Adaptation in general temporally changing environments

Roques Lionel, Patout Florian, Bonnefon Olivier, Martin Guillaume. 2020. Adaptation in general temporally changing environments. SIAM Journal on Applied Mathematics, 80 (6) : 2420-2447.

https://doi.org/10.1137/20M1322893

Article de revue ; Article de recherche ; Article de revue à facteur d'impact

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Quartile : Q2, Sujet : MATHEMATICS, APPLIED

Liste HCERES des revues (en SHS) : oui

Thème(s) HCERES des revues (en SHS) : Economie-gestion

Résumé : We analyze a nonlocal partial differential equation (PDE) model describing the dynamics of adaptation of a phenotypically structured population, under the effects of mutation and selection, in a changing environment. Previous studies have analyzed the large-time behavior of such models, with particular forms of environmental changes - either linearly changing or periodically fluctuating. We use here a completely different mathematical approach, which allows us to consider very general forms of environmental variations and to give an analytic description of the full trajectories of adaptation, including the transient phase, before a stationary behavior is reached. The main idea behind our approach is to study a bivariate distribution of two “fitness components" that contains enough information to describe the distribution of fitness at any time. This distribution solves a degenerate parabolic equation that is dealt with by defining a multidimensional cumulant generating function associated with the distribution and solving the associated transport equation. We apply our results to several examples and check their accuracy using stochastic individual-based simulations as a benchmark. These examples illustrate the importance of being able to describe the transient dynamics of adaptation to understand the development of drug resistance in pathogens.

Mots-clés Agrovoc : modèle mathématique, modélisation environnementale, adaptation, résistance aux médicaments, agent pathogène, dynamique des populations

Mots-clés libres : Nonlocal, Partial differential equation, Adaptation, Moving optimum, Mutation, Generating functions

Classification Agris : S50 - Santé humaine
U10 - Informatique, mathématiques et statistiques

Champ stratégique Cirad : CTS 4 (2019-) - Santé des plantes, des animaux et des écosystèmes

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