Diagnostic Efficiency of Three‐Taxon Analysis

Abstract

Matrices of three-taxon statements (3ts) represent a transformation of original data in that they are calculated from normal data matrices. Normal matrices cannot be considered transformational (or 3ts matrices original) in that sense, because the 3ts transformation cannot be reversed. That the 3ts transformation cannot be reversed also means that the transformation discards information. Use of 3ts greatly reduces the efficiency with which data can be represented through the diagnoses of a classification. This happens because, unlike normal characters, 3ts provide no direct way of identifying a feature as the same in several different organisms. The ensemble retention index R does not have the same interpretation in three-taxon analysis (3ta) as it does with normal data matrices. In normal analyses R measures diagnostic efficiency, whereas 3ta always has minimal efficiency. Although usually interpreted phylogenetically, parsimony analysis can be applied descriptively without assuming any evolutionary process. This means that objecting to evolution as theoretical, unknown, or nonexistent would provide no grounds for rejecting parsimony in favor of 3ta, even if one did believe the objection.