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Statistical Properties and Performance of Ecological Indices Based On Relative Abundances
Authors: Gebriel M. Shamia
Abstract:The Improved Generalized Diversity Index (IGDI) has been proposed as a tool that can be used to identify areas that have high conservation value and measure the ecological condition of an area. IGDI is based on the species relative abundances. This paper is concerned with particular attention is given to comparisons involving the MacArthur model of species abundances. The properties and performance of various species indices were assessed. Both IGDI and species richness increased with sampling area according to a power function. IGDI were also found to be acceptable ecological indicators of conditions and consistently outperformed coefficient of conservatism indices.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1328054Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1618
 A. J. Baczkowski, D. N. Joanes, and G. M. Shamia, "Properties of a generalized diversity index," Journal of Theoretical Biology, 188, 1997, pp. 207-213.
 A. J. Baczkowski, D. N. Joanes, and G. M. Shamia, "Range of validity of ╬▒ and β for a generalized diversity index H(╬▒,β) due Good," Mathematical Bioscience, 148:2, 1998, pp. 115-128.
 I. J. Good, "The population frequencies of species and the estimation of population parameters," Biometrika, 40, 1953, pp. 237-264.
 M. O. Hill, "Diversity and evenness: a unifying notation and its consequences," Ecology, 54, 1973, pp. 427-32.
 A. Howard, Calculus with analytic Geometr, John Wiley and Sons. Inc., 1995.
 L. Jost, "Entropy and diversity," Oikos, 113, 2006, pp. 363-375.
 C. J. Keylock, "Simpson diversity and the Shannon-Wiener index as special cases of a generalized entropy," Oikos, 109:1, 2005, pp. 203-207.
 P. J. D. Lambshead , H. M. Platt, and H. M. Shaw, "The detection of differences among assemblages of marine benthic species based on an assessment of dominance and diversity," Journal of Natural History, 17, 1983, pp. 859-74.
 R. H. MacArthur, "On the relative abundance of bird species. proceedings of the national academy of science," USA, 43, 1957, pp. 293-5."
 R. H. MacArthur, "Patterns of species diversity, "Biological reviews of the cambridge philosophical society," 40, 1965, pp. 510-533.
 A. E. Magurran, Ecological Diversity and its Measurement. Croom Helm, London, 1988.
 A. W. Marshall, and I. Olkin, Inequalities: Theory of moralization and its applications, Academic Press, 1979.
 C. P. Patil, and C. Taillie, An Overview of Diversity: In ecological diversity in theory and practice, edited by J.F. Grassle, G.P. Patil, W.K. Smith and C. Taillie,. Fairland, Maryland: International Co-operative Publishing House, 1979, pp. 3-27.
 G. P. Patil, and C. Taillie, "Diversity as a concept and its measurement," Journal of the American Statistical Association, 77, 1982, pp. 548-67.
 R. K. Peet, "The measurement of species diversity," Annual Review of Ecology and Systematics, 5, 1974, pp. 285-307.
 E. C. Pielou, Ecological Diversity, Wiley, London, 1975.
 F. W. Preston, "The anonical distribution of commonness and rarity," Ecology, 43, 1962, pp. 185-215.
 R. D. Routledge, "Diversity index: which ones are admissible?" Journal of Theoretical Biology, 76, 1979, pp. 503-15
 G. M. Shamia, Statistical Properties of the Generalized Diversity Index. PhD, Dept. of Statistics, University of Leeds, 1997.
 C. E.Shannon, "A mathematical theory of communication," The Bell System Technical Journal, 27, 1948, pp. 379-423.
 A. L. Sheldon, "Equitability indices: dependence on the species count," Ecology, 50, 1969, pp. 476-77.
 E. H. Simpson, "Measurement of diversity," Nature, 163, 1949, pp. 688.
 G. Sugihara, "Minimal community structure: an explanation of species abundances pattern," American Nature, 116, 1980, pp. 770-787.
 H. William, Durfee Calculus and Analytic Geometry. Mc Grow Hill, Inc, 1971.