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Weighted Gini-Simpson Quadratic Index of Biodiversity for Interdependent Species

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DOI: 10.4236/ns.2014.67044    2,547 Downloads   3,511 Views   Citations


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.

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The authors declare no conflicts of interest.

Cite this paper

Guiasu, R. and Guiasu, S. (2014) Weighted Gini-Simpson Quadratic Index of Biodiversity for Interdependent Species. Natural Science, 6, 455-466. doi: 10.4236/ns.2014.67044.


[1] Gini, C. (1912) Variabilità e mutabilità. In: Pizetti, E. and Salvemini, T., Eds., Rome: Libreria Eredi Virgilio Veschi, Memorie di metodologica statistica.
[2] Simpson, E.H. (1949) Measurement of Diversity. Nature, 163, 688.
[3] Jost, L. (2007) Partitioning Diversity into Independent Alpha and Beta Components. Ecology, 88, 2427-2439.
[4] Jost, L. (2009) Mismeasuring Biological Diversity: Response to Hoffmann and Hoffmann. Ecological Economics, 68, 925-928.
[5] Jost, L., DeVries, P., Walla, T., Greeney, H., Chao, A. and Ricotta, C. (2010) Partitioning Diversity for Conservation Analyses. Diversity and Distributions, 16, 65-76.
[6] Guiasu, R.C. and Guiasu, S. (2010) The Rich-Gini-Simpson Quadratic Index of Biodiversity. Natural Science, 2, 11301137.
[7] Guiasu, R.C. and Guiasu, S. (2003) Conditional and Weighted Measures of Ecological Diversity. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 11, 283-300.
[8] Lande, R. (1996) Statistics and Partitioning of Species Diversity and Similarity among Multiple Communities. Oikos, 76, 5-13.
[9] Guiasu, R.C. and Guiasu, S. (2010) New Measures for Comparing the Species Diversity Found in Two or More Habitats. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 18, 691-720.
[10] Whittaker, R.H. (1972) Evolution and Measurement of Species Diversity. Taxon, 21, 213-251.
[11] Whittaker, R.H. (1977) Evolution of Species Diversity in Land Communities. In: Hecht, M.K. and Steere, B.W.N.C., Eds., Evolutionary Biology, Plenum Press, New York, 1-67.
[12] MacArthur, R.H. (1965) Patterns of Species Diversity. Biological Review, 40, 510-533.
[13] MacArthur, R.H. and Wilson, E.O. (1967) The Theory of Island Biogeography. Princeton University Press, Princeton.
[14] Hill, M. (1973) Diversity and Evenness. A Unifying Notation and Its Consequences. Ecology, 88, 2427-2439.
[15] Rao, C.R. (1982) Diversity and Dissimilarity Coefficients: A Unified Approach. Theoretical Population Biology, 21, 24-43.
[16] Pavoine, S., Ollier, S. and Pontier, D. (2005) Measuring Diversity from Dissimilarities with Rao’s Quadratic Entropy: Are Any Dissimilarities Suitable? Theoretical Population Biology, 67, 231-239.
[17] Ricotta, C. (2005) Additive Partitioning of Rao’s Quadratic Diversity: A Hierarchical Approach. Ecological Modelling, 183, 365-371.
[18] Ricotta, C. and Szeidel, L. (2006) Towards a Unifying Approach to Diversity Measures: Bridging the Gap between the Shannon Entropy and Rao’s Quadratic Index. Theoretical Population Biology, 70, 237-243.
[19] Hardy, O.J. and Senterre, B. (2007) Characterizing the Phylogenetic Structure of Communities by an Additive Partitioning of Phylogenetic Diversity. Journal of Ecology, 95, 493-506.
[20] Villéger, S. and Mouillot, D. (2008) Additive Partitioning of Diversity Including Species Differences: A Comment on Hardy and Senterre (2007). Journal of Ecology, 96, 845-848.
[21] Hardy, O.J. and Jost, L. (2008) Interpreting Measures of Community Phylogenetic Structuring. Journal of Ecology, 96, 849-852.
[22] Ricotta, C. and Szeidel, L. (2009) Diversity Partitioning of Rao’s Quadratic Entropy. Theoretical Population Biology, 76, 299-302.
[23] Sherwin, W.B. (2010) Entropy and Information Approaches to Genetic Diversity and Its Expression: Genomic Geography. Entropy, 12, 1765-1798.
[24] De Bello, F., Lavergne, S., Meynard, C.N., Leps, J. and Thuiller, W. (2010) The Partitioning of Diversity: Showing Theseus a Way out of the Labyrinth. Journal of Vegetation Science, 21, 992-1000.
[25] Tuomisto, H. (2010) A Diversity of Beta Diversities: Straightening up a Concept Gone Awry. Part 1. Defining Beta Diversity as a Function of Alpha and Gamma Diversity. Ecography, 33, 2-22.
[26] Tuomisto, H. (2010) A Diversity of Beta Diversities: Straightening up a Concept Gone Awry. Part 2. Quantifying Beta Diversity and Related Phenomena. Ecography, 33, 23-45.
[27] Guiasu, R.C. and Guiasu, S. (2011) The Weighted Quadratic Index of Biodiversity for Pairs of Species: A Generalization of Rao’s Index. Natural Science, 3, 795-801.
[28] Guiasu, R.C. and Guiasu, S. (2012) The Weighted Gini-Simpson Index: Revitalizing an Old Index of Biodiversity. International Journal of Ecology, 2012, 10 p.
[29] Crooks, K.R. and Soulé, M.E. (1999) Mesopredator Release and Avifaunal Extinctions in a Fragmented System. Nature, 400, 563-566.
[30] Shannon, C.E. (1948) A Mathematical Theory of Communication. Bell System Technical Journal, 27, 379-423,
[31] Watanabe, S. (1969) Knowing and Guessing. Wiley, New York.
[32] Guiasu, S. (1977) Information Theory with Applications. McGraw-Hill, New York.

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