The relationship between diversity profiles, evenness and species richness based on partial ordering
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Problems with the notion of evenness, such as ambiguity, proliferation of indices, choice of indices, etc. can be overcome by a more fundamental, mathematical approach. We show that the Lorenz curve is an adequate representation of evenness. The corresponding Lorenz order induces a partial order in the set of equivalent abundance vectors. Also diversity can adequately be studied through a partial order and represented by a curve derived from the classical Lorenz curve. This curve is known as the intrinsic diversity profile (or k-dominance curve) and was introduced by Patil and Taillie (1979) and Lambshead et al. (1981).
- Dalton, H. (1920) The measurement of the inequality of incomes. The Economic Journal, 30, 348-61.
- Gove, J.H., Patil, G.P., Swindel, B.F., and Taillie, C. (1994) Ecological diversity and forest management. In Handbook of Statistics Volume 12: Environmental Statistics, G.P. Patil and C.R. Rao (eds.), Elsevier, Amsterdam, pp. 409-62.
- Hill, M.O. (1973) Diversity and evenness: a unifying notation and its consequences. Ecology, 54, 427-32.
- Hurlbert, S.H. (1971) The nonconcept of species diversity: a critique and alternative parameters. Ecology, 52, 577-86.
- Lambshead, P.J.D., Platt, H.M., and Shaw, K.M. (1981) Detection of differences among assemblages of benthic species based on an assessment of dominance and diversity. Journal of Natural History (London), 17, 859-74.
- Lorenz, M.O. (1905) Methods of measuring concentration of wealth. Journal of the American Statistical Association, 9, 209-19.
- Magurran, A.E. (1991) Ecological diversity and its measurement, Chapman & Hall, London, England.
- Nijssen, D., Rousseau, R., and Van Hecke, P. (1998) The Lorenz curve: a graphical representation of evenness. Coenoses, 13, 33-8.
- Patil, G.P. and Taillie, C. (1979) An overview of diversity. In Ecological Diversity in Theory and Practice, J.F. Grassle, G.P. Patil, W. Smith and C. Taillie (eds), International Co-operative Publishing House, Fairland, MD, pp. 3-27.
- Patil, G.P. and Taillie, C. (1982) Diversity as a concept and its measurement. Journal of the American Statistical Association, 77, 548-67.
- Peet, R.K. (1974) The measurement of species diversity. Annual Review of Ecology and Systematics, 5, 285-307.
- Peet, R.K. (1975) Relative diversity indices. Ecology, 56, 496-8.
- Pielou, E.C. (1975) Ecological diversity, John Wiley & Sons, New York.
- Platt, H.M., Shaw, K.M., and Lambshead, P.J.D. (1984) Nematode species abundance patterns and their use in the detection of environmental perturbations. Hydrologia, 119, 59-66.
- Roberts, F. (1979) Measurement theory, Addison-Wesley, Reading, MA.
- Rousseau, R. (1992a) Concentration and diversity in informetric research. Ph.D. thesis, Universitaire Instelling Antwerpen.
- Rousseau, R. (1992b) Concentration and diversity measures: dependence on the number of classes. Belgian Journal of Operations Research, Statistics and Computer Science, 32, 99-126.
- Rousseau, R. and Van Hecke, P. (1998) Measuring biodiversity. Acta Biotheoretica (accepted).
- Shorrocks, A.F. (1983) Ranking income distributions. Economica, 50, 3-17.
- Swindel, B.F., Conde, L.F., and Smith, J.E. (1987) Index-free diversity orderings: concept, measurement, and observed response to clearcutting and site-preparation. Forest Ecology and Management, 20, 195-208.
- Taillie, C. (1979) Species equitability: a comparative approach. In Ecological Diversity in Theory and Practice, J.F. Grassle, G.P. Patil, W. Smith and C. Taillie (eds). International Co-operative Publishing House, Fairland, MD, pp. 51-62.
- The relationship between diversity profiles, evenness and species richness based on partial ordering
Environmental and Ecological Statistics
Volume 6, Issue 2 , pp 211-223
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- Gini coefficient
- coefficient of variation
- partially ordered sets
- adapted Gini coefficient
- intrinsic diversity profiles
- k-dominance curves.
- Author Affiliations
- 1. Informatie- en Bibliotheekwetenschap, UIA, Universiteitsplein 1, B-2610, Wilrijk, Belgium; and
- 2. Department of Industrial Sciences and Technology, KHBO, Zeedijk 101, B-8400, Oostende, Belgium
- 3. Department of Biology, Laboratory of Plant Ecology, UIA, Universiteitsplein 1, B-2610, Wilrijk, Belgium
- 4. Wildbroekstraat 14, B–3700, Tongeren, Belgium