Similarity-based testing for community pattern: the two-way layout with no replication
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The large, sparse arrays of species counts arising in both field and experimental community studies do not lend themselves to standard statistical tests based on multivariate normality. Instead, a valid and more revealing approach uses informal display methods, such as clustering or multi-dimensional scaling ordination (MDS), based on a biologically-motivated definition of pairwise similarity of samples in terms of species composition. Formal testing methods are still required, however, to establish that real assemblage differences exist between sites, times, experimental treatments, pollution states, etc. Earlier work has described a range of Manteltype permutation or randomisation procedures, making no distributional assumptions, which are termed ANOSIM tests because of their dependence only on (rank) similarities and the analogy to one and two-way ANOVA. This paper extends these tests to cover an important practical case, previously unconsidered, that of a two-way layoutwithout replication. Such cases arise for single samples (or pseudo-replicates) taken in a baseline monitoring survey of several sites over time, or a mesocosm experiment in which “treatments” are replicated only once within each experimental “block”. Significance tests are given for the overall presence of a treatment (or time) effect, based on a measure of concordance between rank similarities of samples within each block (or site); the role of the two factors can be reversed to obtain a test for block effects. As in the analogous univariate ANOVA test, the method relies on absence or relative weakness of treatment x block “interactions”. Its scope is illustrated with data from two experimental and two field studies, involving meiofaunal communities from soft-sediment and macro-algal habitats. It is seen also to accommodate a modest derree of missing data. Whilst the failure to replicate adequately is not encouraged—a richer inference is available with genuine replication—the paper does provide a limited way forward for hypothesis testing in the absence of replicates.
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