A link between ecological diversity indices and measures of biodiversity

The practice of environmental planning and protection frequently necessitates the quantification of ecological diversity. Traditional ‘ecological diversity indices’ are based on the abundances of species present. However, such indices are insensitive to taxonomic or similar differences. With equal species abundances they measure the species richness (species number) only. Conversely, so-called ‘biodiversity indices’ are based on species differences, but are insensitive to the abundance conditions. The quadratic entropy index is the only ecological diversity index, the value of which reflects both the differences ‘and’ abundances of the species. When a species list is given without abundance data, then, using the quadratic entropy index and postulating equal abundances, one gets the only biodiversity index derived from a traditional ecological index of diversity. Its extensive form is identical with the sum of differences or distances between the species present. This index trivially satisfies set monotonicity, an important property for biodiversity indices.