Recombination Analysis Using Directed Graphical Models

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Abstract
In Strimmer and Moulton (2000) , we described a method for computing the likelihood of a set of sequences assuming a phylogenetic network as an evolutionary hypothesis. That approach relied on converting a given graph into a directed graphical model or stochastic network from which all desired probability distributions could be derived. In particular, we investigated how to compute likelihoods using split-graphs (Huson 1998 ). However, in the presence of recombination, split-graphs may not provide an appropriate choice of the underlying graph. In this letter, we propose basing the stochastic network on an ancestral recombination graph (ARG) (Hudson 1983 ; Griffiths and Marjoram 1996, 1997 ). We show that our approach using directed graphical models extends in a straightforward fashion to ARGs, and we outline the computation of their likelihoods. In particular, we provide an example of an ARG whose likelihood is greater than that of a competing nonnested tree, even though the ARG has a smaller number of free parameters.