Existence and nonexistence of steady-state solutions for a selection-migration model in population genetics
We discuss a selection-migration model in population genetics, involving two alleles A1 and A2 such that A1 is at an advantage over A2 in certain subregions and at a disadvantage in others. It is shown that if A1 is at an overall disadvantage to A2 and the rate of gene flow is sufficiently large than A1 must die out; on the other hand, if the two alleles are in some sense equally advantaged overall, then A1 and A2 can coexist no matter how great the rate of gene flow.