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Adaptation in a heterogeneous environment. I: Persistence versus extinction

Abstract : Understanding how a diversity of plants in agroecosystems affects the adaptation of pathogens in 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-patches 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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Contributor : Francois Hamel <>
Submitted on : Tuesday, May 19, 2020 - 10:30:41 AM
Last modification on : Thursday, May 21, 2020 - 1:41:05 AM


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  • HAL Id : hal-02612415, version 1
  • ARXIV : 2005.09869


François Hamel, Florian Lavigne, Lionel Roques. Adaptation in a heterogeneous environment. I: Persistence versus extinction. 2020. ⟨hal-02612415⟩



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