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Pierre-Emmanuel Jabin : Selection-Mutation models

I present an overview of models of the Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Starting from a stochastic birth and death process, several types of deterministic or probabilistic models can be derived. When advantageous mutations are rare and small, a time scale separation takes place in the models leading to the concentration of the population along a few selected traits. Those then evolve according to a PDE of Hamilton-Jacobi type or to the canonical equation of adaptive dynamics.

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