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Simpson diversity and the Shannon–Wiener index as special cases of a generalized entropy
Author(s) -
Keylock C. J.
Publication year - 2005
Publication title -
oikos
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.672
H-Index - 179
eISSN - 1600-0706
pISSN - 0030-1299
DOI - 10.1111/j.0030-1299.2005.13735.x
Subject(s) - diversity index , mathematics , generalized entropy index , zipf's law , entropy (arrow of time) , statistical physics , index (typography) , rényi entropy , statistics , principle of maximum entropy , ecology , physics , computer science , species richness , thermodynamics , biology , world wide web , panel data
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.