While an increasing number of indices for estimating the functional trait diversity of biological communities are being proposed, there is a growing demand by ecologists to clarify their actual implications and simplify index selection. Several key indices relate to mean trait dissimilarity between species within biological communities. Among them, the most widely used include (a) the mean species pairwise dissimilarity (MPD) and (b) the Rao quadratic entropy (and related indices). These indices are often regarded as redundant and promote the unsubstantiated yet widely held view that Rao is a form of MPD. Worryingly, existing R functions also do not always simplify the use and differentiation of these indices. In this paper, we show various distinctions between these two indices that warrant mathematical and biological consideration. We start by showing an existing form of MPD that considers species abundances and is different from Rao both mathematically and conceptually. We then show that the mathematical relationship between MPD and Rao can be presented simply as Rao = MPD × Simpson, where the Simpson diversity index is defined as 1 - dominance. We further show that this relationship is maintained for both species abundances and presence/absence. This evidence dismantles the paradigm that the Rao diversity is an abundance-weighted form of MPD and indicates that both indices can differ substantially at low species diversities. We discuss the different interpretations of trait diversity patterns in biological communities provided by Rao and MPD and then provide a simple R function, called "melodic," which avoids the unintended results that arise from existing mainstream functions.

Department of Botany Faculty of Science University of South Bohemia Branišovská 31 370 05 České Budějovice Czech Republic

Institute of Botany Czech Academy of Sciences 379 82 Třeboň Czech Republic

Institute of Ecology and Earth Sciences University of Tartu Lai 40 51005 Tartu Estonia

Institute of Entomology Biology Centre of Czech Academy of Science 370 05 České Budějovice Czech Republic

Terrestrial Ecology Group Department of Ecology Autonomous University of Madrid 28049 Madrid Spain

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