A geometrical index for measuring species diversity

During the past decades several biodiversity indices have been proposed and employed in ecological literature. Although each one has been partially justified on practical or quasi-theoretical grounds, recommendations of ecological theorists differ from describing which index to use. The goal of this article is to introduce a new index for measuring biological diversity that is sensitive to the number of different species (species richness, ), and the relative abundance of them. We take advantage from the mathematical relation between Simpson index and the geometrical concept of a -dimensional sphere of radius r, where r is the square root of the Simpson index. Full applications of the method are developed, first with hypothetical communities and then with real data for 1761 specimens of 82 weevil species collected in several forest types (Ohsawa, M., 2005. Species richness and composition of Curculionidae (Coleopters) in a conifer plantation, secondary forest, and old-growth forest in the central mountainous region of Japan. Ecological Research. 20, 632).