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.