Diffusion approximations in population genetics and the rate of Muller's ratchet

TL;DR

This paper extends the use of diffusion approximations in population genetics beyond traditional limits, providing improved estimates for fixation times of deleterious alleles and insights into Muller's ratchet.

Contribution

It demonstrates that diffusion equations can approximate the Wright-Fisher model under broader conditions, including strong selection and mutation regimes.

Findings

Diffusion approximations are valid beyond the inverse population size scaling.

Improved estimates for the expected fixation time of deleterious alleles.

Enhanced understanding of Muller's ratchet dynamics.

Abstract

Diffusion theory is a central tool of modern population genetics, yielding simple expressions for fixation probabilities and other quantities that are not easily derived from the underlying Wright-Fisher model. Unfortunately, the textbook derivation of diffusion equations as scaling limits requires evolutionary parameters (selection coefficients, mutation rates) to scale like the inverse population size -- a severe restriction that does not always reflect biological reality. Here we note that the Wright-Fisher model can be approximated by diffusion equations under more general conditions, including in regimes where selection and/or mutation are strong compared to genetic drift. As an illustration, we use a diffusion approximation of the Wright-Fisher model to improve estimates for the expected time to fixation of a strongly deleterious allele, i.e. the rate of Muller's ratchet.