ArticleJournal of mathematical biology2023
Extinction scenarios in evolutionary processes: a multinomial Wright-Fisher approach.
Article in Journal of mathematical biology, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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4 authors.
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Abstract
We study a discrete-time multi-type Wright-Fisher population process. The mean-field dynamics of the stochastic process is induced by a general replicator difference equation. We prove several results regarding the asymptotic behavior of the model, focusing on the impact of the mean-field dynamics on it. One of the results is a limit theorem that describes sufficient conditions for an almost certain path to extinction, first eliminating the type which is the least fit at the mean-field equilibrium. The effect is explained by the metastability of the stochastic system, which under the conditions of the theorem spends almost all time before the extinction event in a neighborhood of the equilibrium. In addition to the limit theorems, we propose a maximization principle for a general deterministic replicator dynamics and study its implications for the stochastic model.
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