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The evolutionary limit for models of populations interacting competitively via several resources
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 $\varphi$.
Cited literature [27 references]
https://hal.inria.fr/inria-00488979
Contributor : Nicolas Champagnat <>
Submitted on : Wednesday, March 9, 2016 - 6:33:51 PM
Last modification on : Tuesday, May 18, 2021 - 2:32:03 PM
Long-term archiving on: : Monday, June 13, 2016 - 8:42:48 AM
Contributor : Nicolas Champagnat <>
Submitted on : Wednesday, March 9, 2016 - 6:33:51 PM
Last modification on : Tuesday, May 18, 2021 - 2:32:03 PM
Long-term archiving on: : Monday, June 13, 2016 - 8:42:48 AM
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