From alpha to beta functional and phylogenetic redundancy

Plot-level redundancy or alpha redundancy is usually defined as the fraction of species diversity not expressed by functional or phylogenetic diversity. Redundancy is zero when all species in one plot are maximally dissimilar from each other. In contrast, redundancy tends to its maximum if the functional or phylogenetic differences between species tend to be minimal.To explore the ecological drivers of community assembly, ecologists also use dissimilarity measures between pairs of plots (a component of beta diversity). Traditional dissimilarity measures summarize compositional differences between pairs of plots based either on species presence and absence data or on species abundances, thus attributing equal distinctiveness between any two species.In the last decades a number of dissimilarity measures which incorporate information on functional or phylogenetic differences among species have been proposed. On the basis of such improved measures, we can define an index of beta redundancy for a pair of plots as the fraction of species dissimilarity not expressed by functional or phylogenetic dissimilarity.A necessary condition to get a meaningful index of beta redundancy is that for a given pair of plots, the functional or phylogenetic dissimilarity is always lower or equal to the corresponding species dissimilarity. However, many of the existing indices of functional or phylogenetic dissimilarity can lead to values greater than for species dissimilarity.The aim of this paper was thus to introduce a new family of tree-based measures of phylogenetic and functional dissimilarity that conform to this requirement. To show the behaviour of the proposed measures, a worked example with data on Alpine vegetation is used.