Simpson diversity and the Shannon–Wiener index as special cases of a generalized entropy
Top Cited Papers
- 22 February 2005
- Vol. 109 (1) , 203-207
- https://doi.org/10.1111/j.0030-1299.2005.13735.x
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.Keywords
This publication has 29 references indexed in Scilit:
- The fractal nature of nature: power laws, ecological complexity and biodiversityPhilosophical Transactions Of The Royal Society B-Biological Sciences, 2002
- Beta-Diversity in Tropical Forest TreesScience, 2002
- When species accumulation curves intersect: implications for ranking diversity using small samplesOikos, 2000
- Self-Similarity in the Distribution and Abundance of SpeciesScience, 1999
- Fractal binary sequences: Tsallis thermodynamics and the Zipf lawPhysics Letters A, 1997
- Statistics and Partitioning of Species Diversity, and Similarity among Multiple CommunitiesOikos, 1996
- Diversity and rank-abundance relationship concerning biotic compartmentsEcological Modelling, 1995
- Generalized statistical mechanics: connection with thermodynamicsJournal of Physics A: General Physics, 1991
- Diversity and Evenness: A Unifying Notation and Its ConsequencesEcology, 1973
- The Apportionment of Human DiversityPublished by Springer Nature ,1972