ArticleJournal of mathematical biology2021
Adaptation in a heterogeneous environment I: persistence versus extinction.
Article in Journal of mathematical biology, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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2 citing papers in PubMed, 0 citations in OpenAlex.
- Phenotype structuring in collective cell migration: a tutorial of mathematical models and methods.Journal of mathematical biology · 2025Review
- A research agenda for scaling up agroecology in European countries.Agronomy for sustainable development · 2022Review
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3 authors at 3 institutions in 1 country.
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Abstract
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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