Functional and phylogenetic β diversities and their link with clustering/overdispersion and uniqueness/redundancy

In recent decades, research on biodiversity in community ecology has been marked by the consideration of species' evolutionary histories and functional traits. Among the different spatial levels at which functional or phylogenetic (hereafter FP) diversity can be quantified, the definition of the general concept of between-community (β) diversity has been given less attention than that of local, within-community (α) and regional, merged-community (γ) diversities. Here, we develop a new method for partitioning FP β diversity into elementary components to determine how and why FP β diversity differs from species β diversity, with the latter reflecting only differences in species' abundances between communities. As a reference example, we consider two distinct measures of FP β diversity: Rao's dissimilarity coefficient (Q_β), which expresses the average FP dissimilarity between communities, and its transformation (E_β), which expresses the effective number of distinct communities. Through analytical partitioning and simulations, we show that Q_β and E_β are connected differently to typical patterns of community structure. The search for the ecological and evolutionary processes that drive community assembly and the assessment of community resilience and stability have indeed revealed typical community structures: the local clustering of species with similar traits or shared evolutionary histories and the local (α) or regional (γ) presence of functionally or phylogenetically redundant versus unique species. We show that while Q_β and E_β are both increasing functions of species β diversity and FP γ uniqueness, Q_β increases with FP clustering, while E_β increases with FP α redundancy. We also show that the component of FP clustering included in Q_β partitioning formula allows the detection of an overall trend of overdispersion or clustering in a dataset without the need to use null models. To facilitate and secure the selection of an index of β diversity for a given study, we call, through our study, for the development of formal and precise definitions for FP β diversity in light of the concepts of clustering versus overdispersion and redundancy versus uniqueness. In particular, we call for further research on when and why FP β diversity should increase with FP clustering.