SPR Distance Computation for Unrooted Trees

The subtree prune and regraft distance (d(SPR)) between phylogenetic trees is important both as a general means of comparing phylogenetic tree topologies as well as a measure of lateral gene transfer (LGT). Although there has been extensive study on the computation of d(SPR) and similar metrics between rooted trees, much less is known about SPR distances for unrooted trees, which often arise in practice when the root is unresolved. We show that unrooted SPR distance computation is NP-Hard and verify which techniques from related work can and cannot be applied. We then present an efficient heuristic algorithm for this problem and benchmark it on a variety of synthetic datasets. Our algorithm computes the exact SPR distance between unrooted tree, and the heuristic element is only with respect to the algorithm's computation time. Our method is a heuristic version of a fixed parameter tractability (FPT) approach and our experiments indicate that the running time behaves similar to FPT algorithms. For real data sets, our algorithm was able to quickly compute d(SPR) for the majority of trees that were part of a study of LGT in 144 prokaryotic genomes. Our analysis of its performance, especially with respect to searching and reduction rules, is applicable to computing many related distance measures.