Persistence in the Moran model with random switching

2019/11/04 by Arnaud Guillin, Guillin, Arnaud, Arnaud Personne +3
Biochemistry, Genetics and Molecular Biology · Medicine · Social Sciences · #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1911.01108

openalex publication_date 2019/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper is devoted to the study of the asymptotic behaviour of Moran process in random environment, say random selection. In finite population, the Moran process may be degenerate in finite time, thus we will study its limiting process in large population which is a Piecewise Deterministic Markov Process, when the random selection is a Markov jump process. We will then study its long time behaviour via the stochastic persistence theory of Benaïm \citebenaimpersistence. It will enable us to show that persistence can occur, i.e. asymptotic coexistence of all species, when there are enough switching possibilities. This is true even if one species has never a predominant selection.

Citations

• Diffusion models in population genetics
• On a predator-prey system with random switching that never converges to\n its equilibrium

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