  We consider an individual based model of phenotypic evolution in
hermaphroditic populations which includes random and assortative mating of
individuals. By increasing the number of individuals to infinity we obtain a
nonlinear transport equation, which describes the evolution of distribution of
phenotypic traits. Existence of an one-dimensional attractor is proved and the
formula for the density of phenotypic traits in the limiting (asymptotic)
population is derived in some particular case.

Probability;Classical Analysis and ODEs;Populations and Evolution