On age‐space structure of an autosomal diploid population dynamics model

Abstract

We discuss an age‐structured autosomal polylocal multiallelic diploid population dynamics deterministic model taking into account random mating of sexes, females’ pregnancy and its dispersal in whole space. Dispersal mechanism is described by the diffusion one with constant dispersal moduli while the birth moduli depend on the spatial density of the total population with a time delay. It is assumed that the population consists of male, single (nonfertilized) female, and fertilized female subclasses. Using the method of the fundamental solution for the uniformly parabolic second‐order differential operator with bounded Hölder continuous coefficients we prove the existence and uniqueness theorem for the classic solution of the Cauchy problem for this model. We analyze population's growth and decay, too. Mutation is not considered in this paper.

First Published Online: 14 Oct 2010