SPR-based Tree Reconciliation: Non-binary Trees and Multiple Solutions

The SPR (subtree prune and regraft) operation is used as the basis for reconciling incongruent phylo-genetic trees, particularly for detecting and analyzing non-treelike evolutionary histories such as horizontal gene transfer, hybrid speciation, and recombination. The SPR-based tree reconciliation problem has been shown to be NP-hard, and several efficient heuristics have been designed to solve it. A major drawback of these heuristics is that for the most part they do not handle non-binary trees appropriately. Further, their computational efficiency suffers significantly when computing multiple optimal reconciliations. In this paper, we present algorithmic techniques for efficient SPR-based reconciliation of trees that are not necessarily binary. Further, we present divide-and-conquer approaches that enable efficient computing of multiple optimal reconciliations. We have implemented our techniques in the PhyloNet software package, which is publicly available at http://bioinfo.cs.rice.edu. The resulting method outperforms all existing methods in terms of speed, and performs at least as well as those methods in terms of accuracy.