Limiting fitness distributions in evolutionary dynamics

Matteo Smerlak; Ahmed Youssef

doi:10.1016/j.jtbi.2017.01.005

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arXiv · 1511.00296

Limiting fitness distributions in evolutionary dynamics

Matteo Smerlak·Ahmed Youssef

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Abstract

Darwinian evolution can be modeled in general terms as a flow in the space of fitness (i.e. reproductive rate) distributions. In the diffusion approximation, Tsimring et al. have showed that this flow admits "fitness wave" solutions: Gaussian-shape fitness distributions moving towards higher fitness values at constant speed. Here we show more generally that evolving fitness distributions are attracted to a one-parameter family of distributions with a fixed parabolic relationship between skewness and kurtosis. Unlike fitness waves, this statistical pattern encompasses both positive and negative (a.k.a. purifying) selection and is not restricted to rapidly adapting populations. Moreover we find that the mean fitness of a population under the selection of pre-existing variation is a power-law function of time, as observed in microbiological evolution experiments but at variance with fitness wave theory. At the conceptual level, our results can be viewed as the resolution of the "dynamic insufficiency" of Fisher's fundamental theorem of natural selection. Our predictions are in good agreement with numerical simulations.

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q-bio.PE cond-mat.stat-mech cs.NE

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Matteo Smerlak, Ahmed Youssef. 2016-02-16. Limiting fitness distributions in evolutionary dynamics. https://doi.org/10.1016/j.jtbi.2017.01.005

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