(1) |
independently for each . Then the prior for the frequencies in population is
(2) |
independently for each and . In this model, the s have a close relationship to the standard measure of genetic distance, . In the standard parametrization of , the expected frequency in each population is given by overall mean frequency, and the variance in frequency across subpopulations of an allele at overall frequency is . The model here is much the same, except that we generalize the model slightly by allowing each population to drift away from the ancestral population at a different rate (), as might be expected if populations have different sizes. We also try to estimate ``ancestral frequencies'', rather than using the mean frequencies. We have placed independent priors on the , proportional to a gamma distribution with means of 0.01 and standard deviation 0.05 (but with ). The parameters of the gamma prior can be modified by the user. Some experimentation suggests that the prior mean of 0.01, which corresponds to very low levels of subdivision, often leads to good performance for data that are difficult for the independent frequencies model. In other problems, where the differences among populations are more marked, it seems that the data usually overwhelm this prior on .