From dissimilarities among species to dissimilarities among communities: a double principal coordinate analysis.

This paper presents a new ordination method to compare several communities containing species that differ according to their taxonomic, morphological or biological features. The objective is first to find dissimilarities among communities from the knowledge about differences among their species, and second to describe these dissimilarities with regard to the feature diversity within communities. In 1986, Rao initiated a general framework for analysing the extent of the diversity. He defined a diversity coefficient called quadratic entropy and a dissimilarity coefficient and proposed a decomposition of this diversity coefficient in a way similar to ANOVA. Furthermore, Gower and Legendre (1986) built a weighted principal coordinate analysis. Using the previous context, we propose a new method called the double principal coordinate analysis (DPCoA) to analyse the relation between two kinds of data. The first contains differences among species (dissimilarity matrix); the second the species distribution among communities (abundance or presence/absence matrix). A multidimensional space assembling the species points and the community points is built. The species points define the original differences between species and the community points define the deduced differences between communities. Furthermore, this multidimensional space is linked with the diversity decomposition into between-community and within-community diversities. One looks for axes that provide a graphical ordination of the communities and project the species onto them. An illustration is proposed comparing bird communities which live in different areas under mediterranean bioclimates. Compared to some existing methods, the double principal coordinate analysis can provide a typology of communities taking account of an abundance matrix and can include dissimilarities among species. Finally, we show that such an approach generalizes some of these methods and allows us to develop new analyses.