  A population evolving in an inhomogeneous environment will adapt differently
to different regions. We study the conditions under which such a population can
maintain adaptations to a particular region when that region is not stationary,
but can move. In particular, we study a quasispecies living near a favorable
patch ("oasis") in the middle of a large "desert." The population has two
genetic states, one of which which conveys a relative advantage while in the
oasis at the cost of a disadvantage in the desert. We consider the population
dynamics when the oasis is moving, or equivalently some form of "wind" is
blowing the population away from the oasis. We find that the ratio of the two
types of individuals exhibits sharp transitions at particular oasis velocities.
We calculate an extinction velocity, and a switching velocity above which the
dominance switches from the oasis-adapted genotype to the desert-adapted one.
This switching velocity is analagous to the quasispecies mutational error
threshold. Above this velocity, the population cannot maintain adaptations to
the properties of the oasis.
