A mathematical analysis of an age-space-structured autosomal diploid population dynamics model with random mating and females' pregnancy

Abstract

We discuss a deterministic model of the age-structured autosomal polylocal multiallelic diploid population dynamics that takes into account random mating of sexes, females' pregnancy, and its dispersal in the whole space. This model generalizes the previous one by taking into account the spatial dispersal whose mechanism is described by the general linear elliptic differential operator of the second order. The population consists of male, single (nonfertilized) female, and fertilized female subclasses. Using the fundamental solution method for the uniformly parabolic second-order differential operator with bounded Holder continuous coefficients, we prove the existence and uniqueness theorem for the classic solution of the Cauchy problem for this model. In the case where dispersal moduli of fertilized females do not depend on the age of mated males, we analyze the population growth and decay. Mutation is not consisdered in this paper.