TITLE:
Weighted Gini-Simpson Quadratic Index of Biodiversity for Interdependent Species
AUTHORS:
Radu Cornel Guiasu, Silviu Guiasu
KEYWORDS:
Weighted Gini-Simpson Index, Generalized Rao Index, Interdependent Species, Watanabe’s Entropic Measure of Interdependence, Distribution Pattern Variability of the Subsets of Species
JOURNAL NAME:
Natural Science,
Vol.6 No.7,
April
25,
2014
ABSTRACT: The weighted Gini-Simpson
quadratic index is the simplest measure of biodiversity which takes into account
the relative abundance of species and some weights assigned to the species. These
weights could be assigned based on factors such as the phylogenetic distance between
species, or their relative conservation values, or even the species richness or
vulnerability of the habitats where these species live. In the vast majority of
cases where the biodiversity is measured the species are supposed to be independent,
which means that the relative proportion of a pair of species is the product of
the relative proportions of the component species making up the respective pair.
In the first section of the paper, the main versions of the weighted Gini-Simpson
index of biodiversity for the pairs and triads of independent species are presented.
In the second section of the paper, the weighted Gini-Simpson quadratic index
is calculated for the general case when the species are interdependent. In this
instance, the weights reflect the conservation values of the species and the distribution
pattern variability of the subsets of species in the respective habitat induced
by the inter-dependence between species. The third section contains a numerical
example.