Article ; Online: Adaptation in a heterogeneous environment II: to be three or not to be.
Journal of mathematical biology
2023 Volume 87, Issue 5, Page(s) 68
Abstract: We propose a model to describe the adaptation of a phenotypically structured population in a H-patch environment connected by migration, with each patch associated with a different phenotypic optimum, and we perform a rigorous mathematical analysis of ... ...
| Abstract | We propose a model to describe the adaptation of a phenotypically structured population in a H-patch environment connected by migration, with each patch associated with a different phenotypic optimum, and we perform a rigorous mathematical analysis of this model. We show that the large-time behaviour of the solution (persistence or extinction) depends on the sign of a principal eigenvalue, [Formula: see text], and we study the dependency of [Formula: see text] with respect to H. This analysis sheds new light on the effect of increasing the number of patches on the persistence of a population, which has implications in agroecology and for understanding zoonoses; in such cases we consider a pathogenic population and the patches correspond to different host species. The occurrence of a springboard effect, where the addition of a patch contributes to persistence, or on the contrary the emergence of a detrimental effect by increasing the number of patches on the persistence, depends in a rather complex way on the respective positions in the phenotypic space of the optimal phenotypes associated with each patch. From a mathematical point of view, an important part of the difficulty in dealing with [Formula: see text], compared to [Formula: see text] or [Formula: see text], comes from the lack of symmetry. Our results, which are based on a fixed point theorem, comparison principles, integral estimates, variational arguments, rearrangement techniques, and numerical simulations, provide a better understanding of these dependencies. In particular, we propose a precise characterisation of the situations where the addition of a third patch increases or decreases the chances of persistence, compared to a situation with only two patches. |
|---|---|
| MeSH term(s) | Animals ; Models, Biological ; Population Dynamics |
| Language | English |
| Publishing date | 2023-10-09 |
| Publishing country | Germany |
| Document type | Journal Article ; Research Support, Non-U.S. Gov't |
| ZDB-ID | 187101-8 |
| ISSN | 1432-1416 ; 0303-6812 |
| ISSN (online) | 1432-1416 |
| ISSN | 0303-6812 |
| DOI | 10.1007/s00285-023-01996-4 |
| Database | MEDical Literature Analysis and Retrieval System OnLINE |
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