A new technique for analysing interacting factors affecting biodiversity patterns: crossed-DPCoA.

We developed an approach for analysing the effects of two crossed factors A and B on the functional, taxonomic or phylogenetic composition of communities. The methodology, known as crossed-DPCoA, defines a space where species, communities and the levels of the two factors are organised as a set of points. In this space, the Euclidean distance between two species-specific points is a measure of the (functional, taxonomic or phylogenetic) dissimilarity. The communities are positioned at the centroid of their constitutive species; and the levels of two factors at the centroid of the communities associated with them. We develop two versions for crossed-DPCoA, the first one moves the levels of factor B to the centre of the space and analyses the axes of highest variance in the coordinates of the levels of factor A. It is related to previous ordination approaches such as partial canonical correspondence analysis and partial non-symmetrical correspondence analysis. The second version projects all points on the orthogonal complement of the space generated by the principal axes of factor B. This second version should be preferred when there is an a priori suspicion that factor A and B are associated. We apply the two versions of crossed-DPCoA to analyse the phylogenetic composition of Central European and Mediterranean bird communities. Applying crossed-DPCoA on bird communities supports the hypothesis that allopatric speciation processes during the Quaternary occurred in open and patchily distributed landscapes, while the lack of geographic barriers to dispersal among forest habitats may explain the homogeneity of forest bird communities over the whole western Palaearctic. Generalizing several ordination analyses commonly used in ecology, crossed-DPCoA provides an approach for analysing the effects of crossed factors on functional, taxonomic and phylogenetic diversity, environmental and geographic structure of species niches, and more broadly the role of genetics on population structures.