Institut de Mathématiques de Toulouse

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Séminaire de Probabilités

par Jonas Kahn, Manon Costa, Max Fathi - publié le , mis à jour le

Organisateurs : Manon Costa, Max Fathi, Jonas Kahn.

Horaire et lieu habituels : le mardi à 9h45 en amphithéâtre L. Schwartz (bâtiment 1R3).

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  • Mardi 19 février 09:45-10:45 - Charline Smadi - IRSTEA - LISC

    Multidimensional Lambda-Wright-Fisher processes with general frequency-dependent selection

    Résumé : We construct a multitype constant size population model allowing for general selective interactions as well as extreme reproductive events. It generalizes the idea of Krone and Neuhauser and Gonzalez Casanova and Spano, who represented the selection by allowing individuals to sample several potential parents in the previous generation before choosing the ’strongest’ one, by allowing individuals to use any rule to choose their real parent. The real parent can even not be one of the potential parents, which allows modelling mutations. Via a large population limit, we obtain a generalisation of Lambda-Fleming Viot processes, with a diffusion term and a general frequency-dependent selection, which allows for non transitive interactions between the different types present in the population. We provide some properties of these processes related to extinction and fixation events, and give conditions for them to be realised as unique strong solutions of multidimensional stochastic differential equations with jumps. Finally, we illustrate the generality of our model with applications to some classical biological interactions.
    It is a joint work with Adrian Gonzalez Casanova.


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