A higher order parsimony method to reduce long-branch attraction

Abstract

Results are presented for the problem of reconstructing a phylogenetic tree for a quartet of four species from DNA strings for the species. For quartets, a notion of order of approximation is defined. It is shown that choosing the topology for a given quartet by maximum parsimony (MP) is of order 2. A new method of order 3 is described. This method, called higher order parsimony (HOP), gives improved results on artificial data of nucleotides, greatly reducing the effect of long-branch attraction. Comparisons are made with MP, maximum likelihood (ML), and Hadamard conjugation on many artificial data sets chosen such that long-branch attraction would be a problem. Both HOP and ML are much more accurate than MP. The accuracies of HOP and ML appear comparable, with ML somewhat more accurate when the model used to generate substitutions closely matches that assumed by ML, and transitions dominate over transversions. When the model for substitutions differs substantially from that assumed by ML, then HOP may outperform ML, suggesting that HOP is more model-independent. The required computer time for HOP is, moreover, much shorter than that for ML, giving HOP a major practical advantage. HOP works best when the alphabet corresponds to sequences of nucleotides; hence, a modification is also presented that applies when the alphabet corresponds to amino acid residues.