Existence of recombination-selection equilibria for sexual populations

Thibault Bourgeron 1, 2 Vincent Calvez 1, 3 Jimmy Garnier 4 Thomas Lepoutre 5, 6, 3
1 NUMED - Numerical Medicine
Inria Grenoble - Rhône-Alpes, UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
3 MMCS - Modélisation mathématique, calcul scientifique
ICJ - Institut Camille Jordan [Villeurbanne]
5 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
CGPhiMC - Centre de génétique et de physiologie moléculaire et cellulaire, Inria Grenoble - Rhône-Alpes, ICJ - Institut Camille Jordan [Villeurbanne]
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 Kre˘ ın-Rutman theory cannot be applied to this problem.
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  • HAL Id : hal-01489695, version 2


Thibault Bourgeron, Vincent Calvez, Jimmy Garnier, Thomas Lepoutre. Existence of recombination-selection equilibria for sexual populations. 2017. ⟨hal-01489695v2⟩



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