Decomposing functional diversity

1. One aspect of biodiversity, functional diversity, reflects the functional role of species within a community as measured by species characteristics. We present a new metric, functional trait dispersion, based on the concept of species distinctiveness measured as the distance among species in the multidimensional space defined by trait values. This metric can be decomposed into components of species richness, functional evenness and mean dispersion, and into parts that measure diversity within and among subgroups. 2. Using an appropriate distance measure, mean dispersion (M') is calculated as the average distance among all possible pairs of species. Functional evenness [E-q(T)] is derived from Hill diversity based on the proportional distances between pairs of species and species richness (S). Functional trait dispersion [D-q(TM)] is then computed as 1 + (S-1) x E-q(T) x M'. It has a range of [1, S] and measures the effective number of functionally distinct species for a given level of species dispersion. 3. Using constructed data, we demonstrate that D-q(TM) captures appropriate ecological properties such that a community with greater species richness, greater dispersal in trait space or greater mean dispersion has greater functional diversity. Functional trait dispersion can also provide measures of within-community dispersion and the effective number of functionally distinctive compartments (groups of communities with similar functional structure). Using empirical data of bats along an elevational gradient in Peru, we demonstrate that functional trait dispersion and its components provide insights about gradients of biodiversity. 4. Functional trait dispersion comports to reasonable criteria for a metric of functional diversity and can be decomposed in a variety of ways that facilitate understanding of patterns of variation. Other metrics of functional diversity neither integrate all three diversity components, nor can many be decomposed into variation within and among subgroups. Because functional trait dispersion measures properties of distance and the effective number of functionally distinct species, it can be used in conjunction with other biodiversity metrics that are based on species identity, abundance or phylogenetic relatedness to inform management and the preservation of biodiversity.