Functional diversity through the mean trait dissimilarity: resolving shortcomings with existing paradigms and algorithms
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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.
KeywordsAssembly rules Biodiversity indices Community Phylogenetic diversity Trait variance
The study was financed by the Grant Agency of the Czech Republic (P505/12/1296, 13-17118S), the long-term research development project no. RVO 67985939, the CGL2014-53789-R project (Spanish MINECO), the Estonian Research Council (ETF 8613), the Estonian Ministry of Education and Research (IUT 20-29), and the European Regional Development Fund (Center of Excellence FIBIR). CPC was supported by a Marie Curie Intra-European Fellowship within the 7th European Community Framework Programme (TANDEM; project id. 626392). We are grateful to Fernando Valladares and Adrián Escudero for their editorial work on this manuscript and to Olivier Hardy, two anonymous reviewers, and Pille Gerhold for discussions of these indices.
Author contribution statement
All authors conceived the ideas and wrote the manuscript; CPC wrote the R code and the help file for the function “melodic.”
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