We consider n phenotypes of a species in a continuous but heterogeneou
s environment, it is assumed that the phenotypes differ only in their
diffusion rates. With haploid genetics and a small rate of mutation, i
t is shown that the only nontrivial equilibrium is a population domina
ted by the slowest diffusing phenotype. We also prove that if there ar
e only two possible phenotypes, then this equilibrium is a global attr
actor and conjecture that this is true in general. Numerical simulatio
ns supporting this conjecture and suggesting that this is a robust phe
nomenon are also discussed.