We describe a general method for finding the probability distribution of neutral genealogies, which allows for migration between demes, splitting of demes (as in the isolation-with-migration (IM) model), and recombination between linked loci. These processes are described by a set of linear recursions for the generating function of branch lengths. Under the infinite-sites model, the probability of any configuration of mutations can then be found by differentiating this generating function. Such calculations are feasible for small numbers of sampled genomes, and can readily be automated. We show how the method extends to continuous genomes, giving the joint distribution of coalescence times and recombination break-points. This allows an assessment of the accuracy of the sequential Markov coalescent, and of methods that assume non-recombining blocks.

Joint work with Konrad Lohse.