# The evolutionary limit for models of populations interacting competitively with many resources - Mathematics > Analysis of PDEs

Abstract: We consider a integro-differential nonlinear model that describes theevolution of a population structured by a quantitative trait. The interactionsbetween traits occur from competition for resources whose concentrations dependon the current state of the population. Following the formalism of\cite{DJMP},we study a concentration phenomenon arising in the limit of strong selectionand small mutations. We prove that the population density converges to a sum ofDirac masses characterized by the solution $\phi$ of a Hamilton-Jacobi equationwhich depends on resource concentrations that we fully characterize in terms ofthe function $\phi$.

Author: Nicolas Champagnat INRIA Sophia Antipolis - INRIA Lorraine - IECN, Pierre-Emmanuel Jabin INRIA Sophia Antipolis - INRIA Lorraine

Source: https://arxiv.org/