Convex Groups and Consistent Classifications

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Abstract
The claim has been made that all convex groups are consistent with phylogenetic hypotheses that contain members of these groups. Convex groups may be either clades (monophyletic groups sensu Hennig) or paraphyletic grades. Convex characters are shared homologues. The logical meaning of consistency is explored and Hull''s concept of consistency between classifications and phylogenies is applied to this claim and expanded to include consistency between grouping of organisms, character evolution, and other natural processes. Any classification containing only clades is consistent with both the branching sequence and character evolution of the organisms classified. Indeed there are many such consistent classifications. Some contain more information than others. In contrast, classifications containing paraphyletic grades are never consistent with the branching sequence of the organisms classified and, unless neutrality is claimed, will lead to inconsistent deductions about character evolution. Further, if neutrality is claimed, paraphyletic grades cannot be defined by characters, and classifications containing paraphyletic grades are usually less informative than the least informative classification containing only clades. In those cases where this is not true, the classification containing paraphyletic grades gives inconsistent (and misleading) information on character evolution.