THE COMPARISON OF DENDROGRAMS BY OBJECTIVE METHODS

Abstract

The purpose of this paper is to present a technique for comparing dendrograms resulting from numerical taxonomic research with one another and with dendrograms produced by conventional methods. One of the most frequent ways of depicting the results of studies in numerical taxonomy (Sokal, 1960; Sneath and Sokal, 1962) is by so-called dendrograms or diagrams of relationships. These are tree-like schemes which indicate the affinity of taxa to their nearest relatives (on the basis of similarity or phenetic resemblance alone, without any necessary phylogenetic implications). These diagrams resemble the customary phylogenetic trees, but are preferred for classificatory purposes; first, because phylogenetic inferences are speculative, while similarities are factual; secondly, because they are quantitative evaluations of these similarities; and thirdly, because they lack some of the other meanings often implied in phylogenetic trees (Sneath and Sokal, 1962). Such dendrograms have been published in bacteriological work (Sneath and Cowan, 1958), in studies of bees (Michener and Sokal 1957; Sokal and Michener 1958), butterflies (Ehrlich, 1961), rice (Morishima and Oka, 1960), members of the nightshade genus Solanum (Soria and Heiser, 1961) and others. With the increasing acceptance of the philosophy of numerical taxonomy an experimental phase in using various types of coefficients is beginning, which will involve the comparison of the results of numerical taxonomic research based on these different coefficients. So far we have lacked a procedure for such comparisons. The cophenetic correlations which will be developed below provide an extremely simple and effective method for comparing dendrograms of various sorts. Before proceeding to a detailed account of the technique, it will be useful to discuss briefly the four types of comparisons of dendrograms that we wish to make in numerical taxonomy and the reasons for them: