ON PRIMARY GENETIC DIVERGENCE IN A SYSTEM OF POPULATIONS IN A RING AREA

Abstract

The article proposes and studies a discrete time model of the numberdynamics and genotype frequencies in a one-dimensional ring of populations coupled by migration. We consider panmictic populations with Mendelian rules of inheritance and monolocus selection directed against heterozygotes. The model has two layers of connected maps  (ensembles). The first layer describes the number dynamics in each local site, including migration from adjacent sites. The growth rates of each subpopulation depend on the genotype frequencies, which change during evolution towards one of the limiting genetic structures. The second level describes the dynamics of genotype frequencies, considering the fact that gene influx depends on the ratio of population abundance. Here, the more numerous is the population giving the migrant flow(or less numerous is the receiving population), the stronger is the gene flow. We have considered two variants of migration: constant (deterministic), in which the fraction of migrants is fixed, and random, in which the number of emigrants from the local population is chosen randomly (random drift) and is not constant. The model studies the conditions and mechanisms of differentiation by genotypes between different parts of a homogeneous range (divergence). It has been shown that with reduced fitness of heterozygotes, spatial-temporal dynamics are characterized by stripes where homozygotes predominate. Between the stripes with opposite forms (alleles), there locate the stripes with heterozygotes, their existence supporting due to migrations from opposite sites. With deterministic migration, this pattern exists for a short time and most often appears as vertical stripes. With random drift, the stripes take the form of traveling waves, which persist for a long time under certain limitations on population growth. The authors show thatsignificant differences inevitably arising in the number anddynamics patterns in different parts of the area,  are caused by divergence.