  We consider a mutation-selection model of a population structured by the
spatial variables and a trait variable which is the diffusion rate. Competition
for resource is local in spatial variables, but nonlocal in the trait variable.
We focus on the asymptotic profile of positive steady state solutions. Our
result shows that in the limit of small mutation rate, the solution remains
regular in the spatial variables and yet concentrates in the trait variable and
forms a Dirac mass supported at the lowest diffusion rate. [Hastings, Theor.
Pop. Biol. 24, 244-251, 1983] and [Dockery et al., J. Math. Biol. 37, 61-83,
1998] showed that for two competing species in spatially heterogeneous but
temporally constant environment, the slower diffuser always prevails, if all
other things are held equal. Our result suggests that their findings may hold
for arbitrarily many traits.
