Primary genetic divergence in a system of limited population coupled by migration in a ring habitat

The paper is devoted to the study of conditions and mechanisms leading to genetic divergence in a system of panmictic populations coupled by migration. We propose a discrete-time model of the dynamics of abundance and genotype frequencies in a system consisting of such populations that inhabit a homogeneous ring-shaped area. The model describes natural selection acting on a single locus that is the same in all populations, as well as density-dependent factors described by the Ricker stock-recruitment model. The model consists of two layers of coupled maps (ensembles). The first layer describes the dynamics of population size for coupled subpopulations, with growth rates depending on the frequency of genotypes in each local site. The second layer describes changes in genotype frequencies, assuming that migratory gene flow depends on the ratio of abundances between the coupled populations. In this case, the gene flow into a subpopulation is stronger if the subpopulation from which migrants originate is more numerous (or if the receiving subpopulation is less numerous). We demonstrate that, with disruptive (diversifying) selection directed against heterozygotes, primary genetic divergence occurs depending on the initial conditions and persists indefinitely, resulting in a heterogeneous spatial distribution of individuals within the population range. It is shown that groups of monomorphic populations (clusters), where homozygotes predominate, are formed in the spatial distribution. It is shown that adjacent groups of monomorphic populations in which homozygotes predominant and form clusters in spatial distribution. Between these clusters with opposite genetic forms (alleles), there are small polymorphic groups whose presence is maintained by migration from neighboring sites and by hybridization. With constant migration, such groups persist for long periods of time. When individuals wander randomly, they form waves with a long period. We show that genetic divergence is accompanied by emerging significant differences in abundance and patterns of dynamics in different parts of the range (synchronous clusters).