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Article Dans Une Revue Journal of Mathematical Biology Année : 2021

Adaptation in a heterogeneous environment. I: Persistence versus extinction

Résumé

Understanding how a diversity of plants in agroecosystems affects the adaptation of pathogens is a key issue in agroecology. We analyze PDE systems describing the dynamics of adaptation of two phenotypically structured populations, under the effects of mutation, selection and migration in a two-patch environment, each patch being associated with a different phenotypic optimum. We consider two types of growth functions that depend on the n-dimensional phenotypic trait: either local and linear or nonlocal nonlinear. In both cases, we obtain existence and uniqueness results as well as a characterization of the large-time behaviour of the solution (persistence or extinction) based on the sign of a principal eigenvalue. We show that migration between the two environments decreases the chances of persistence, with in some cases a ‘lethal migration threshold’ above which persistence is not possible. Comparison with stochastic individual-based simulations shows that the PDE approach accurately captures this threshold. Our results illustrate the importance of cultivar mixtures for disease prevention and control.
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Dates et versions

hal-02612415 , version 1 (19-05-2020)
hal-02612415 , version 2 (04-03-2021)

Identifiants

Citer

François Hamel, Florian Lavigne, Lionel Roques. Adaptation in a heterogeneous environment. I: Persistence versus extinction. Journal of Mathematical Biology, 2021, 83 (2), pp.14. ⟨10.1007/s00285-021-01637-8⟩. ⟨hal-02612415v2⟩
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