On the functional diversity of partially distinct species: some theory and a practical example

Due to its nonlinearity with respect to species addition, some applications of the Rao quadratic diversity are meaningful only if they are first transformed into their equivalent number of species, which is the theoretical species richness of a maximally distinct and perfectly even community with the same diversity as the original community. In this paper, relaxing the requirement of maximal distinction among species, we generalize the notion of the equivalent number of species for the Rao diversity to partially distinct species. The biological meaning of this proposal is illustrated with one dedicated case study in sand dune communities in Italy. According to our results, the proposed approach proved appropriate for comparing the functional diversity of different plant communities with varying levels of environmental constraints.