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

Analysis of smilarities (ANOSIM) has been widely used for testing hypotheses about spatial differences and temporal changes in assemblages and particularly for detecting environmental mpacts. ANOSIM generates a value of R which is scaled to lie between -1 and +l, a value of zero representing the null 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 samples. 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 differences among replicates within and between samples to test the hypothesis that particular patterns of differences generated consistent negative R values. The hypothesised patterns were then tested by analys~ng simple assemblages generated by computer simulation and examining the frequencies of R values. In natural assemblages, negative R values were found when assemblages were very patchy so that replicates were variable, but each sample had similar amounts of variability anlong replicates. Large negative values of R were particularly common when either or both samples contained an outlier, or when the assemblage being sampled had 2 different states and the replicates had sampled each of these states. Negative values of R may therefore indicate the need for stratification of the sampling design, or problems of positive correlation between the different sets of samples. When negative values occur, they should not simply be ignored as anomalies. In fact, they identify important ecological information and identify issues about the design of sampling.