Categorical Ranks and Evolutionary Taxa in Numerical Taxonomy

The merits of various measures of divergence within a taxon are discussed, and it is concluded that the difference between the two most different OTU's in a taxon is the most reliable measure of divergence. This “maximum difference” criterion of divergence is shown to be related to the categorical rank of a taxon by an equation of the form cd(R) = k2R, where R is the rank of the taxon, and cd(R) is the greatest amount of divergence permitted within a taxon designated to be of rank R. The rank criterion is related to a modification of the intensional “difference-from-type” form of taxon definition. It is noted that, if evolution does not proceed by saltation, certain intensional definitions of taxa imply extensional differences between monotypic overlapping taxa of different ranks, so that Gregg's Paradox is resolved. A classification of ferns is generated as an example of the use of the techniques proposed. It is concluded that the continuity of evolution invalidates the use of “gaps” between groups as criteria of rank. Continuity also implies that very similar OTU's may be placed in distinct taxa of high rank.