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We present a Bayesian statistical inference approach for simultaneously estimating mutation rate, population sizes, and migration rates in an island-structured population, using temporal and spatial sequence data. Markov chain Monte Carlo is used to collect samples from the posterior probability distribution. We demonstrate that this chain implementation successfully reaches equilibrium and recovers truth for simulated data. A real HIV DNA sequence data set with two demes, semen and blood, is used as an example to demonstrate the method by fitting asymmetric migration rates and different population sizes. This data set exhibits a bimodal joint posterior distribution, with modes favoring different preferred migration directions. This full data set was subsequently split temporally for further analysis. Qualitative behavior of one subset was similar to the bimodal distribution observed with the full data set. The temporally split data showed significant differences in the posterior distributions and estimates of parameter values over time.
Ewing et al. (Wed,) studied this question.