A sampling theory of selectively neutral alleles in a subdivided population

Ewens' sampling distribution is investigated for a structured population. Samples are assumed to be taken from a single subpopulation that exchanges migrants with other subpopulations. A complete description of the probability distribution for such samples is not a practical possibility but an equilibrium approximation can be found. This approximation extracts the information necessary for constructing a continuous approximation to the complete distribution using known values of the distribution and its derivatives in randomly mating populations. It is shown that this approximation is as complete a description of a single biologically realistic subpopulation as is possible given standard uncertainties about the actual size of the migration rates, relative sizes of each of the subpopulations and other factors that might affect the genetic structure of a subpopulation. Any further information must be gained at the expense of generality. This approximation is used to investigate the effect of population subdivision on Watterson's test of neutrality. It is known that the infinite allele, sample distribution is independent of mutation rate when made conditional on the number of alleles in the sample. It is shown that the conditional, infinite allele, sample distribution from this approximation is also independent of population structure and hence Watterson's test is still approximately valid for subdivided populations.