The central role of mean-variance relationships in the analysis of multivariate abundance data: a response to Roberts (2017)

The mean-variance relationship is a central property of multivariate abundances – it has been shown that when not accounted for, potentially serious artifacts can be introduced to analyses. One such effect is the confounding of location and dispersion. Roberts (in press) recently argued that mean-variance relationships are not important in understanding properties of distance-based analyses, and that row standardisation fixes the problem of apparent location-dispersion confounding. We use simulation to disprove both statements. In situations where there is a shift in total abundance from one location to the next, the effects of location-dispersion confounding can be considerable. But we also show that even if there is no systematic difference in total abundance between two communities, and no change in dispersion, distance-based analysis may falsely claim that there is a change. We agree that multivariate abundance data are hierarchical, and that it is helpful to study effects at both the species-level and the community level. However, disentangling species-level from community-level effects is not possible without a hierarchical method of analysis. Recently proposed model-based approaches to ordination offer a way forward to resolve the issues discussed here.