation of coupled Wright–Fisher diffusions

In this paper an exact rejection algorithm for simulating paths of the coupled Wright–Fisher diffusion is introduced. The coupled Wright–Fisher diffusion is a family of multivariate Wright–Fisher diffusions that have drifts depending on each other through a coupling term and that find applications in the study of networks of interacting genes. The proposed rejection algorithm uses independent neutral Wright–Fisher diffusions as candidate proposals, which are only needed at a finite number of points. Once a candidate is accepted, the remainder of the path can be recovered by sampling from neutral multivariate Wright–Fisher bridges, for which an exact sampling strategy is also provided. Finally, the algorithm’s complexity is derived and its performance demonstrated in a simulation study.

Inference from the stationary distribution of allele frequencies in a family of Wright-Fisher models with two levels of genetic variability

The distribution of allele frequencies obtained from diffusion approximations to Wright-Fisher models is useful in developing intuition about the population level effects of evolutionary processes. The statistical properties of the stationary distributions of K-allele models have been extensively studied under neutrality or under selection. Here, we introduce a new family of Wright-Fisher models in which there are two hierarchical levels of genetic variability. The genotypes composed of alleles differing from each other at the selected level have fitness differences with respect to each other and evolve under selection. The genotypes composed of alleles differing from each other only at the neutral level have the same fitness and evolve under neutrality. We show that with an appropriate scaling of the mutation parameter with respect to the number of alleles at each level, the frequencies of alleles at the selected and the neutral level are conditionally independent of each other, conditional on knowing the number of alleles at all levels. This conditional independence allows us to simulate from the joint stationary distribution of the allele frequencies. We use these simulated frequencies to perform inference on parameters of the model with two levels of genetic variability using Approximate Bayesian Computation.

A NOVEL SPECTRAL METHOD FOR INFERRING GENERAL DIPLOID SELECTION FROM TIME SERIES GENETIC DATA

The increased availability of time series genetic variation data from experimental evolution studies and ancient DNA samples has created new opportunities to identify genomic regions under selective pressure and to estimate their associated fitness parameters. However, it is a challenging problem to compute the likelihood of non-neutral models for the population allele frequency dynamics, given the observed temporal DNA data. Here, we develop a novel spectral algorithm to analytically and efficiently integrate over all possible frequency trajectories between consecutive time points. This advance circumvents the limitations of existing methods which require fine-tuning the discretization of the population allele frequency space when numerically approximating requisite integrals. Furthermore, our method is flexible enough to handle general diploid models of selection where the heterozygote and homozygote fitness parameters can take any values, while previous methods focused on only a few restricted models of selection. We demonstrate the utility of our method on simulated data and also apply it to analyze ancient DNA data from genetic loci associated with coat coloration in horses. In contrast to previous studies, our exploration of the full fitness parameter space reveals that a heterozygote-advantage form of balancing selection may have been acting on these loci.

Inference on the strength of balancing selection for epistatically interacting loci

Existing inference methods for estimating the strength of balancing selection in multi-locus genotypes rely on the assumption that there are no epistatic interactions between loci. Complex systems in which balancing selection is prevalent, such as sets of human immune system genes, are known to contain components that interact epistatically. Therefore, current methods may not produce reliable inference on the strength of selection at these loci. In this paper, we address this problem by presenting statistical methods that can account for epistatic interactions in making inference about balancing selection. A theoretical result due to Fearnhead (2006) is used to build a multi-locus Wright-Fisher model of balancing selection, allowing for epistatic interactions among loci. Antagonistic and synergistic types of interactions are examined. The joint posterior distribution of the selection and mutation parameters is sampled by Markov chain Monte Carlo methods, and the plausibility of models is assessed via Bayes factors. As a component of the inference process, an algorithm to generate multi-locus allele frequencies under balancing selection models with epistasis is also presented. Recent evidence on interactions among a set of human immune system genes is introduced as a motivating biological system for the epistatic model, and data on these genes are used to demonstrate the methods.

Estimation of selection intensity under overdominance by Bayesian methods

A balanced pattern in the allele frequencies of polymorphic loci is a potential sign of selection, particularly of overdominance. Although this type of selection is of some interest in population genetics, there exists no likelihood based approaches specifically tailored to make inference on selection intensity. To fill this gap, we present Bayesian methods to estimate selection intensity under k-allele models with overdominance. Our model allows for an arbitrary number of loci and alleles within a locus. The neutral and selected variability within each locus are modeled with corresponding k-allele models. To estimate the posterior distribution of the mean selection intensity in a multilocus region, a hierarchical setup between loci is used. The methods are demonstrated with data at the Human Leukocyte Antigen loci from world-wide populations.

Perfect simulation from nonneutral population genetic models: variable population size and population subdivision

We show how the idea of monotone coupling from the past can produce simple algorithms for simulating samples at a nonneutral locus under a range of demographic models. We specifically consider a biallelic locus and either a general variable population size mode or a general migration model for population subdivision. We investigate the effect of demography on the efficacy of selection and the effect of selection on genetic divergence between populations.