, Volume 180, Issue 4, pp 933–940 | Cite as

Functional diversity through the mean trait dissimilarity: resolving shortcomings with existing paradigms and algorithms

  • Francesco de Bello
  • Carlos P. Carmona
  • Jan Lepš
  • Robert Szava-Kovats
  • Meelis Pärtel
Special Topic on Functional Traits


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.


Assembly 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.”

Supplementary material

442_2016_3546_MOESM1_ESM.pdf (148 kb)
Supplementary material 1 (PDF 147 kb)
442_2016_3546_MOESM2_ESM.docx (802 kb)
Supplementary material 2 (DOCX 893 kb)
442_2016_3546_MOESM3_ESM.r (3 kb)
Supplementary material 3 (R 4 kb)
442_2016_3546_MOESM4_ESM.r (4 kb)
Supplementary material 4 (R 4 kb)


  1. Bermudez R, Retuerto R (2014) Together but different: co-occurring dune plant species differ in their water- and nitrogen-use strategies. Oecologia 174:651–663CrossRefPubMedGoogle Scholar
  2. Botta-Dukat Z (2005) Rao’s quadratic entropy as a measure of functional diversity based on multiple traits. J Veg Sci 16:533–540CrossRefGoogle Scholar
  3. Clarke KR, Warwick RM (1998) A taxonomic distinctness index and its statistical properties. J Appl Ecol 35:523–531CrossRefGoogle Scholar
  4. de Bello F, Lavorel S, Albert CH, Thuiller W, Grigulis K, Dolezal J, Janecek S, Lepš J (2011) Quantifying the relevance of intraspecific trait variability for functional diversity. Methods Ecol Evol 2:163–174CrossRefGoogle Scholar
  5. de Bello F, Price JN, Muenkemueller T, Liira J, Zobel M, Thuiller W, Gerhold P, Goetzenberger L, Lavergne S, Lepš J, Zobel K, Pärtel M (2012) Functional species pool framework to test for biotic effects on community assembly. Ecology 93:2263–2273CrossRefPubMedGoogle Scholar
  6. Desrochers R, Anand M (2004) From traditional diversity indices to taxonomic diversity indices. Int J Ecol Environ Sci 30:85–92Google Scholar
  7. Gerhold P, Price JN, Püssa K, Kalamees R, Aher K, Kaasik A, Pärtel M (2013) Functional and phylogenetic community assembly linked to changes in species diversity in a long-term resource manipulation experiment. J Veg Sci 24:843–852CrossRefGoogle Scholar
  8. Hill MO (1973) Diversity and evenness—unifying notions and its consequences. Ecology 54:427–432CrossRefGoogle Scholar
  9. Laliberte E, Legendre P (2010) A distance-based framework for measuring functional diversity from multiple traits. Ecology 91:299–305CrossRefPubMedGoogle Scholar
  10. MacArthur R, Levins R (1967) Limiting similarity convergence and divergence of coexisting species. Am Nat 101:377–385CrossRefGoogle Scholar
  11. Miklos I, Podani J (2004) Randomization of presence-absence matrices: comments and new algorithms. Ecology 85:86–92CrossRefGoogle Scholar
  12. Miller ET, Zanne AE, Ricklefs RE (2013) Niche conservatism constrains Australian honeyeater assemblages in stressful environments. Ecol Lett 16:1186–1194CrossRefPubMedGoogle Scholar
  13. O’Gorman EJ, Yearsley JM, Crowe TP, Emmerson MC, Jacob U, Petchey KJ (2010) Loss of functionally unique species may gradually undermine ecosystems. Proc R Soc B 278:1886–1893CrossRefPubMedPubMedCentralGoogle Scholar
  14. Pavoine S, Bonsall MB (2011) Measuring biodiversity to explain community assembly: a unified approach. Biol Rev 86:792–812CrossRefPubMedGoogle Scholar
  15. Pavoine S, Vallet J, Dufour AB, Gachet S, Daniel H (2009) On the challenge of treating various types of variables: application for improving the measurement of functional diversity. Oikos 118:391–402CrossRefGoogle Scholar
  16. Rao CR (1982) Diversity and dissimilarity coefficients—a unified approach. Theor Popul Biol 21:24–43CrossRefGoogle Scholar
  17. Ricklefs RE, Schluter D (1993) Diversity in ecological communities: historical and geographical perspectives. University of Chicago Press, Chicago, p 414Google Scholar
  18. Ricotta C, Moretti M (2011) CWM and Rao’s quadratic diversity: a unified framework for functional ecology. Oecologia 167:181–188CrossRefPubMedGoogle Scholar
  19. Shimatani K (2001) On the measurement of species diversity incorporating species differences. Oikos 93:135–147CrossRefGoogle Scholar
  20. Schleuter D, Daufresne M, Massol F, Argillier C (2010) A user’s guide to functional diversity indices. Ecol Monogr 80:469–484CrossRefGoogle Scholar
  21. Swenson NG (2014) Functional and phylogentic ecology in R. Springer, New YorkCrossRefGoogle Scholar
  22. Villeger S, Mason NWH, Mouillot D (2008) New multidimensional functional diversity indices for a multifaceted framework in functional ecology. Ecology 89:2290–2301CrossRefPubMedGoogle Scholar
  23. Webb CO, Ackerly DD, McPeek MA, Donoghue MJ (2002) Phylogenies and community ecology. Annu Rev Ecol Syst 33:475–505CrossRefGoogle Scholar
  24. Weiher E, Keddy PA (1995) The assembly of experimental wetland plant communities. Oikos 73:323–335Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Francesco de Bello
    • 1
    • 2
  • Carlos P. Carmona
    • 1
    • 3
  • Jan Lepš
    • 1
    • 4
  • Robert Szava-Kovats
    • 5
  • Meelis Pärtel
    • 5
  1. 1.Department of Botany, Faculty of ScienceUniversity of South BohemiaČeské BudějoviceCzech Republic
  2. 2.Institute of Botany, Czech Academy of SciencesTřeboňCzech Republic
  3. 3.Terrestrial Ecology Group, Department of EcologyAutonomous University of MadridMadridSpain
  4. 4.Institute of Entomology, Biology Centre of Czech Academy of ScienceČeské BudějoviceCzech Republic
  5. 5.Institute of Ecology and Earth SciencesUniversity of TartuTartuEstonia

Personalised recommendations