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arXiv · 1006.0803

The evolutionary limit for models of populations interacting competitively with many resources

Nicolas Champagnat·Pierre-Emmanuel Jabin
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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 $\phi$ of a Hamilton-Jacobi equation which depends on resource concentrations that we fully characterize in terms of the function $\phi$.

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Nicolas Champagnat, Pierre-Emmanuel Jabin. 2010-06-04. The evolutionary limit for models of populations interacting competitively with many resources. https://doi.org/10.1016/j.jde.2011.03.007

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