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Dynamics of sexual populations structured by a space variable and a phenotypical trait. (English) Zbl 1275.92098
Summary: We study sexual populations structured by a phenotypic trait and a space variable, in a non-homogeneous environment. Departing from an infinitesimal model, we perform an asymptotic limit to derive the system introduced in [M. Kirkpatrick and N. H. Barton, “Evolution of a species’ range”. Amer. Nat. 150, No. 1, 1–23 (1997)]. We then perform a further simplification to obtain a simple model. Thanks to this simpler equation, we can describe rigorously the dynamics of the population. In particular, we provide an explicit estimate of the invasion speed, or extinction speed of the species. Numerical computations show that this simple model provides a good approximation of the original infinitesimal model, and in particular describes quite well the evolution of the species’ range.

92D40 Ecology
62P10 Applications of statistics to biology and medical sciences; meta analysis
35Q92 PDEs in connection with biology, chemistry and other natural sciences
92D15 Problems related to evolution
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