Taxic homology and three-taxon statement analysis.

Three-taxon statement analysis (3TA) and standard cladistic analysis (SCA) were evaluated relative to propositions of taxic homology. There are definite distinctions between complement relation homologs and paired homologs. The complement relation is discussed, relative to rooting, parsimony, and taxic propositions of homology. The complement relation, as implemented in SCA, makes sense only because SCA is a simple evolutionary model of character-state transformation. 3TA is a method for implementing complement relation data from a taxic perspective. The standard approach to cladistic analysis distinguishes taxa by rooting a tree, which means that that approach is incompatible with taxic propositions of homology, because a taxic homology is a hypothesis of relationship between taxa that possess a homolog relative to taxa that lack a homolog. It is not necessary to treat paired homologs from a transformational perspective to distinguish informative from uninformative data. 3TA yields results markedly different from those of SCA. SCA, which seeks to minimize tree length, may not maximize the relation of homology (congruence) relative to a tree.