PROTEST - A PROCRUSTEAN RANDOMIZATION TEST OF COMMUNITY ENVIRONMENT CONCORDANCE

A multivariate measure of the concordance or association between matri ces of species abundances and environmental variables was generally la cking in ecology until recently. Traditional statistical procedures co mparing such relationships are often unsuitable because of non-lineari ty among species and/or environmental data. To address these problems, I propose a randomization test based on Procrustes analysis. One matr ix is subject to reflection, rigid rotation, translation, and dilation to minimize the sum of the squared residual deviations between points for each observation and the identical observation in the target matr ix. This is a classical Procrustes approach to matrix analysis. To ass ess the significance of this measure of matrix concordance, I use a ra ndomization test to determine whether the sum of residual deviations i s less than that expected by chance. The PROcrustean randomization TES T (PROTEST) may be used with either raw data matrices or with multivar iate summaries of the original data (i.e. both direct or indirect grad ient analysis). I provide examples of PROTEST analyses with benthic in vertebrate communities, lake-water chemistry, lake morphology, and lak e geographic position. Significant concordance between the benthic com munity and both lake-water chemistry and geographic position were foun d. PROTEST results differed from Mantel test results as the choice of distance measure with Mantel tests will influence the level of signifi cance obtained.