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Noisy traveling waves: effect of selection on genealogies

E. Brunet·B. Derrida·A. H. Mueller·S. Munier
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Abstract

For a family of models of evolving population under selection, which can be described by noisy traveling wave equations, the coalescence times along the genealogical tree scale like $\log^αN$, where $N$ is the size of the population, in contrast with neutral models for which they scale like $N$. An argument relating this time scale to the diffusion constant of the noisy traveling wave leads to a prediction for $α$ which agrees with our simulations. An exactly soluble case gives trees with statistics identical to those predicted for mean-field spin glasses in Parisi's theory.

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E. Brunet, B. Derrida, A. H. Mueller, S. Munier. 2006-10-04. Noisy traveling waves: effect of selection on genealogies. https://doi.org/10.1209/epl%2Fi2006-10224-4

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