[Dynamique de sélection pour un modèle non local structuré par le phénotype]
Ce document est consacré à l’analyse du comportement à long terme d’un modèle structuré par le phénotype dans lequel les changements phénotypiques ne se produisent pas. Nous présentons une description mathématique du processus par lequel le trait le mieux adapté est sélectionné dans un environnement donné créé par la population totale. Il est démontré que la limite à long terme de la solution unique de l’équation non locale est représentée par un delta de Dirac concentré sur l’ensemble des ’s où le pic de l’aptitude est atteint. De plus, nos expériences numériques fournissent un critère suffisant pour identifier les positions du pic. Les résultats numériques obtenus sont en bon accord qualitatif avec les études théoriques et les données expérimentales rapportées dans la littérature.
This paper is devoted to the analysis of the long-time behavior of a phenotype-structured model in which phenotypic changes do not occur. We present a mathematical description of the process through which the best adapted trait is selected in a given environment created by the total population. It is demonstrated that the long-time limit of the unique solution to the nonlocal equation is represented by a delta Dirac concentrated on the set of ’s where the peak of the fitness is attained. Furthermore, our numerical experiments provide a sufficient criterion to identify the positions of the peak. The obtained numerical results are in good qualitative agreement with theoretical studies and experimental data reported in the literature.
Révisé le :
Accepté le :
Publié le :
Shen Bian 1 ; Jiale Bu 1
CC-BY 4.0
@article{CRMATH_2025__363_G1_13_0,
author = {Shen Bian and Jiale Bu},
title = {On selection dynamics for a nonlocal phenotype-structured model},
journal = {Comptes Rendus. Math\'ematique},
pages = {13--27},
publisher = {Acad\'emie des sciences, Paris},
volume = {363},
year = {2025},
doi = {10.5802/crmath.696},
language = {en},
}
Shen Bian; Jiale Bu. On selection dynamics for a nonlocal phenotype-structured model. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 13-27. doi : 10.5802/crmath.696. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.696/
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