The partitioning of diversity: showing Theseus a way out of the labyrinth


  • de Bello, F. (corresponding author,, Lavergne, S. ( & Thuiller, W. ( Laboratoire d'Ecologie Alpine, UMR CNRS 5553, Université Joseph Fourier, 38041, Grenoble Cedex 9, France.
    Meynard, C.N. ( UMR 5554 - ISEM, Université Montpellier II, Place Eugène Bataillon, CC 065, 34095 Montpellier Cedex 5, France.
    Lepš, J. ( Faculty of Science, University of South Bohemia and Institute of Entomology, Biology Centre of ASCR, Branišovská 31, CZ-37005 Ceské Budejovice, Czech Republic.
    de Bello, F.: Present address: Department of Functional Ecology, Institute of Botany, Czech Academy of Sciences, Dukelská 135, CZ-379 82 Třeboň, Czech Republic.

  • Co-ordinating Editor: Dr. Valério Pillar.


A methodology for partitioning of biodiversity into α, β and γ components has long been debated, resulting in different mathematical frameworks. Recently, use of the Rao quadratic entropy index has been advocated since it allows comparison of various facets of diversity (e.g. taxonomic, phylogenetic and functional) within the same mathematical framework. However, if not well implemented, the Rao index can easily yield biologically meaningless results and lead into a mathematical labyrinth. As a practical guideline for ecologists, we present a critical synthesis of diverging implementations of the index in the recent literature and a new extension of the index for measuring β-diversity. First, we detail correct computation of the index that needs to be applied in order not to obtain negative β-diversity values, which are ecologically unacceptable, and elucidate the main approaches to calculate the Rao quadratic entropy at different spatial scales. Then, we emphasize that, similar to other entropy measures, the Rao index often produces lower-than-expected β-diversity values. To solve this, we extend a correction based on equivalent numbers, as proposed by Jost (2007), to the Rao index. We further show that this correction can be applied to additive partitioning of diversity and not only its multiplicative form. These developments around the Rao index open up an exciting avenue to develop an estimator of turnover diversity across different environmental and temporal scales, allowing meaningful comparisons of partitioning across species, phylogenetic and functional diversities within the same mathematical framework. We also propose a set of R functions, based on existing developments, which perform different key computations to apply this framework in biodiversity science.