‘Size’ and ‘shape’ in the measurement of multivariate proximity

摘要: Summary Ordination and clustering methods are widely applied to ecological data that non-negative, for example, species abundances or biomasses. These rely on a measure of multivariate proximity quantifies differences between the sampling units (e.g. individuals, stations, time points), leading results such as: (i) ordinations units, where interpoint distances optimally display measured differences; (ii) into homogeneous clusters (iii) assessing pre-specified groups regions, periods, treatment–control groups). These all conceal fundamental question: To what extent computed according chosen function, capturing ‘size’ in observations, their ‘shape’? ‘Size’ means overall level measurements: some samples contain higher total more biomass, others less. ‘Shape’ relative levels have different abundances, i.e. compositions. answer this question, several well-known measures considered two datasets, one which is used simulation exercise ‘shape’ been eliminated by randomization. For any dataset measure, quantification achieved proportion variance capturing, as well confounds together. The consistently show Bray–Curtis coefficient incorporates both differences, varying degrees. components thus always confounded determination ordinations, clusters, group comparisons relations environmental variables. There implications these results, main being researchers should be aware issue when they choose measure. They compute particular can radically affect interpretation results. It recommended separate components: analysing other univariate methods, using analysis size has specifically excluded.