The weighted quadratic index of biodiversity for pairs of species: a generalization of Rao’s index

• 作者: Radu Cornel Guiasu Silviu Guiasu
• 来源期刊: 自然科学期刊(英文)
• 学科: 数学
• 关键词: Additive Partitioning of BIODIVERSITY BIODIVERSITY Measures Rao’s INDEX of DISSIMILARITY Replication Property WEIGHTED Alpha- Beta- and Gamma-Diversities WEIGHTED Gini-Simpson INDEX
• 年，卷（期）: 2011,（9）
• 页码范围: 795-801
• 页数: 7页
• 分类号: O1

摘要

The distribution of biodiversity at multiple sites of a region has been traditionally investigated through the additive partitioning of the regional biodiversity, called γ-diversity, into the average within-site biodiversity or α-diversity, and the biodiversity among sites, or β-diversity. 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, like the Shannon entropy or the Gini- Simpson index, for instance. When a phylogenetic distance between species is also taken into account, Rao’s quadratic index has been used as a measure of dissimilarity. Rao’s index, however, is not a concave function of the distribution of relative abundance of either individual species or pairs of species and, consequently, only some nonstandard additive partitionings of diversity have been given using this index. The objective of this paper is to show that the weighted quadratic index of biodiversity, a generalization of the weighted Gini-Simpson index to the pairs of species, is a concave function of the joint distribution of the relative abundance of pairs of species and, therefore, may be used in the standard additive partitioning of diversity instead of Rao’s index. The replication property of this new measure is also discussed.