%0 Journal Article
%T The evolutionary limit for models of populations interacting competitively with many resources
%A Nicolas Champagnat
%A Pierre-Emmanuel Jabin
%J Mathematics
%D 2010
%I arXiv
%R 10.1016/j.jde.2011.03.007
%X 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 $\phi$ of a Hamilton-Jacobi equation which depends on resource concentrations that we fully characterize in terms of the function $\phi$.
%U http://arxiv.org/abs/1006.0803v1