A fixed interface boundary value problem for differential equations: a problem arising from population genetics

Abstract

Genetic materials (genes) disperse in spatially distributed populations subject to the joint action of evolutionary forces such as migration and selection. Recent study has shown that regions in the population’s habitat of geographical obstacles, reduced population den- sity, or spatial frequency patterns of linked genes may perform as barriers to the gene diffusion, and cause sharp changes of gene frequencies across the region (cf. e.g., [8]). It is suggested that barriers be a significant factor inducing the genetic diversity and specious isolation in ecological systems.