Small populations corrections for selection-mutation models

Details Small populations corrections for selection-mutation models Small populations corrections for selection-mutation models

2012-03-19

arxiv.org/abs/1203.4123v1

Mathematics

Analysis of PDEs

Scientific paper

We consider integro-differential models describing the evolution of a population structured by a quantitative trait. Individuals interact competitively, creating a strong selection pressure on the population. On the other hand, mutations are assumed to be small. Following the formalism of Diekmann, Jabin, Mischler, and Perthame, this creates concentration phenomena, typically consisting in a sum of Dirac masses slowly evolving in time. We propose a modification to those classical models that takes the effect of small populations into accounts and corrects some abnormal behaviours.

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