"A Fisher-KPP equation with a phenotypic dimension : persistence and spreading speed"Boutillon, NathanaëlWe consider a nonlocal reaction-diffusion equation which models a population structured in space and in phenotype. We assume that the population lives in a heterogeneous environment, so that the same individual may be more or less fit according to its spatial position. We give a criterion for the persistence of the population, we prove that (on persistence) the population spreads and give a formula for the spreading speed. The arguments are based on principal eigenvalues of elliptic operators. To get a better intuition of how these eigenvalues behave, we give a representation of the associated principal eigenfunction as a quasi-stationary distribution of a killed process corresponding to the elliptic operator. |
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