  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.
