A Quasispecies on a Moving Oasis

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.