The Evolutionary Forest Algorithm 

We describe a Bayesian Markov Chain Monte Carlo method for
approximating posterior distributions of parameters based on multiple
summary statistics. In this application, we address the demographic
history of closely related members of the Drosophila pseudoobscura
group. We estimate the joint posterior distribution of the time since
speciation, backward migration rates and effective population sizes of
the extant and ancestral populations. We base estimation on the
multi-locus regions of DPS2002, a noncoding region tightly linked to a
paracentric inversion which strongly contributes to reproductive
isolation, and Rhodopsin 1, a region where genetic introgression is
likely to exist. Summary statistics, rather than entire nucleotide
sequences, permits a compact description of the genealogy of the
sample. Consideration of an augmented random variable, comprised of
multiple genealogies or forest, dramatically increases sampling
efficiency. This method of using a forest of genealogical histories
converges marginally to the posterior distributions of interest and
convergence is improved on compared to methods in which a single
history is considered. Analysis of a subset of the data, for which
recursive computation of the exact posterior distribution was
feasible, indicated close agreement between approximate and exact
calculations.