### Summary

We consider a model with two types of genes (alleles) A_{1} A_{2}. 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.