Nicolas Champagnat
Université de Lorraine
The limit of small mutations in a stochastic individual-based model and the canonical equation of adaptive dynamics
[When and where]
The goal of this talk is to present a new approach to justify the canonical equation of adaptive dynamics, intermediate between the historical one of Metz, Geritz et al. (1996), based on a limit of rare mutations in a large population, followed by a limit of small mutation, and the PDE approach of Diekmann, Jabin, Mischler, Perthame (2005), based on a limit of small mutations in an infinite population. The canonical equation arises on a very long time scale in the first one, and the second one suffers from an irrealistic influence of very small population densities. Our approach assumes small mutations in a large but finite, stochastic population. The convergence to the canonical equation follows from a decomposition of the population dynamics on slow-fast scales, and from a careful study of the genealogy of the population.
Invited talk Mini-symposium 7
Updated May 13, 2015, by Minus