Reaction-diffusion model for a population structured in phenotype and space I - Criterion for persistence - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

Reaction-diffusion model for a population structured in phenotype and space I - Criterion for persistence

Résumé

We consider a reaction-diffusion model for a population structured in phenotype. We assume that the population lives in a heterogeneous periodic environment, so that a given phenotypic trait may be more or less fit according to the spatial location. The model features spatial mobility of individuals as well as mutation. We first prove the well-posedness of the model. Next, we derive a criterion for the persistence of the population which involves the generalised principal eigenvalue associated with the linearised elliptic operator. This notion allows us to handle the possible lack of coercivity of the operator. We then obtain a monotonicity result for the generalised principal eigenvalue, in terms of the frequency of spatial fluctuations of the environment and in terms of the spatial diffusivity. We deduce that the more heterogeneous is the environment, or the higher is the mobility of individuals, the harder is the persistence for the species. This work lays the mathematical foundation to investigate some other optimisation problems for the environment to make persistence as hard or as easy as possible, which will be addressed in the forthcoming companion paper.
Fichier principal
Vignette du fichier
1st-part.pdf (431.85 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04714273 , version 1 (30-09-2024)

Identifiants

  • HAL Id : hal-04714273 , version 1

Citer

Nathanaël Boutillon, Luca Rossi. Reaction-diffusion model for a population structured in phenotype and space I - Criterion for persistence. 2024. ⟨hal-04714273⟩
0 Consultations
0 Téléchargements

Partager

More