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arXiv · 1703.09078

Existence of recombination-selection equilibria for sexual populations

Thibault Bourgeron·Vincent Calvez·Jimmy Garnier·Thomas Lepoutre
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Abstract

We study a birth and death model for the adapatation of a sexual population to an environment. The population is structured by a phenotypical trait, and, possibly, an age variable. Recombination is modeled by Fisher's infinitesimal operator. We prove the existence of principal eigenelements for the corresponding eigenproblem. As the infinitesimal operator is 1-homogeneous but nor linear nor monotone, the general Krein-Rutman theory cannot be applied to this problem.

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Thibault Bourgeron, Vincent Calvez, Jimmy Garnier, Thomas Lepoutre. 2017-03-24. Existence of recombination-selection equilibria for sexual populations. https://arxiv.org/abs/1703.09078

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