  Migration between different habitats is ubiquitous among biological
populations. In this Letter, we study a simple quasispecies model for evolution
in two different habitats, with different fitness landscapes, coupled through
one-way migration. Our model applies to asexual, rapidly evolving organisms
such as microbes. Our key finding is a dynamical phase transition at a critical
value of the migration rate. The time to reach steady state diverges at this
critical migration rate. Above the transition, the population is dominated by
immigrants from the primary habitat. Below the transition, the genetic
composition of the population is highly non-trivial, with multiple coexisting
quasispecies which are not native to either habitat. Using results from
localization theory, we show that the critical migration rate may be very small
--- demonstrating that evolutionary outcomes can be very sensitive to even a
small amount of migration.
