Measuring biological diversity: Beyond the Shannon index

Abstract

The study of biodiversity is the concern of countless biologists, but the mathematical tools they use to measure it are not always adequate to make inferences about changes in biological diversity, or about the relative impor tance of within- and between- group diversity. The abundance-based diversity indices most used in ecology, the Shannon or Gini-Simpson indices, which combine both species richness and equitability, are genuine measures of something related to the complexity of biological communities; but they are not directly compatible with the rules of inference biologists apply to them. Conclusions based on them will often be invalid. They are also not in the same units as each other, or as species richness, so they cannot be compared across indices. Nevertheless, they can be converted to a linear species richness scale by taking their equivalent number of species, the number of equally common, equiprobable species needed to produce a community with the same complexity as that indicated by the original measure. After this conversion, measures can be directly compared with each other. All standard complexity measures of given order q have the same formula when converted: qD ? [? pi q]1/(1 – q). The most useful diversity measure, and the only one that weighs all species exactly according to their relative contribution to the community, is the limit of this expression as q approaches 1, which equals the exponential of the Shannon index, 1D = e[–?pi×ln(pi)]. Differences between true diversity measures and the unconverted Shannon and GiniSimpson indices are highlighted by means of examples, and inappropriate use of standard indices is illustrated. In order to adequately assess spatial and temporal changes in biological diversity, and to avoid conservation mistakes with potentially irreversible consequences, it is important to use measures whose properties match the rules of inference used. Shannon and Gini-Simpson indices fail in this, but equivalent number of species succeeds.