An integro-differential equation from population genetics and perturbations of differentiable semigroups in Fréchet spaces

Abstract

SynopsisExistence and uniqueness of solutions of an integro-differential equation that arises in population genetics are proved. This equation describes the evolution of type densities in a population that is subject to mutation and directional selection on a quantitative trait. It turns out that a certain Fréchet space is the natural framework to show existence and uniqueness. One of the main steps in the proof is the investigation of perturbations of generators of differentiable semigroups in Fréchet spaces.