Rao's quadratic entropy as a measure of functional diversity based on multiple traits

Abstract Question: Is Rao's quadratic entropy a suitable measure of functional diversity if several traits are considered? Methods: It is checked whether Rao's quadratic entropy (FDQ) satisfies a priori criteria suggested by Mason et al. A real data set is used to show that there are often zeros in abundance distributions which maximize functional diversity. Results and Conclusion: FDQ fulfils all a priori criteria and it surpasses other proposed indices, because it includes species abundances and more than one trait. Therefore, it seems to be an improvement compared to measures of functional diversity that are currently available. An unexpected property of FDQ is that its value may decrease if species richness increases. The reason is that functional diversity is influenced by both species-abundance based diversity and differences among species. Introduction of a new species into the community increases the species-abundance based diversity, while it may decrease the average dissimilarity among species.