Commentary on Bayer's use of incomplete data matrices and weighted qualitative characters in phenetic studies of North American Antennaria: Commentary

Abstract

Listen

Translate article

Bayer (1987) recognized eight sexual species of Antennaria, A. arornatica Evert, A. corymbosa E., Nels., A. marginata E. L. Greene, A. media E. L. Greene, A. microphylla Rydb., A. racemosa Hook., A. rosulata Rydb., and A. umbrinella Rydb., on the basis of morphometric analysis. We agree that the eight sexual species are morphologically distinct and recognizable (they are generally treated as such), but we disagree with the contention that the species are well defined morphologically by the results obtained from multivariate analysis, specifically, principal components analysis. We contest the analyses of the basic data matrix and submatrices by principal components analysis because the data was (i) known to consist of distinct entities, (ii) for hypothetical OTUs, (iii) incomplete, (iv) both ordinal and nominal, and (v) weighted. Bayer (1987) assumed that principal components analysis was the most appropriate multivariate test for analyzing morphological similarities and differences among the western North American sexual species of Antennaria. We contend that principal components analysis was not the most appropriate multivariate test for this purpose because it is most suitable for the analysis of structure utilizing multivariate observations when no a priori patterns of interrelationships can be discerned (Blackith and Reyment 1971). In truth, any such analysis involves a priori limitation of morphological variation and of potential groups. By selecting 16 specimens of each taxon, except A. arornatica and A. racemosa, Bayer (1987) defined eight groups (species) prior to analysis. Having defined these groups a priori. the data may have been more appropriately analyzed with canonical analysis that maximizes intergroup distances, thereby confirming the a priori groups. In any case, principal components analysis may be an unsatisfactory analytical technique to apply if missing data or qualitative character states are included in the data matrix (Pimentel 1979). The basic data matrix analyzed by Bayer (1987) included qualitative data of the nominal type and was incomplete. Considering these limitations, a more appropriate method of analysis for the purpose of ordination may have been principal coordinate analysis. Although these analytical techniques are similar, the two methods differ in that principal components analysis extracts eigenvalues and eigenvectors from a dispersion matrix of variables or individuals, whereas principal coordinate analysis extracts eigenvalues and eigenvectors from an association matrix of individuals (Gower 1966; Digby