Methods of Comparing + 4071 Classifications

The word "classification" can be used in a broad sense to include various types of diagrams that indicate either the relative degrees of similarities or the lines of descent, as well as the traditional Linnean classification (32). For example, DuPraw (12) referred to his bivariate scatter diagrams (based upon canonical variate analysis) as being a form of "non-Linnean classification." The present paper is mainly concerned with methods for comparing classification where the objects under study (OTUs) (44) are placed into nonoverlapping classes either at a single level or in a hierarchy. However, the other applications must be kept in mind since ordination analyses and analyses based upon graph theory are becoming routine in both systematics and ecology. It is desirable to be able to compare these and measure the extent to which each preserves information about the patterns of similarity among the OTUs. It is possible to classify the various approaches to comparing classifications in several ways. Some methods are applicable only to traditional classifications, whereas others are applicable to classifications in a very broad sense. Jardine & Sibson (25) distinguish three types of situations in which one would wish to compare two or more classifications: (a) testing independence (such as testing whether a classification based on soil type is independent of a classification based on the growth form of the plants found on these soils), (b) measuring dependence (for example, one may wish to measure the degree to which a classification based upon one set of variables can be predicted based on another set), and (c) measurement of congruence of classifications (testing, for example, whether or not classifications based upon larval characters are congruent with classifications based upon adult characters). In this paper, we are mainly concerned with congruence.