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International Journal of Ecology
Volume 2012 (2012), Article ID 478728, 10 pages
http://dx.doi.org/10.1155/2012/478728
Research Article

The Weighted Gini-Simpson Index: Revitalizing an Old Index of Biodiversity

1Environmental and Health Studies Program, Department of Multidisciplinary Studies, Glendon College, York University, 2275 Bayview Avenue, Toronto, ON, Canada M4N 3M6
2Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON, Canada M3J 1P3

Received 19 September 2011; Revised 22 November 2011; Accepted 6 December 2011

Academic Editor: Jean-Guy Godin

Copyright © 2012 Radu Cornel Guiasu and Silviu Guiasu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The distribution of biodiversity at multiple sites of a region has been traditionally investigated through the additive partitioning of the regional biodiversity into the average within-site biodiversity and the biodiversity among sites. The standard additive partitioning of diversity requires the use of a measure of diversity, which is a concave function of the relative abundance of species, such as the Gini-Simpson index, for instance. Recently, it was noticed that the widely used Gini-Simpson index does not behave well when the number of species is very large. The objective of this paper is to show that the new weighted Gini-Simpson index preserves the qualities of the classic Gini-Simpson index and behaves very well when the number of species is large. The weights allow us to take into account the abundance of species, the phylogenetic distance between species, and the conservation values of species. This measure may also be generalized to pairs of species and, unlike Rao’s index, this measure proves to be a concave function of the joint distribution of the relative abundance of species, being suitable for use in the additive partitioning of biodiversity. The weighted Gini-Simpson index may be easily transformed for use in the multiplicative partitioning of biodiversity as well.