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arXiv · 2005.09869

Adaptation in a heterogeneous environment. I: Persistence versus extinction

François Hamel·Florian Lavigne·Lionel Roques
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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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François Hamel, Florian Lavigne, Lionel Roques. 2020-05-20. Adaptation in a heterogeneous environment. I: Persistence versus extinction. https://arxiv.org/abs/2005.09869

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