Island models and the coalescent process

Using a coalescent approach, we derive several classical results and extend them to more general models. We find that the classic result for constant population size and constant migration rates holds in models with varying population size and varying migration rates with the obvious substitution of effective population size and mean migration fraction. In addition, the relationship of a 'local' F-ST to local gene flow is derived. This result may be useful for analysing gene flow in a regional subset of a large global population, using only data from the regional subset.