The Necessity of Convex Groups in Biological Classification

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Abstract
A discussion is presented of convexity as a consistency criterion for evaluating classifications in relation to cladograms. Convex groups are monophyletic groups of Haeckel. Two types of convex groups are defined, holophyletic and paraphyletic groups. Polyphyletic groups are not convex. Constructing holophyletic classifications when ancestor-descendant relationships are asserted is impossible. A logical conflict exists between Popperian logic and Hennigian grouping by synapomorphy. The practical benefits of convex classification, particularly simplicity and stability, are discussed using entomological, zoological, and botanical examples. Contrary to assertions recently presented in the cladistic literature, convexity is a valid and useful consistency criterion. The definition of this criterion that we present is an explicit formulation of traditional evolutionary systematics.

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