Obtaining highly accurate topology estimates of evolutionary trees from very short sequences

The evolutionary history of a set of species is represented by a phylogenetic tree, in other words, by a rooted, leaf-labelled tree, where internal nodes represent ancestral species and the leaves represent modern day species. Accurate (or even boundedly inaccurate) topology reconstructions of large and divergent trees has long been considered one of the major challenges in systematic biology. None of the polynomial time methods developed by the theoretical computer science community has been shown to outperform the popular Neighbor-Joining method used by systematic biologists, with respect to topology estimation. (However, preliminary experiments indicate that two new variants of Neighbor-Joining, Bio-NJ and Weighbor, do exhibit improved performance.) In this paper, we present a simple polynomial time method, the Disk-Covering Method (DCM), which boosts the performance of base phylogenetic methods. We analyze the performance of DCM-boosted distance methods under the general Markov model of evolution , and prove that, by using the DCM-boosted Bune-man method, for almost all trees, polylogarithmic length sequences suuce for complete accuracy with high probability , while polynomial length sequences always suuce. Our experimental study (based upon simulating sequence evolution on model trees, generating about 1000 datasets) con-rms these substantial reductions in error rates and extremely fast convergence rates. In particular, we report that DCM-boosted Neighbor-Joining has only 8% of the error of Neighbor-Joining under conditions that are adverse to Neighbor-Joining, and on some trees achieving acceptable error rates (less than 5% error in the topology estimation) from sequences of a few hundred nucleotides, while Neighbor-Joining needs more than 10K nucleotides to achieve the same level of accuracy. 1 Introduction The evolution of biomolecular sequences can be modeled as a Markov process operating on a rooted binary tree: A biomolecular sequence at the root of the tree \evolves down" the tree, with each edge of the tree introducing point mutations , thereby generating sequences at the leaves of the tree, each of the same length as the root sequence. The phylo-genetic tree reconstruction problem is to take the sequences that occur at the leaves of the tree, and infer, as accurately as possible, the tree that generated the sequences. The tree reconstruction problem has two objectives: rst, to recover the branching process, as represented by the rooted leaf-labelled topology of the evolutionary tree, and second, to estimate the parameters of the evolutionary process (the mutation probabilities on the edges of the tree, the rates of change across …