Inductive determination of allele frequency spectrum probabilities in structured populations

We present a method for inductively determining exact allele frequency spectrum (AFS) probabilities for samples derived from a population comprising two demes under the infinite-allele model of mutation. This method builds on a labeled coalescent argument to extend the Ewens sampling formula (ESF) to structured populations. A key departure from the panmictic case is that the AFS conditioned on the number of alleles in the sample is no longer independent of the scaled mutation rate (θ). In particular, biallelic site frequency spectra, widely-used in explorations of genome-wide patterns of variation, depend on the mutation rate in structured populations. Variation in the rate of substitution across loci and through time may contribute to apparent distortions of site frequency spectra exhibited by samples derived from structured populations.