The influence of a geographical barrier on the balance of selection and migration

摘要

AbstractIn biology, a cline is defined as a usually gradual change in gene frequency or phenotype of a population in equilibrium, from one place to another.We define a cline as a nonconstant stable steady state solution. However, for the model studied in this paper, these two definitions coincide: a nonconstant stable steady state solution is necessarily monotone. It is proved that for small values of the penetrability of the barrier, exactly two clines exist.Since we prove that the Ω‐limit set of any initial condition is a steady state solution, the information thus obtained yields a rather complete understanding of the qualitative behaviour of the solutions of the evolution problem under considerati