Distance‐based multivariate analyses confound location and dispersion effects

Abstract

Summary 1.A critical property of count data is its mean-variance relationship, yet this is rarely considered in multivariate analysis in ecology. 2. This study considers what is being implicitly assumed about the mean-variance relationship in distance-based analyses -multivariate analyses based on a matrix of pairwise distances -and what the effect is of any misspecification of the mean-variance relationship. 3. It is shown that distance-based analyses make implicit assumptions that are typically out-of-step with what is observed in real data, which has major consequences. 4. Potential consequences of this mean-variance misspecification are: confounding location and dispersion effects in ordinations; misleading results when trying to identify taxa in which an effect is expressed; failure to detect a multivariate effect unless it is expressed in high-variance taxa. 5. Data transformation does not solve the problem. 6. A solution is to use generalised linear models and their recent multivariate generalisations, which is shown here to have desirable properties.

Spatially Heterogeneous Perturbations Homogenize the Regulation of Insect Herbivores

“…PERMANOVA analyses are more robust than other similar tests (e.g., Mantel) but still tend to confound differences in species composition across treatments (location) versus within-treatment (dispersion) differences in community dissimilarity (Warton et al 2012). In order to separate these two effects, for each significant term from the PERMANOVA, we used a PERMDISP analysis to test for a change in within-treatment variance (Anderson 2001;Anderson and Walsh 2013).…”

The effects of land-use change on the endemic avifauna of Makira, Solomon Islands: endemics avoid monoculture

“…However, as we found no support for 284 seasonal effects (p = 0.19), it was removed from the model (Crawley 2007). A negative binomial 285 error structure was specified in our model, because our count data was over-dispersed (O'Hara and 286 Kotze 2010; Wang et al 2012). Note though that this second modelling approach is simply another 287 way of testing for the effects of habitat type on individual species' density, and the results for each 288 species were very similar to the first presence/absence mixed model approach.…”

“…variation in abundance rather than simply presence/absence) 274 within a relative simple modelling framework that would allow model convergence. We modelled 275 the difference in abundance of each species individually and from this inferred differences in 276 community assemblage between habitat types, using a multivariate generalised linear model on 277 species count data with the mvabund package (Wang et al 2012). Multivariate generalised linear 278 models provide a powerful framework for analysing species abundance data and have been shown 279 to be more robust than distance based methods, such as multidimensional scaling and redundancy 280 analysis (Warton et al 2012).…”

Guidelines to Statistical Analysis of Microbial Composition Data Inferred from Metagenomic Sequencing

“…The methods differ by their approach to the variance comparison: ANOSIM compares ranks of variances similar to Kruskal-Wallis test, while PERMANOVA compares variance values by estimating the significance via a permutation method. A disadvantage of these methods is that they require equal withingroup variances -however, usually this is not the case for metagenomic data (Warton et al, 2012). PERMANOVA was shown to be more robust to the failure of this restriction than ANOSIM (Anderson and Walsh, 2013).…”