Squared Euclidean distance: a statistical test to evaluate plant community change

Abstract

The concepts and a procedure for evaluating plant community change using the squared Euclidean distance (SED) resemblance function are described. Analyses are based on the concept that Euclidean distances constitute a sample from a population of distances between sampling units (SUs) for a specific number of times and SUs. With different times, the distances will be intracluster or intercluster. Intercluster distances represent a control treatment. If the communities differ between times, the population will contain clusters (regions of high density with short distances between SUs) that are separated by regions of low density (great distances between SUs). Within- and between-years mean squares from analyses of variance for each species (sp) in the data matrix can be used to compute the intracluster and intercluster mean distances. A multivariate ANOV A gives a test of the hypothesis that the intracluster mean distance is equal to the intercluster mean distance at an overall error rate approximately equal to ex. The statistical distribution of SEDs is the distribution of a linear combination of independent Chi-square random variables. Knowledge of this distribution and use of the usual approximations make the estimation of approximate confidence intervals for the mean intercluster and intracluster distances and their difference possible and reliable. The confidence intervals may be examined and a decision made regarding any indicated change in the community. A simple example is provided to permit study of computational methods.