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Generalization of the Partitioning of Shannon Diversity

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  • Eric Marcon
  • Ivan Scotti
  • Bruno Hérault
  • Vivien Rossi
  • Gabriel Lang

Abstract

Traditional measures of diversity, namely the number of species as well as Simpson's and Shannon's indices, are particular cases of Tsallis entropy. Entropy decomposition, i.e. decomposing gamma entropy into alpha and beta components, has been previously derived in the literature. We propose a generalization of the additive decomposition of Shannon entropy applied to Tsallis entropy. We obtain a self-contained definition of beta entropy as the information gain brought by the knowledge of each community composition. We propose a correction of the estimation bias allowing to estimate alpha, beta and gamma entropy from the data and eventually convert them into true diversity. We advocate additive decomposition in complement of multiplicative partitioning to allow robust estimation of biodiversity.

Suggested Citation

  • Eric Marcon & Ivan Scotti & Bruno Hérault & Vivien Rossi & Gabriel Lang, 2014. "Generalization of the Partitioning of Shannon Diversity," PLOS ONE, Public Library of Science, vol. 9(3), pages 1-8, March.
    • Handle: RePEc:plo:pone00:0090289
    DOI: 10.1371/journal.pone.0090289
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    References listed on IDEAS

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    1. Tsallis, Constantino & Mendes, RenioS. & Plastino, A.R., 1998. "The role of constraints within generalized nonextensive statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 534-554.
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    Cited by:

    1. Ponta, Linda & Carbone, Anna, 2018. "Information measure for financial time series: Quantifying short-term market heterogeneity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 132-144.
    2. Pietro Murialdo & Linda Ponta & Anna Carbone, 2020. "Long-Range Dependence in Financial Markets: a Moving Average Cluster Entropy Approach," Papers 2004.14736, arXiv.org.
    3. Chai, Yuan & Pardey, Philip G. & Silverstein, Kevin A.T., 2022. "Scientific Selection: A Century of Increasing Crop Varietal Diversity in U.S. Wheat," Staff Papers 320518, University of Minnesota, Department of Applied Economics.

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