Towards a basis for classification: the incompleteness of distance measures, incompatibility analysis and phenetic classification

Abstract

There has been a long term controversy in biology whether relationships between organisms should be expressed in evolutionary terms, or on clusters based on overall similarity. Phenetic methods are those that use a measure of overall similarity (dissimilarity, or distance) between pairs of taxa, rather than the original data. It is shown that information is lost in converting the original data to distances in that it is in general not possible to recover the original data from a distance matrix. In particular it is shown that: 1. (a) different data sets may give the same dissimilarity matrix, 2. (b) even data sets that give different minimal trees can give the same dissimilarity matrix, 3. (c) as the number of taxa and/or characters increase there may be many more data sets than similarity matrices, 4. (d) even when there are fewer data sets than similarity matrices it is possible to find cases where the same similarity matrix can be obtained from different data sets. It is concluded that because of this loss of information the methods of phenetic classification are inherently weaker than methods that retain the original data. An indication is given of how information is lost in transforming to distances. Incompatibility matrices are shown not to contain all the original information but these methods usually retain the original data for tree building.