Evolutionary Attractors in the Chemostat Model
We consider the evolutive chemostat model with a continuous phenotypic trait of the micro-organisms that impacts both the specific growth rate and the yield conversion, and whose evolution is driven by a mutation kernel. We study the evolutionary attractors (EAs) for a general class of non-linear growth functions, without assuming that the dynamics of the resource is fast compared to the growth. We generalize the well-known reproduction number as a function of the trait, and show a concentration of the asymptotic state on values of the trait that maximize the reproduction number. However, in the case of multiple maxima, we show that the system can have a unique globally stable EA, depending on a total order defined on the trait values.
Authors
- Ramsès Djidjou‐Demasse (ORCID: https://orcid.org/0000-0003-1684-5190)
- Ousmane Seydi (ORCID: https://orcid.org/0000-0001-5702-2575)
- Alain Rapaport (ORCID: https://orcid.org/0000-0002-8515-0838)
Institutions
- Centre National de la Recherche Scientifique (FR)
- Université Le Havre Normandie (FR)
- Agropolis International (FR)
- Maladies Infectieuses et Vecteurs: Écologie, Génétique, Évolution et Contrôle (FR)
- Institut National de Recherche pour l'Agriculture, l'Alimentation et l'Environnement (FR)
- Normandie Université (FR)
- Mathématiques, Informatique et Statistique pour l'Environnement et l'Agronomie (FR)
- Institut Agro Montpelier (FR)
- Services déconcentrés d'appui à la recherche Occitanie-Montpellier (FR)
- École Polytechnique de Thiès (SN)
- Institut de Recherche pour le Développement (FR)
Publication Details
- Journal
- SIAM Journal on Applied Mathematics
- Published
- 2025-11-04
- DOI
- https://doi.org/10.1137/24m1706001
- Citations
- 1
- Primary Topic
- Evolutionary Algorithms and Applications
- Type
- article
- Field-Weighted Citation Impact
- 2.48