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Distance-Based Functional Diversity Measures and Their Decomposition: A Framework Based on Hill Numbers

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  • Chun-Huo Chiu
  • Anne Chao

Abstract

Hill numbers (or the “effective number of species”) are increasingly used to characterize species diversity of an assemblage. This work extends Hill numbers to incorporate species pairwise functional distances calculated from species traits. We derive a parametric class of functional Hill numbers, which quantify “the effective number of equally abundant and (functionally) equally distinct species” in an assemblage. We also propose a class of mean functional diversity (per species), which quantifies the effective sum of functional distances between a fixed species to all other species. The product of the functional Hill number and the mean functional diversity thus quantifies the (total) functional diversity, i.e., the effective total distance between species of the assemblage. The three measures (functional Hill numbers, mean functional diversity and total functional diversity) quantify different aspects of species trait space, and all are based on species abundance and species pairwise functional distances. When all species are equally distinct, our functional Hill numbers reduce to ordinary Hill numbers. When species abundances are not considered or species are equally abundant, our total functional diversity reduces to the sum of all pairwise distances between species of an assemblage. The functional Hill numbers and the mean functional diversity both satisfy a replication principle, implying the total functional diversity satisfies a quadratic replication principle. When there are multiple assemblages defined by the investigator, each of the three measures of the pooled assemblage (gamma) can be multiplicatively decomposed into alpha and beta components, and the two components are independent. The resulting beta component measures pure functional differentiation among assemblages and can be further transformed to obtain several classes of normalized functional similarity (or differentiation) measures, including N-assemblage functional generalizations of the classic Jaccard, Sørensen, Horn and Morisita-Horn similarity indices. The proposed measures are applied to artificial and real data for illustration.

Suggested Citation

  • Chun-Huo Chiu & Anne Chao, 2014. "Distance-Based Functional Diversity Measures and Their Decomposition: A Framework Based on Hill Numbers," PLOS ONE, Public Library of Science, vol. 9(7), pages 1-17, July.
  • Handle: RePEc:plo:pone00:0100014
    DOI: 10.1371/journal.pone.0100014
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    References listed on IDEAS

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    2. 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.
    3. Hu, Xiaojun & Leydesdorff, Loet & Rousseau, Ronald, 2017. "Heterogeneity in an undirected network: Definition and measurement," Journal of Informetrics, Elsevier, vol. 11(2), pages 669-682.
    4. Ricotta, Carlo & Pavoine, Sandrine, 2022. "A new parametric measure of functional dissimilarity: Bridging the gap between the Bray-Curtis dissimilarity and the Euclidean distance," Ecological Modelling, Elsevier, vol. 466(C).
    5. Aisling J. Daly & Jan M. Baetens & Bernard De Baets, 2018. "Ecological Diversity: Measuring the Unmeasurable," Mathematics, MDPI, vol. 6(7), pages 1-28, July.
    6. Marcon, Eric & Hérault, Bruno, 2015. "entropart: An R Package to Measure and Partition Diversity," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 67(i08).

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