Abstract : We consider a integro-differential nonlinear model that describes the evolution of a population structured by a quantitative trait. The interactions between traits occur from competition for resources whose concentrations depend on the current state of the population. Following the formalism of~\cite{DJMP}, we study a concentration phenomenon arising in the limit of strong selection and small mutations. We prove that the population density converges to a sum of Dirac masses characterized by the solution $\varphi$ of a Hamilton-Jacobi equation which depends on resource concentrations that we fully characterize in terms of the function $\varphi$.
https://hal.inria.fr/inria-00488979
Contributeur : Nicolas Champagnat
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Soumis le : mercredi 9 mars 2016 - 18:33:51
Dernière modification le : vendredi 12 janvier 2018 - 01:50:38
Document(s) archivé(s) le : lundi 13 juin 2016 - 08:42:48
Nicolas Champagnat, Pierre-Emmanuel Jabin. The evolutionary limit for models of populations interacting competitively via several resources. Journal of Differential Equations, Elsevier, 2011, 251 (1), pp.179-195. 〈10.1016/j.jde.2011.03.007〉. 〈inria-00488979v2〉
