NS  Vol.2 No.10 , October 2010
The Rich-Gini-Simpson quadratic index of biodiversity
Abstract: The Gini-Simpson quadratic index is a classic measure of diversity, widely used by ecologists. As shown recently, however, this index is not suitable for the measurement of beta diversity when the number of species is very large. The objective of this paper is to introduce the Rich- Gini-Simpson quadratic index which preserves all the qualities of the classic Gini-Simpson index but behaves very well even when the number of species is very large. The additive partitioning of species diversity using the Rich-Gini- Simpson quadratic index and an application from island biogeography are analyzed.
Cite this paper: Guiasu, R. and Guiasu, S. (2010) The Rich-Gini-Simpson quadratic index of biodiversity. Natural Science, 2, 1130-1137. doi: 10.4236/ns.2010.210140.

[1]   Sarkar, S. (2007) From ecological diversity to biodiversity. In: Hull, D.L. and Ruse, M. Eds., The Philosophy of Biology. Cambridge University Press, Cambridge, 388- 409.

[2]   Gini, C. (1912) Variabilità e mutabilità. In: Pizetti, E. and Salvemini, T. Eds., Rome: Libreria Eredi Virgilio Veschi, Memorie di metodologica statistica.

[3]   Simpson, E.H. (1949) Measurement of diversity. Nature, 163, 688.

[4]   Shannon, C.E. (1948) A mathematical theory of commu-nication. Bell System Technical Journal, 27, 379-423, 623- 656.

[5]   Boltzmann, L. (1896) Vorlesungen über Gastheorie. J.A. Barth edition, Akademische Druck-u, Leipzig.

[6]   Pielou, E.C. (1966) Shannon’s formula as a measure of specific diversity: Its use and misuse. American Naturalist, 100, 463-465.

[7]   Pielou, E.C. (1966) Species-diversity and pattern-diversity in the study of ecological succession. Journal of Theo-retical Biology, 10, 370-383.

[8]   Pielou, E.C. (1975) Ecological Diversity. Wiley, New York.

[9]   Guiasu, S. (1977) Information Theory with Applications. McGraw-Hill, New York.

[10]   Patil, G.P. and Taillie, C. (1982) Diversity as a concept and its measurement. Journal of American Statistical Association, 77, 548-567.

[11]   Harper, J.L. and Hawksworth, D.L. (1994) Biodiversity: Measurement and estimation. Philosophical Transactions: Biological Sciences, 345, 5-12.

[12]   Magnussen, S. and Boyle, T.J.B. (1995) Estimating sam-ple size for inference about the Shannon-Weaver and the Simpson indices of species diversity. Forest Ecology and Management, 78, 71-84.

[13]   Krebs, C.J. (2001) Ecology: The experimental analysis of distribution and abundance. 5th Edition, Benjamin Cummings, San Francisco.

[14]   Guiasu, R.C. and Guiasu, S. (2003) Conditional and weight- ed measures of ecological diversity. International Journal of Uncertainty, Fuzziness and Knowledge-Based Sys- tems, 11, 283-300.

[15]   Guiasu, R.C. and Guiasu, S. (2003) Entropy in ecology and ethology. Nova Science Publishers, New York.

[16]   Magurran, A.E. (2004) Measuring biological diversity. Blackwell Publishing, Malden MA.

[17]   Maclaurin, J. and Sterelny, K. (2008) What is biodiversity? University of Chicago Press, Chicago and London.

[18]   Jost, L. (2006) Entropy and diversity. Oikos, 113, 363- 375.

[19]   Jost, L. (2007) Partitioning diversity into independent alpha and beta components. Ecology, 88, 2427-2439.

[20]   Hill, M. (1973) Diversity and evenness. A unifying nota-tion and its consequences. Ecology, 54, 427-432.

[21]   Rényi, A. (1961) On measures of entropy and information. In: Neyman, J. Ed., Fourth Berkeley Symposium on Mathematical Statistics and Probability. Berkeley, 547- 561.

[22]   Hoffmann, S. and Hoffmann, A. (2008) Is there a “true” diversity? Ecological Economics, 65, 213-215.

[23]   Ricotta, C. (2005) Through the jungle of biological di-versity. Acta Biotheoretica, 53, 29-38.

[24]   Jost, L. (2009) Mismeasuring biological diversity: Re-sponse to Hoffmann and Hoffmann. Ecological Econom-ics, 68, 925-928.

[25]   Adler, G.H. (1994). Avifaunal diversity and endemism on tropical Indian Ocean islands. Journal of Biogeography, 21, 85-95.

[26]   MacArthur, R.H. (1965) Patterns of species diversity. Bio- logical Review, 40, 510-533.

[27]   MacArthur, R.H., Recher, H. and Cody, M. (1966) On the relation between habitat selection and species diversity. American Naturalist, 100, 319-332.

[28]   MacArthur, R.H. and Wilson, E.O. (1967) The theory of island biogeography. Princeton University Press, Prince-ton.

[29]   Rao, C.R. (1982) Diversity and dissimilarity coefficients: A unified approach. Theoretical Population Biology, 21, 24-43.

[30]   Whittaker, R.H. (1972) Evolution and measurement of species diversity. Taxon, 21, 213-251.

[31]   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, 10, 1-67.

[32]   Harrison, S. and Quinn, J. (2006) The importance of - diversity. In: Groom, M.J., Meffe, G.K. and Carroll, C.R. Eds., Principles of Conservation Biology, 3rd Edition, Sinauer Associates Inc. Publishers, Sunderland, 44-45.

[33]   Routledge, R.D. (1977) On Whittaker’s components of diversity. Ecology, 58, 1120-1127.

[34]   Routledge, R.D. (1979) Niche metrics and diversity com- ponents. Oecologia, 43, 121-124.

[35]   Allan, J.D. (1975) Components of diversity. Oecologia, 18, 359-367.

[36]   Lande, R. (1996) Statistics and partitioning of species di- versity and similarity among multiple communities. Oikos, 76, 5-13.

[37]   Wagner, H.H., Wildi, O. and Ewald, K.C. (2000) Additive partitioning of plant species diversity in an agricultural mosaic landscape. Landscape Ecology, 15, 219-227.

[38]   Veech, J.A., Summerville, K.S., Crist, T.O. and Gering, J.C. (2002) The additive partioning of species diversity: Recent revival of an old idea. Oikos, 99, 3-9.

[39]   Tramer, E.J. (1969) Bird species diversity: Components of Shannon’s formula. Ecology, 50, 927-929.

[40]   Fager, E.W. (1972) Diversity: A sampling study. Ameri- can Naturalist, 106, 293-310.

[41]   Brown, J.H. and Lomolino, M.V. (1998) Biogeography. 2nd Edition, Sinauer Associates Inc. Publishers, Sunder-land, MA.

[42]   Stirling, G. and Wilsey, B. (2001) Empirical relationships between species richness, evenness, and proportional di-versity. American Naturalist, 158, 286-299.

[43]   Cox, C.B. and Moore, P.D. (2005) Biogeography: An ecological and evolutionary approach. 7th Edition, Black- well Publishing, Oxford.

[44]   Quammen, D. (1997) The song of the Dodo-Island bio-geography in an Age of Extinction. Simon & Schuster Inc., New York.

[45]   Powledge, F. (2003) Island biogeography’s lasting impact. BioScience, 53, 1032-1038.