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arXiv · 2111.13344

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

Camila Bräutigam·Matteo Smerlak
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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.

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Camila Bräutigam, Matteo Smerlak. 2021-11-26. Diffusion approximations in population genetics and the rate of Muller's ratchet. https://doi.org/10.1016/j.jtbi.2022.111236

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