Multidimensional scaling as a research tool in Quaternary palynology: A review of theory and methods

Multidimensional scaling (MDS) methods include principal components analysis (PCA), principal co-ordinates analysis (PCO), canonical variates analysis (CVA) and non-metric MDS. All these can be used for comparing levels within and between pollen diagrams, for ordination of modern pollen spectra, or for comparing modern with fossil pollen spectra. All exist in numerous variants, depending on a choice of dissimilarity coefficient (DC) (except CVA, which is a specialized technique for use when prior groupings are available). It is shown that the many methods and variants that have been applied to pollen data can nevertheless be understood within a single conceptual frame. Guidelines for choice are established. PCA is shown to have several practical advantages over competitors, but it is suggested that MDS may sometimes be more informative with wide-ranging data sets. PCO allows a wider choice of DCs than PCA but is less convenient in other ways. DCs are categorized according to their meaning in a specifically palynological context. The most useful may be either the simplest (e.g. Manhattan metric, Euclidean distance), or some more complex measures designed to maximize "signal" contribution as against statistical "noise": CVA implies one such measure (Mahalanobis' D²). Standardization in PCA is shown to have drawbacks, and there are plausible alternatives. Correlation coefficients are found unsuitable for comparing pollen spectra. Emphasis throughout is on concepts and assumptions in MDS. The sections covering DCs are also relevant to other applications, including cluster analysis and numerical zonation.