Selection-mutation evolution models are a well known branch of PDEs applied to biology. We explore the possible equilibria that can emerge for the phenotype of a population submitted to three phenomena: a pressure of selection from the environment, mutations and, as the main novelty, horizontal transfer of the phenotype. The horizontal transfer occurs when individuals (not necessarilly relatives) exchange some phenotipical materials by a certain biological process. This horizontal transfer is represented by a non-local convolution term on the PDE and enriches greatly the family of Evolutionary Stable Strategies (ESS) in this problem. These ESS are what we use in order to gain a better undestanding of the steady states to which the evolution will converge.
Romain Duboscq, Ariane Trescases
