Asymptotic and transient behaviour for a nonlocal problem arising in population genetics
| Autor: | Ramsès Djidjou-Demasse, Jean-Baptiste Burie, Arnaud Ducrot |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Santé et agroécologie du vignoble (UMR SAVE), Université de Bordeaux (UB)-Institut des Sciences de la Vigne et du Vin (ISVV)-Ecole Nationale Supérieure des Sciences Agronomiques de Bordeaux-Aquitaine (Bordeaux Sciences Agro)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Maladies infectieuses et vecteurs : écologie, génétique, évolution et contrôle (MIVEGEC), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud]), Institut de Recherche pour le Développement (IRD) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Work (thermodynamics)
transient behaviour Population [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] System of linear equations [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] 01 natural sciences Nonlocal equation Attractor Quantitative Biology::Populations and Evolution [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Statistical physics 0101 mathematics education Selection (genetic algorithm) Mathematics education.field_of_study [SDV.GEN.GPO]Life Sciences [q-bio]/Genetics/Populations and Evolution [q-bio.PE] Applied Mathematics 010102 general mathematics asymptotic behaviour population genetics 010101 applied mathematics Mutation (genetic algorithm) Transient (oscillation) Stationary state |
| Zdroj: | European Journal of Applied Mathematics European Journal of Applied Mathematics, Cambridge University Press (CUP), 2020, 31 (1), pp.84-110. ⟨10.1017/S0956792518000487⟩ European Journal of Applied Mathematics, Cambridge University Press (CUP), In press, ⟨10.1017/S0956792518000487⟩ |
| ISSN: | 0956-7925 1469-4425 |
| DOI: | 10.1017/S0956792518000487⟩ |
| Popis: | International audience; This work is devoted to the study of an integro-differential system of equations modelling the genetic adaptation of a pathogen by taking into account both mutation and selection processes. First we study the asymptotic behaviour of the system and prove that it eventually converges to a stationary state. Next we more closely investigate the behaviour of the system in the presence of multiple evolutionary attractors. Under suitable assumptions and based on a small mutation variance asymptotic, we describe the existence of a long transient regime during which the pathogen population remains far from its asymptotic behaviour and highly concentrated around some phenotypic value that is different from the one described by its asymptotic behaviour. In that setting, the time needed for the system to reach its large time configuration is very long and multiple evolutionary attractors may act as a barrier of evolution that can be very long to bypass. |
| Databáze: | OpenAIRE |
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