Distance-based multivariate analyses confound location and dispersion effects

A critical property of count data is its mean-variance relationship, yet this is rarely considered in multivariate analysis in ecology. 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. 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. 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. 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. © 2011 The Authors. Methods in Ecology and Evolution © 2011 British Ecological Society