Analysis of similarities (ANOSIM) for 2-way layouts using a generalised ANOSIM statistic, with comparative notes on Permutational Multivariate Analysis of Variance (PERMANOVA)

Abstract

ANOSIM (Analysis of Similarities) is a robust non-parametric hypothesis testing framework for differences in resemblances among groups of samples. The generalised ANOSIM statistic RO is defined as the slope of the linear regression of ranked resemblances from observations against ranked distances in a model describing the unordered or ordered distances among samples under an alternative to the null hypothesis. In the absence of ordering, this becomes the standard ANOSIM R statistic. The construction of 2-way tests using the generalised statistic in various nested and crossed designs, with and without ordered factors, and with or without replication, is described. Examples are given of 2-way tests with ordered factors in marine ecological studies: 1. phytal meiofaunal communities in species of macroalgae with increasing physical complexity, among islands in the Isles of Scilly; 2. coral community composition across intertidal flats in Thailand, sampled in different years; 3. macrofauna inhabiting kelp holdfasts from different places in response to an oil spill; 4. experimental effects of salinity stress and food restriction on nematode communities. ANOSIM is fully non-parametric and thus cannot, for two-way crossed designs, decompose factors into (metric-based) main effects and interactions; this requires at least semi-parametric modelling, such as provided by PERMANOVA. The two approaches therefore test very different hypotheses: ANOSIM gives a robust, comparable and globally interpretable measure of magnitude of overall community change associated with each factor, having excised any possible effect from the factor(s) it is crossed with, irrespective of whether the factors interact or not. PERMANOVA cannot do this because the presence of interactions will compromise (sometimes totally) any overall measures of the main effects of each factor. Conversely, PERMANOVA can test for interactions involving directional (but non-magnitudinal) community change, which are entirely invisible to ANOSIM. The two methods are therefore seen as complementary, rather than as alternatives.