Divisive Polythetic Classification of Vegetation data by Optimized Division on Ordination Components

Divisive methods have an advantage over agglomerative ones in that they use all available information at the initial stage and are less likely to be irrevocably led astray by chance (Lambert & Dale 1964; Dale 1964; Lambert & Williams 1966; Williams 1971). Polythetic methods use the available information at each step more fully than monothetic ones; the latter often 'misclassify'. Thus methods which are both divisive and polythetic should theoretically be optimal (Williams 1971). However, only few methods of this type have so far been suggested, and these are computationally rather demanding (MacnaughtonSmith et al. 1964; Edwards & Cavalli-Sforza 1965; Wallace & Boulton 1968; Boulton & Wallace 1970). A simple mechanism for obtaining a divisive polythetic classification of vegetation data is through ordination by principal components analysis. This extracts the set of generalized variables which account for most of the variation in the data; each variable is a weighted sum of species (or site) scores, hence an 'optimized polythetic' entity. A division of the elements (sites, species) according to their values (scores, loadings) on these components is thus a divisive polythetic classification. This procedure was considered in principle by Goodall (1954) and by Dale (1964) but was not fully implemented*. In particular the problem of choosing the division point on each component axis was not solved. This paper examines this and some other problems in the application of this approach to the classification of vegetation, based on both theoretical considerations and on experiments with three sets of vegetation data. (a) The semi-arid vegetation of southeastern Australia: 193 sites (Noy-Meir 1970, 1971); presence and cover data. (b) The montane tropical forest of Mt Wilhelm, New Guinea: thirty-three sites (Wade 1968); presence data.