Changes of a continuous character caused by gene flow. A Monte Carlo study

We introduce a model of a large, sexual, population in which partners for reproduction are chosen randomly, without any bias. This large population is composed of two groups of local populations living in different environments and being in contact. We propose a dynamic equation describing, like the existing one for the allele frequency, the temporal changes of a continuous character due to gene flow, i.e. the transfer of the allels resulting from migration of individuals between the populations, and natural selection. We show that the gene flow can be described by the linear term in the proposed equation and the natural selection by the nonlinear term. Additional killing rule introduces a random factor into our model. We discuss the role of both factors (gene flow and selection) on the structure of the population, i.e. spatial distribution of the considered character and the resulting from it existence of hybrid zones. We use the standard Monte Carlo simulations.