An ordination approach to explore similarities among communities

Analysis of similarities among communities can help to decipher the biogeographical, evolutionary, and ecological factors that drive local diversity. Recent indices of similarity among communities incorporate not only information on species presence and abundance but also information on how similar species are in their traits and how closely related they are in terms of taxonomy or phylogeny. Towards this aim, trait-based, taxonomic or phylogenetic similarities among species have been defined and bounded between 0 (species are maximally distinct) and 1 (species are similar). A required property for an index of similarity between two communities is that it must provide minimum similarity (0) where communities have maximally distinct species, as well as maximum similarity (1) where communities are equivalent in their trait, taxonomic or phylogenetic compositions. Here, I developed a new ordination methodology that conforms to the requirement: double similarity principal component analysis (DSPCA). DSPCA summarizes multidimensional trait-based, taxonomic or phylogenetic similarities among communities into orthogonal axes. The species that drive each similarity pattern can be identified together with their traits or with their taxonomic or phylogenetic positions. I applied this methodology to theoretical examples and to empirical data sets on bird and bat communities to illustrate key properties of DSPCA. I compared the results obtained with DSPCA with those provided by related approaches. Theoretical and empirical case studies highlight the following additional properties of DSPCA: (i) axes are orthogonal and identify independent (dis)similarity patterns between communities; (ii) the more functionally, taxonomically or phylogenetically similar communities are, the closer they are on an axis; (iii) the coordinate of a species on an axis expresses how representative the species is of the pattern identified by the axis; and (iv) a species is representative of x communities if the functional, taxonomic or phylogenetic characteristics of this species are very common within each of these x communities. DSPCA is an efficient approach to visualize functional, taxonomic and phylogenetic similarities between communities. It is also a useful alternative to recent methods dedicated to phylogenetic diversity patterns. It will be an asset for all studies that aim to compare functional, taxonomic, genetic and phylogenetic diversity.