title: Inference Under a Wright-Fisher Model Using an Accurate Beta Approximation.
abstract: The large amount and high quality of genomic data available today enable, in principle, accurate inference of evolutionary histories of observed populations. The Wright-Fisher model is one of the most widely used models for this purpose. It describes the stochastic behavior in time of allele frequencies and the influence of evolutionary pressures, such as mutation and selection. Despite its simple mathematical formulation, exact results for the distribution of allele frequency (DAF) as a function of time are not available in closed analytical form. Existing approximations build on the computationally intensive diffusion limit or rely on matching moments of the DAF. One of the moment-based approximations relies on the beta distribution, which can accurately describe the DAF when the allele frequency is not close to the boundaries (0 and 1). Nonetheless, under a Wright-Fisher model, the probability of being on the boundary can be positive, corresponding to the allele being either lost or fixed. Here we introduce the beta with spikes, an extension of the beta approximation that explicitly models the loss and fixation probabilities as two spikes at the boundaries. We show that the addition of spikes greatly improves the quality of the approximation. We additionally illustrate, using both simulated and real data, how the beta with spikes can be used for inference of divergence times between populations with comparable performance to an existing state-of-the-art method.
authors: Bioinformatics Research Centre, Aarhus University, Aarhus C 8000, Denmark paula@cs.au.dk.
authors: Paula
authors: P
authors: Tataru
authors: Bioinformatics Research Centre, Aarhus University, Aarhus C 8000, Denmark.
authors: Thomas
authors: T
authors: Bataillon
authors: Bioinformatics Research Centre, Aarhus University, Aarhus C 8000, Denmark.
authors: Asger
authors: A
authors: Hobolth
mesh_terms: D000483:Alleles; D000818:Animals; D005075:Biological Evolution; D003198:Computer Simulation; D005787:Gene Frequency; D008957:Models, Genetic; D002679:Pan troglodytes; D013995:Time
keywords: Wright-Fisher; beta; divergence times; linear evolutionary pressures; pure genetic drift