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arXiv · 2212.02631

Branching with selection and mutation I: Mutant fitness of Fr\'echet type

Su-Chan Park·Joachim Krug·Léo Touzo·Peter Mörters
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Abstract

We investigate two stochastic models of a growing population subject to selection and mutation. In our models each individual carries a fitness which determines its mean offspring number. Many of these offspring inherit their parent's fitness, but some are mutants and obtain a fitness randomly sampled from a distribution in the domain of attraction of the Fr\'echet distribution. We give a rigorous proof for the precise rate of superexponential growth of these stochastic processes and support the argument by a heuristic and numerical study of the mechanism underlying this growth.

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Su-Chan Park, Joachim Krug, Léo Touzo, Peter Mörters. 2022-12-05. Branching with selection and mutation I: Mutant fitness of Fr\'echet type. https://doi.org/10.1007/s10955-023-03125-3

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