Inference Under a Wright-Fisher Model Using an Accurate Beta Approximation

Genetics
Paula TataruAsger Hobolth

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 ...Continue Reading

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Citations

Sep 13, 2016·Scientific Reports·Bhavin S Khatri
Jun 27, 2017·Journal of Theoretical Biology·Hassan Shafiey, D Waxman
Jan 19, 2018·Genetics·Peter R WiltonRasmus Nielsen
Feb 9, 2019·Journal of Mathematical Biology·Maria Simonsen SpeedAsger Hobolth
Feb 1, 2018·PLoS Genetics·Florian ClementeRenaud Vitalis
Dec 2, 2020·Nature Biotechnology·Muhammad Saqib SohailJohn P Barton

Related Concepts

Alleles
Metazoa
Pan troglodytes
In Silico
Biological Evolution
Genetic Equilibrium
Longterm Effects
Alleles
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Fixation - Action

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