The DOI matches its Crossref record; 36 of the 36 references it cites were found in a registry or an index.
Simpson diversity and the Shannon–Wiener index as special cases of a generalized entropy
Abstract
Many indices for measuring species diversity have been proposed. In this article, a link is noted between a common family of diversity indices and non‐additive statistical mechanics. This makes the Shannon index and the Simpson diversity (or Gini coefficient) special cases of a more general index. The general index includes a parameter q that can be interpreted from a statistical mechanics perspective for systems with an underlying (multi)fractal structure. A q ‐ generalised version of the Zipf–Mandelbrot distribution sometimes used to characterise rank–abundance relationships may be obtained by maximising this entropy.
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“The use of different q values in the construction of Δ measures for the comparison of the genetic diversities of two (or more) populations will have the same effect50, 130, 131: small q values will impact differences in rare variants and large q values emphasize differences in common variants132.”
From Statistical analysis strategies for association studies involving rare variants (2010) · cites this paper as [130]
Citations
Cites
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Possible generalization of Boltzmann-Gibbs statistics
Tsallis, C. (1988) · Journal of Statistical Physics · doi:10.1007/bf01016429 · Cited by 9,589
Diversity and Evenness: A Unifying Notation and Its Consequences
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The Unified Neutral Theory of Biodiversity and Biogeography
Jetschke, G., & Hubbell, S. P. (2002) · Ecology · doi:10.2307/3071998 · Cited by 5,699
EVOLUTION AND MEASUREMENT OF SPECIES DIVERSITY
WHITTAKER, R. H. (1972) · Taxon · doi:10.2307/1218190 · Cited by 5,398
The Unified Neutral Theory of Biodiversity and Biogeography
Jetschke, G. (2002) · Ecology · doi:10.1890/0012-9658(2002)083[1771:tuntob]2.0.co;2 · Cited by 3,285
Ecology and Evolution of Communities
Cody, M. L., & Diamond, J. M. (1976) · Nature · doi:10.1038/260204c0 · Cited by 3,094
The Apportionment of Human Diversity
Lewontin, R. C. (1972) · Evolutionary Biology · doi:10.1007/978-1-4684-9063-3_14 · Cited by 2,472
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PRESTON, F. W. (1948) · Ecology · doi:10.2307/1930989 · Cited by 2,010
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Research works printed but not linked: 2
- Frontier S., 1985, Diversity and structure in aquatic ecosystems, Mar. Biol. Annu. Rev., 23, 253
- Solé R. V., 1994, Fractals in the natural and applied sciences, 397
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Jost, L. (2006) · Oikos · doi:10.1111/j.2006.0030-1299.14714.x · Cited by 4,669
Zheng, P., Zeng, B., Zhou, C., Liu, M., Fang, Z., Xu, X., Zeng, L., Chen, J., Fan, S., Du, X., et al. (2016) · Molecular Psychiatry · doi:10.1038/mp.2016.44 · Cited by 2,023
Statistical analysis strategies for association studies involving rare variants
Bansal, V., Libiger, O., Torkamani, A., & Schork, N. J. (2010) · Nature Reviews Genetics · doi:10.1038/nrg2867 · Cited by 455
Sex differences in gut microbiota in patients with major depressive disorder
Chen, J.-J., Zheng, P., Liu, Y.-Y., Zhong, X.-G., Wang, H.-Y., Guo, Y.-J., & Xie, P. (2018) · Neuropsychiatric Disease and Treatment · doi:10.2147/ndt.s159322 · Cited by 272
Metadata
- Authors
- Keylock, C. J.
- Affiliations
- University of Leeds (GB)
- Corresponding author
- Keylock, C. J.
- ORCID
- Keylock, C. J.
- Venue
- Oikos
- Publisher
- Wiley
- Published
- 2005-02-22
- Volume
- 109
- Issue
- 1
- Pages
- 203-207
- ISSN
- 0030-1299 (ISSN-L)
- 1600-0706
- OpenAlex
- W2090933635
- Cited by
- 495
- References
- 36
- Citations by year
- 2026: 27 · 2025: 47 · 2024: 43 · 2023: 35 · 2022: 44 · 2021: 34 · 2020: 32 · 2019: 35 · 2018: 37 · 2017: 21 · 2016: 20 · 2015: 27 · 2014: 16 · 2013: 15 · 2012: 12
- FWCI
- 6.12
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Oikos (publishedVersion)
- Funders
- Japan Society for the Promotion of Science
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Statistical Mechanics and Entropy
- Physical Sciences › Environmental Science › Nature and Landscape Conservation › Ecology and Vegetation Dynamics Studies
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Complex Systems and Time Series Analysis
- Keywords
- species diversity index, Simpson index, Shannon diversity index, generalized entropy, q-statistics, Zipf-Mandelbrot distribution, Gini coefficient
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