  We investigate the stochastic dynamics of entities which are confined to a
set of islands, between which they migrate. They are assumed to be one of two
types, and in addition to migration, they also reproduce and die. Systems which
fall into this class are common in biology and social science, occurring in
ecology, population genetics, epidemiology, biochemistry, linguistics, opinion
dynamics, and other areas. In all these cases the governing equations are
intractable, consisting as they do of multidimensional Fokker-Planck equations
or, equivalently, coupled nonlinear stochastic differential equations with
multiplicative noise. We develop a methodology which exploits a separation in
time scales between fast and slow variables to reduce these equations so that
they resemble those for a single island, which are amenable to analysis. The
technique is generally applicable, but we choose to discuss it in the context
of population genetics, in part because of the extra features that appear due
to selection. The idea behind the method is simple, its application systematic,
and the results in very good agreement with simulations of the full model for a
range of parameter values.
