  The stationary distribution of the diffusion limit of the 2-island, 2-allele
Wright-Fisher with small but otherwise arbitrary mutation and migration rates
is investigated. Following a method developed by Burden and Tang (2016, 2017)
for approximating the forward Kolmogorov equation, the stationary distribution
is obtained to leading order as a set of line densities on the edges of the
sample space, corresponding to states for which one island is bi-allelic and
the other island is non-segregating, and a set of point masses at the corners
of the sample space, corresponding to states for which both islands are
simultaneously non-segregating. Analytic results for the corner probabilities
and line densities are verified independently using the backward generator and
for the corner probabilities using the coalescent.
