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

2005; Wiley; Volume: 109; Issue: 1 Linguagem: Inglês

10.1111/j.0030-1299.2005.13735.x

1600-0706

Christopher J. Keylock,

Evolutionary Game Theory and Cooperation

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.