Access the full text.
Sign up today, get DeepDyve free for 14 days.
Lepš (2006)
Quantifying and interpreting functional diversity of natural communitiesPreslia, 78
Calyampudi Rao (1982)
Diversity and dissimilarity coefficients: A unified approach☆Theoretical Population Biology, 21
C. Ricotta, L. Szeidl (2009)
Diversity partitioning of Rao's quadratic entropy.Theoretical population biology, 76 4
M. Hill (1973)
Diversity and Evenness: A Unifying Notation and Its ConsequencesEcology, 54
Pavoine Pavoine, Dufur Dufur, Chessel Chessel (2004)
From dissimilarities among species to dissimilarities among communitiesJournal of Theoretical Biology, 228
R. Lande (1996)
Statistics and partitioning of species diversity, and similarity among multiple communitiesOikos, 76
Prinzing Prinzing, Reiffers Reiffers, Braakhekke Braakhekke, Hennekens Hennekens, Tackenberg Tackenberg, Ozinga Ozinga, Schaminee Schaminee, Van Groenendael Van Groenendael (2008)
Less lineages – more trait variationEcology Letters, 11
Patricia Koleff, K. Gaston, J. Lennon (2003)
Measuring beta diversity for presence–absence dataJournal of Animal Ecology, 72
Veech Veech, Summerville Summerville, Crist Crist, Gering Gering (2002)
The additive partitioning of species diversityOikos, 99
L. Jost (2008)
GST and its relatives do not measure differentiationMolecular Ecology, 17
Campbell Webb, M. Donoghue (2005)
Phylomatic: tree assembly for applied phylogeneticsMolecular Ecology Notes, 5
Botta-Dukát (2005)
Rao's quadratic entropy as a measure of functional diversity based on multiple traitsJournal of Vegetation Science, 16
K. Shimatani (2001)
On the measurement of species diversity incorporating species differencesOikos, 93
Webb Webb, Donoghue Donoghue (2005)
PhylomaticMolecular Ecology Notes, 5
I. Hiscock (1970)
Communities and EcosystemsThe Yale Journal of Biology and Medicine, 43
O. Hardy, L. Jost (2008)
Interpreting and estimating measures of community phylogenetic structuringJournal of Ecology, 96
J. Lepš, F. Bello, S. Lavorel, S. Berman (2006)
Quantifying and interpreting functional diversity of natural communities: practical considerations matterPreslia, 78
O. Hardy, Bruno Senterre (2007)
Characterizing the phylogenetic structure of communities by an additive partitioning of phylogenetic diversityJournal of Ecology, 95
Villeger Villeger, Mouillot Mouillot (2008)
Additive partitioning of diversity including species differencesJournal of Ecology, 96
L. Jost, P. DeVries, Thomas Walla, H. Greeney, A. Chao, C. Ricotta (2010)
Partitioning diversity for conservation analysesDiversity and Distributions, 16
D. Ackerly, William Cornwell (2007)
A trait-based approach to community assembly: partitioning of species trait values into within- and among-community components.Ecology letters, 10 2
L. Jost (2006)
Entropy and diversityOikos, 113
A. Solow, S. Polasky (2006)
Measuring biological diversityEnvironmental and Ecological Statistics, 1
P. Legendre, D. Borcard, P. Peres‐Neto (2005)
ANALYZING BETA DIVERSITY: PARTITIONING THE SPATIAL VARIATION OF COMMUNITY COMPOSITION DATAEcological Monographs, 75
T. Crist, J. Veech (2006)
Additive partitioning of rarefaction curves and species-area relationships: unifying alpha-, beta- and gamma-diversity with sample size and habitat area.Ecology letters, 9 8
Z. Botta‐Dukát (2005)
Rao's quadratic entropy as a measure of functional diversity based on multiple traits, 16
Ricotta Ricotta (2005b)
Additive partitioning of Rao's quadratic diversityEcological Modeling, 183
J. Veech, K. Summerville, T. Crist, Jon Gering (2002)
The additive partitioning of species diversity: recent revival of an old ideaOikos, 99
F. Bello, W. Thuiller, J. Lepš, P. Choler, J. Clément, P. Macek, M. Sebastià, S. Lavorel (2009)
Partitioning of functional diversity reveals the scale and extent of trait convergence and divergenceJournal of Vegetation Science, 20
M. Vellend (2001)
Do commonly used indices of β‐diversity measure species turnover?Journal of Vegetation Science, 12
A. Prinzing, R. Reiffers, W. Braakhekke, S. Hennekens, O. Tackenberg, W. Ozinga, J. Schaminée, J. Groenendael (2008)
Less lineages - more trait variation: phylogenetically clustered plant communities are functionally more diverse.Ecology letters, 11 8
T. Crist, J. Veech (2006)
Additive partitioning of rarefaction curves and species–area relationships: unifying α‐, β‐ and γ‐diversity with sample size and habitat areaEcology Letters, 9
S. Villéger, D. Mouillot (2008)
Additive partitioning of diversity including species differences: a comment on Hardy & Senterre (2007)Journal of Ecology, 96
C. Ricotta (2005)
Additive partitioning of Rao's quadratic diversity: a hierarchical approachEcological Modelling, 183
S. Pavoine, A. Dufour, D. Chessel (2004)
From dissimilarities among species to dissimilarities among communities: a double principal coordinate analysis.Journal of theoretical biology, 228 4
L. Jost (2007)
Partitioning diversity into independent alpha and beta components.Ecology, 88 10
C. Ricotta (2005)
A note on functional diversity measuresBasic and Applied Ecology, 6
F. Bello, J. Lepš, S. Lavorel, M. Moretti (2007)
Importance of species abundance for assessment of trait composition: an example based on pollinator communitiesCommunity Ecology, 8
Jay O'Keeffe (2004)
Measuring Biological DiversityAfrican Journal of Aquatic Science, 29
S. Pavoine, S. Ollier, D. Pontier (2005)
Measuring diversity from dissimilarities with Rao's quadratic entropy: are any dissimilarities suitable?Theoretical population biology, 67 4
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.
Journal of Vegetation Science – Wiley
Published: Oct 1, 2010
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.