General Inconsistency Conditions for Maximum Parsimony: Effects of Branch Lengths and Increasing Numbers of Taxa

Abstract.—Inconsistency of phylogenetic estimations refers to the property of certain estimation methods to converge on the positively wrong estimate with increasing amounts of data. This property, at least with respect to the maximum parsimony method, has been given the catch phrase long branches attract. It has also been suggested that this problem can be alleviated by inclusion of more taxa to break up the long branches. Unfortunately, these observations have been based on computations for trees with small numbers of taxa. Here, I present a decomposition equation that allows determination of inconsistency conditions for large numbers of taxa. I show by counterexamples that long branches are a poor predictor of inconsistent conditions and that even trees with equal branch lengths can produce inconsistent estimates. I also tested the idea of breaking up long branches with additional taxa. The addition of taxa alleviates the inconsistency problem only if the average rate of change in the added taxa is low. If the rate is high, the inconsistency problem can become worse. Sampling of random tree models indicates that the inconsistency problem becomes increasingly acute as the number of taxa becomes larger. Conclu-sions: (1) low rates of change are of paramount importance if the inconsistency problem is to be avoided, (2) if the evolutionary question of interest does not require large numbers of taxa, it