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Pré-Publication, Document De Travail Année : 2021

Exponential convergence to a steady-state for a population genetics model with sexual reproduction and selection

Résumé

We are interested in the dynamics of a population structured by a phenotypic trait. Individuals reproduce sexually, which is represented by a non-linear integral operator. This operator is combined to a multiplicative operator representing selection. When the strength of selection is small, we show that the dynamics of the population is governed by a simple macroscopic differential equation, and that solutions converge exponentially to steady-states that are locally unique. The analysis is based on Wasserstein distance inequalities using a uniform lower bound on distributions. These inequalities are coupled to tail estimates to show the stability of the steady-states.

Dates et versions

hal-03434278 , version 1 (18-11-2021)

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Gaël Raoul. Exponential convergence to a steady-state for a population genetics model with sexual reproduction and selection. 2021. ⟨hal-03434278⟩
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