  We present an individual-based model of phenotypic trait evolution in two-sex
populations, which includes semi-random mating of individuals of the opposite
sex, natural death and intra-specific competition. By passing the number of
individuals to infinity, we derive the macroscopic system of nonlinear
differential equations describing the evolution of trait distributions in male
and female subpopulations. We study solutions, give criteria for persistence or
extinction, and state theorem on asymptotic stability, which we apply later to
particular examples of trait inheritance.
