Abstract. 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). 

 

Key words: metapopulation, genetic divergence, migration, spatio-temporal dynamics, synchronization, clustering.