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.