Theoretical Considerations on the Covariation of Plant Species Along Ecological Gradients with Regard to Multivariate Analysis

Abstract

The objective of multivariate analysis (principal component analysis, cluster analysis and related methods) of vegetation data is to simplify and order the data so that the resulting model shows the relationships among the species and also reflects the relationships between vegetational and habitat variation. A distinction has to be made between a purely phytosociological ordering and an ecological ordering that reflects habitat relationships. The latter type is of most interest to the ecologist. A purely phytosociological ordering would be less difficult to obtain, but it would be only descriptive and would have little or no ecological value. Systems analysis appears to be the only really satisfactory approach to a solution of this problem. The methods are available but the system of relationships is often so complex that it is questionable whether the results will justify the efforts except in the simplest of vegetation types. Thus, it is to be expected that, in the foreseeable future, vegetation analysis by multivariate statistical methods will still serve a real purpose in advancing our insight into vegetation and habitat relationships. Until now, most multivariate methods used for the analysis of vegetation data were based on linearity or monotonicity of the relationships among species, and between species and environmental gradients. From gradient analysis (Whittaker 1956, 1967) and physiological research, the gradient response curves are known often to be bell-shaped and thus, in the test-space used for the analysis, the species relationship curves that are closely related to the environmental or time gradients become very complicated (van Groenewoud 1965; Noy-Meir & Austin 1970; Swan 1970; Austin & Noy-Meir 1971; Gauch & Whittaker 1972a, b). With the foregoing in mind, attempts have been made to improve the multivariate statistical analysis of vegetation data by studying hypothetical models and by comparing graphic models based on hypothetical data with real situations. To obtain an ecologically meaningful order, the choice of parameters expressing either relationships among species or similarities (or distances) among vegetation subsamples is of paramount importance. If the parameter based on phytosociological data does not reflect ecological relationships the subsequent analysis loses much value from an ecological viewpoint. Recently Swan (1970), Noy-Meir & Austin (1970), Austin & Noy-Meir (1971) and Gauch & Whittaker (1972a, b) published results of the multivariate analysis of hypothetical curvilinear distributions along single and multiple gradients. It was shown that the results were not rectilinearly or monotonically related to the original gradient. It