On the Three-Taxon Approach to Parsimony Analysis

The following three basic defects for which three-taxon analysis has been rejected as a method for biological systematics are reviewed: (1) character evolution is a priori assumed to be irreversible; (2) basic statements that are not logically independent are treated as if they are; (3) three-taxon statements that are considered as independent support for a given tree may be mutually exclusive on that tree. It is argued that these criticisms only relate to the particular way the three-taxon approach was originally implemented. Four-taxon analysis, an alternative implementation that circumvents these problems, is derived. Four-taxon analysis is identical to standard parsimony analysis except for an unnatural restriction on the maximum amount of homoplasy that may be concentrated in a single character state. This restriction follows directly from the basic tenet of the three-taxon approach, that character state distributions should be decomposed into basic statements that are, in themselves, still informative with respect to relationships. A reconsideration of what constitutes an elementary relevant statement in systematics leads to a reformulation of standard parsimony as two-taxon analysis and to a rejection of four-taxon analysis as a method for biological systematics.