EWF : simulating exact paths of the Wright--Fisher diffusion

TL;DR

This paper introduces EWF, an exact and efficient simulation method for Wright--Fisher diffusion paths, accommodating complex models with selection and mutation, validated through statistical tests.

Contribution

EWF provides a novel, exact sampling algorithm for Wright--Fisher diffusion paths, including models with frequency-dependent selection, improving over approximate methods.

Findings

EWF accurately reproduces Wright--Fisher diffusion paths.

Validation confirms EWF's outputs match theoretical transition densities.

Software implementation is publicly available for use.

Abstract

The Wright--Fisher diffusion is important in population genetics in modelling the evolution of allele frequencies over time subject to the influence of biological phenomena such as selection, mutation, and genetic drift. Simulating paths of the process is challenging due to the form of the transition density. We present EWF, a robust and efficient sampler which returns exact draws for the diffusion and diffusion bridge processes, accounting for general models of selection including those with frequency-dependence. Given a configuration of selection, mutation, and endpoints, EWF returns draws at the requested sampling times from the law of the corresponding Wright--Fisher process. Output was validated by comparison to approximations of the transition density via the Kolmogorov--Smirnov test and QQ plots. All software is available at https://github.com/JaroSant/EWF