Success of Phylogenetic Methods in the Four-Taxon Case

The success of 16 methods of phylogenetic inference was examined using consistency and simulation analysis. Success—the frequency with which a tree-making method correctly identified the true phylogeny—was examined for an unrooted four-taxon tree. In this study, tree-making methods were examined under a large number of branch-length conditions and under three models of sequence evolution. The results are plotted to facilitate comparisons among the methods. The consistency analysis indicated which methods converge on the correct tree given infinite sample size. General parsimony, transversion parsimony, and weighted parsimony are inconsistent over portions of the graph space examined, although the area of inconsistency varied. Lake's method of invariants consistently estimated phylogeny over all of the graph space when the model of sequence evolution matched the assumptions of the invariants method. However, when one of the assumptions of the invariants method was violated, Lake's method of invariants became inconsistent over a large portion of the graph space. In general, the distance methods (neighbor joining, weighted least squares, and unweighted least squares) consistently estimated phylogeny over all of the graph space examined when the assumptions of the distance correction matched the model of evolution used to generate the model trees. When the assumptions of the distance methods were violated, the methods became inconsistent over portions of the graph space. UPGMA was inconsistent over a large area of the graph space, no matter which distance was used. The simulation analysis showed how tree-making methods perform given limited numbers of character data. In some instances, the simulation results differed quantitatively from the consistency analysis. The consistency analysis indicated that Lake's method of invariants was consistent over all of the graph space under some conditions, whereas the simulation analysis showed that Lake's method of invariants performs poorly over most of the graph space for up to 500 variable characters. Parsimony, neighbor-joining, and the least-squares methods performed well under conditions of limited amount of character change and branch-length variation. By weighting the more slowly evolving characters or using distances that correct for multiple substitution events, the area in which tree-making methods are misleading can be reduced. Good performance at high rates of change was obtained only by giving increased weight to slowly evolving characters (e.g., transversion parsimony, weighted parsimony). UPGMA performed well only when branch lengths were close in length.