A selection-migration model in population genetics
J. Math. Biol., 2 (3):
219--233 (1975)Abstract
We consider a model with two types of genes (alleles) A1 A2. The population lives in a bounded habitat R, contained in r-dimensional space (r= 1, 2, 3). Let u (t, x) denote the frequency of A 1 at time t and place x ɛ R. Then u (t, x) is assumed to obey a nonlinear parabolic partial differential equation, describing the effects of population dispersal within R and selective advantages among the three possible genotypes A 1 A 1, A 1 A 2, A 2 A 2. It is assumed that the selection coefficients vary over R, so that a selective advantage at some points x becomes a disadvantage at others. The results concern the existence, stability properties, and bifurcation phenomena for equilibrium solutions.