  Conditional sampling distributions (CSDs), sometimes referred to as copying
models, underlie numerous practical tools in population genomic analyses.
Though an important application that has received much attention is the
inference of population structure, the explicit exchange of migrants at
specified rates has not hitherto been incorporated into the CSD in a principled
framework. Recently, in the case of a single panmictic population, a
sequentially Markov CSD has been developed as an accurate, efficient
approximation to a principled CSD derived from the diffusion process dual to
the coalescent with recombination. In this paper, the sequentially Markov CSD
framework is extended to incorporate subdivided population structure, thus
providing an efficiently computable CSD that admits a genealogical
interpretation related to the structured coalescent with migration and
recombination. As a concrete application, it is demonstrated empirically that
the CSD developed here can be employed to yield accurate estimation of a wide
range of migration rates.
