Long Time Evolution of Populations under Selection and Vanishing Mutations

@article{Raoul2011LongTE,
  title={Long Time Evolution of Populations under Selection and Vanishing Mutations},
  author={Ga{\"e}l Raoul},
  journal={Acta Applicandae Mathematicae},
  year={2011},
  volume={114},
  pages={1-14}
}
In this paper, we consider a long time and vanishing mutations limit of an integro-differential model describing the evolution of a population structured with respect to a continuous phenotypic trait. We show that the asymptotic population is a steady-state of the evolution equation without mutations, and satisfies an evolutionary stability condition. 

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