Genetic divergence in the system of adjacent populations with density-dependent limitation of gamete production

The paper studies the mechanisms leading to the emergence of genetic divergence (stable genetic differences) between two populations coupled by migration. We considered the classical system of panmictic populations with Mendelian rules of inheritance and monolocus selection directed against heterozygotes. In order to limit the growth of populations, we propose to assume that gamete production and total fertility (birth) decreases with population growth due to limited resources. We have proposed a non-linear discrete time model that describes the concentration dynamics of one of the alleles and each population abundance. To calculate the coordinates of all fixed points corresponding to different types of the limiting genetic structure and the abundance ratio, we have proposed a method for calculating their coordinates. It is shown that with a density-dependent birth limitation in the model, a set of fixed points corresponding to a homogeneous and heterogeneous distribution is possible. At a homogeneous distribution, both populations are monomorphic, with individuals belonging to only one genotype. At this, the limiting values of population abundance do not always coincide. With a non-homogeneous distribution, adjacent populations are polymorphic with individuals of different genotypes, but they differ significantly in the frequencies of alternative alleles and asymptotic population abundance. Bifurcations of the fixed points birth corresponding to heterogeneous distribution and genetic divergence are described. It is found that the movement towards one of the possible limiting genetic structures is accompanied by a change in the reproductive capabilities of populations.It is shown that a reduced fitness of heterozygotes in monomorphic populations results in a higher birth rate as compared to polymorphic populations obviously containing individuals with different reproductive capabilities. As a result, monomorphic and polymorphic populations correspond to different limiting abundances and cycles with different periods and oscillation phases after the loss of stability, even if the populations are completely identical.