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Simpson diversity and the Shannon–Wiener index as special cases of a generalized entropy

Simpson diversity and the Shannon–Wiener index as special cases of a generalized entropy 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Oikos Wiley

Simpson diversity and the Shannon–Wiener index as special cases of a generalized entropy

Oikos , Volume 109 (1) – Apr 1, 2005

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References (37)

Publisher
Wiley
Copyright
Copyright © 2005 Wiley Subscription Services, Inc., A Wiley Company
ISSN
0030-1299
eISSN
1600-0706
DOI
10.1111/j.0030-1299.2005.13735.x
Publisher site
See Article on Publisher Site

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.

Journal

OikosWiley

Published: Apr 1, 2005

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