  We establish convergence to the Kingman coalescent for the genealogy of a
geographically - or otherwise - structured version of the Wright-Fisher
population model with fast migration. The new feature is that migration
probabilities may change in a random fashion. This brings a novel formula for
the coalescent effective population size (EPS). We call it a quenched EPS to
emphasize the key feature of our model - random environment. The quenched EPS
is compared with an annealed (mean-field) EPS which describes the case of
constant migration probabilities obtained by averaging the random migration
probabilities over possible environments.
