Factors Affecting the Power and Validity of Randomization-Based Multivariate Tests for Difference among Ecological Assemblages

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Catterall, Carla
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Chaseling, Janet
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Ecologists often want to determine whether there is a difference between the assemblage occupying one habitat, and that in another. While a number of studies have compared a variety of the multivariate techniques used in community ecology, few have considered the ability of different inferential multivariate techniques to detect differences among ecological assemblages. Those that have considered differences among various techniques have focused on model properties, giving little attention to the comparative power of such techniques when applied to ecological datasets. The primary aim of this study was to determine under what conditions different multivariate tests for difference succeed in detecting differences among ecological assemblages, and which conditions do they fail. The focus in this study was on the power of the various tests for difference between assemblages represented by raw species abundance counts, for small to moderate sample sizes. A possible explanation for the limited knowledge about the appropriateness of different tests for difference is the lack of a statistical framework for comparing multivariate tests. One of the problems in the power analysis of tests for comparing ecological assemblages arises from the difficulties in generating the ecologically realistic replicate datasets needed for such a comparison. The number of ways samples may differ in ecological assemblages datasets presents further complications. For example, a multivariate test might be powerful in detecting one type of ecological difference while being relatively insensitive to another type. There are a number of types of ecological difference that studies of ecological assemblages may address. These include: (1) species richness, the number of species occurring in each assemblage; (2) total abundance, the number of individuals (irrespective of species) that occur in each assemblage; (3) species composition, the actual species observed and their relative abundance; (4) the distribution of individuals of a species (or all individuals) across within-assemblage sites; and (5) the distribution of individuals among species. Two simulation methods capable of generating realistic multi- assemblage datasets portraying different levels and types of ecological difference among component assemblages are presented here. This study demonstrates that the empirically calibrated coenocline simulation method is capable of generating realistic artificial ecological datasets portraying simultaneous species richness, total abundance and compositional differences among assemblages. The resampling simulation method, another empirical method, was shown to be able to generate artificial multi- assemblage datasets where assemblages vary compositionally, while other types of ecological difference are held constant. This study compared five multivariate techniques used to tests for difference among ecological assemblages: (1) Parametric MANOVA; (2) CAP, a randomization-based canonical ordination test for difference; and (3) ANOSIM; (4) MRPP; and (5) NP-MANOVA, three variants of Mantel's randomization-based multivariate tests for difference. In the ecological conditions encompassed in this study, CAP was shown to be the most powerful test for compositional difference among assemblages, and ANOSIM, MRPP and NP-MANOVA were more powerful when other types of ecological difference (such as species richness and total abundance differences) were also present. There was little difference in the power of ANOSIM, MRPP and NP-MANOVA under any situation. Parametric MANOVA exhibited very low power in all of the situations encompassed in the power analysis. Another factor shown to affect the power of a multivariate test for difference is the dissimilarity coefficient on which a test is based, whether this dissimilarity forms an implicit part of the test, or is left to the choice of the researcher (for tests that allows such a choice of dissimilarity coefficient). In this study the power of the four randomization tests (CAP, ANOSIM, MRPP and NP- MANOVA), which allow a choice of dissimilarity coefficient, were compared for the Bray-Curtis, Chi-Square and Euclidean dissimilarity coefficients. Both the Bray-Curtis and the Chi-square dissimilarity coefficients resulted in the most powerful tests, with the more powerful of the two varying with the test for difference under consideration, and/or the type of between assemblage-difference (compositional or general) contained in the dataset. For example, MRPP used in conjunction with the Bray-Curtis dissimilarity coefficient was the most powerful for detecting general differences among assemblages (the type of between-assemblage variation contained in coenocline-generated assemblages), whereas the same test using the Chi- square dissimilarity was more powerful when differences among assemblages were purely compositional (as in resampling simulations). The Euclidean dissimilarity measure almost always resulted in the least power, and never the most power, when used in conjunction with the multivariate tests for difference in realistic ecological assemblage data as represented by raw abundance counts. CAP was shown to be the least sensitive to dissimilarity coefficient choice. The current study has shown a number of the strengths and weaknesses of the tests considered. However, the wide range of ecological situations, and the complexities underlying ecological assemblages, means a lot more work needs to be done before there is a clearer understanding of the relationship between ecological data and appropriateness of multivariate tests. The protocols developed in this study provide a framework for assessing the ability of different multivariate tests for difference and other multivariate techniques used in the analysis of ecological assemblage data.

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Thesis (PhD Doctorate)
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Doctor of Philosophy (PhD)
School of Australian Environmental Studies
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Ecological assemblages
Parametric MANOVA
Dissimilarity coefficients
Species abundance counts
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