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| The mathematical study of adaptive dynamics, and more specifically of the phenomenon of evolutionary branching by which a population is driven by selective forces to subdivide into two interacting subpopulations with different phenotypes, has been done in the last years using either an approach based on an assumption of rare mutations and large population on a stochastic individual-based model, or an approach based on a limit of small mutations on a PDE model. Both approaches suffer from irrealistic features: the first one requires a very long time scale to observe evolutionary branching; in the second one, exponentially small population densities can have a very strong impact on the future evolutionary dynamics. The goal of this talk is to present an intermediate approach that may solve these two drawbacks, consisting in applying a combination of limits of small mutations and large population on the stochastic individual-based model. |
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