A Hamilton-Jacobi Approach to Evolution of Dispersal
| Autor: | King-Yeung Lam, Yuan Lou, Benoît Perthame |
|---|---|
| Přispěvatelé: | Ohio State University [Columbus] (OSU), Shanghai Jiao Tong University [Shanghai], Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Modelling and Analysis for Medical and Biological Applications (MAMBA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité) |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Evolution of dispersal
Constrained Hamilton-Jacobi equation Nonlocal PDE Applied Mathematics Principal Floquet bundle Quantitative Biology::Genomics Mathematics - Analysis of PDEs Mathematical biology FOS: Mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Quantitative Biology::Populations and Evolution 35B25 35F21 35K57 92D15 AMS Subject Class. [2010]: 35B25 35F21 35K57 92D15 Analysis Effective fitness Analysis of PDEs (math.AP) |
| Zdroj: | Communications in Partial Differential Equations Communications in Partial Differential Equations, In press |
| ISSN: | 0360-5302 1532-4133 |
| Popis: | International audience; The evolution of dispersal is a classical question in evolutionary biology, and it has been studied in a wide range of mathematical models. A selection-mutation model, in which the population is structured by space and a phenotypic trait, with the trait acting directly on the dispersal (diffusion) rate, was formulated by Perthame and Souganidis [Math. Model. Nat. Phenom. 11 (2016), 154-166] to study the evolution of random dispersal towards the evolutionarily stable strategy. For the rare mutation limit, it was shown that the equilibrium population concentrates on a single trait associated to the smallest dispersal rate. In this paper, we consider the corresponding evolution equation and characterize the asymptotic behaviors of the time-dependent solutions in the rare mutation limit, under mild convexity assumptions on the underlying Hamiltonian function. |
| Databáze: | OpenAIRE |
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