Parsimony for ecological models of multivariate response data based on dissimilarity matrices

An important challenge in ecology is to analyse and model multivariate ecological data (generally counts of species abundances in a community). The challenges arise primarily because the data tend to have many zeros, the individual variables (counts) tend to have highly skewed distributions and there are also usually many more variables (species) than there are sample units. Thus, traditional statistical approaches are usually inappropriate and dissimilarity-based methods (often coupled with permutation schemes for testing hypotheses) are now being widely used instead (e.g., PRIMER, CANOCO, MRPP, PERMANOVA, etc.). We wish to move forward from a simple hypothesis-testing framework towards methods of model selection. This is especially relevant when environmental variables are being explored in terms of their ability to explain variation in ecological communities. Here, I shall present multivariate dissimilarity-based analogues to some commonly used model selection criteria (such as adjusted R², AIC and BIC). These provide a straightforward solution to the problem of achieving parsimony for multivariate ecological modelling. An analysis that uses combinations of criteria (rather than just one) can also be useful to identify a subset of appropriate models worthy of further study for a given dataset.