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- Title
Adaptation in a heterogeneous environment II: to be three or not to be.
- Authors
Alfaro, Matthieu; Hamel, François; Patout, Florian; Roques, Lionel
- 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, λ H , and we study the dependency of λ H 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 H ≥ 3 , compared to H = 1 or H = 2 , 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.
- Publication
Journal of Mathematical Biology, 2023, Vol 87, Issue 5, p1
- ISSN
0303-6812
- Publication type
Article
- DOI
10.1007/s00285-023-01996-4