Ecological patterns in multivariate assemblages: information and interpretation of negative values in ANOSIM tests

Analysis of similarities (ANOSIM) has been widely used for testing hypothes es about spatial differences and temporal changes in assemblages and partic ularly for detecting environmental impacts. ANOSIM generates a value of R w hich is scaled to lie;between -1 and +1, a value of zero representing the n ull hypothesis. Generally, R lies between zero and +1. Values much smaller than zero have been considered unlikely because they would indicate greater dissimilarity among replicate units within samples than occurs between sam ples. Nevertheless, in some habitats, frequent and large negative values of R are common. In this paper, assemblages that consistently gave negative R values when analysed using ANOSIM were examined to identify patterns of di fferences among replicates within and between samples to test the hypothesi s that particular patterns of differences generated consistent negative R v alues. The hypothesised patterns were then tested by analysing simple assem blages generated by computer simulation and examining the frequencies of R values. In natural assemblages, negative R values were found when assemblag es were very patchy so that replicates were variable, but each sample had s imilar amounts of variability among replicates. Large negative values of R were par particularly common when either or both samples contained an outli er, or when the assemblage being sampled had 2 different states and the rep licates had sampled each of these states. Negative values of R may therefor e indicate the need for stratification of the sampling design, or problems of positive correlation between the different sets of samples. When negativ e values occur, they should not simply be ignored as anomalies. In fact, th ey identify important ecological information and identify issues about the design of sampling.