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
Contributor : Nicolas Champagnat
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Submitted on : Wednesday, March 9, 2016 - 6:33:51 PM
Last modification on : Friday, January 12, 2018 - 1:50:38 AM
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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⟩
