Consensus RDA across dissimilarity coefficients for canonical ordination of community composition data

Understanding how habitat structures species assemblages in a community is one of the main goals of community ecology. To relate community patterns to particular factors defining habitat conditions, ecologists often use canonical ordinations such as canonical redundancy analysis (RDA). It is a common practice to use dissimilarity coefficients to perform canonical ordinations through distance-based RDA (db-RDA) or transformation-based RDA (tb-RDA). Dissimilarity coefficients are measures of resemblance where the information about species communities is condensed into a symmetric square matrix of dissimilarities among sites. In this study, we compared 16 of the most commonly used dissimilarity coefficients to evaluate if the species-abundance distribution (SAD) of a community can be used to select an appropriate coefficient. Of these, 11 are designed to be used primarily with abundance data, although they can also be used with presence-absence data, whereas five can only be applied to presence-absence data. Using simulations, we compared the explained variance of RDAs differing only by their coefficients to evaluate how the abundance patterns of communities influence coefficient choice. We found that coefficients are largely equivalent, independently of the community SAD. In light of these findings, we propose the consensus RDA method, a new canonical ordination procedure that performs a consensus of RDAs across several coefficients. This new method focuses on the common relations found by independent RDAs differing only by their dissimilarity coefficients; this ensures the absence of a coefficient-related bias when interpreting the canonical ordination result. Also, because in our simulations the presence-absence data were directly derived from the abundance data, we were able to evaluate if the information in presence-absence data was equivalent to that in abundance data. We found that although some information was lost by converting abundance data into presence-absence, both data formats may be complementary. When applying consensus RDA to abundance and presence-absence data independently, a more complete understanding and interpretation of the ecological patterns is obtained. An ecological example illustrating consensus RDA and the conclusions of our simulations is presented, using Carabidae data collected at the Ecosystem Management Emulating Natural Disturbances (EMEND) project in northwestern Alberta, Canada.