Abstract
This paper presents several indices to describe multivariate diversity and evenness. Multivariate generalizations of the Gini-Simpson index and the Rosenbluth index are proposed to measure diversity. A multivariate Gini ratio is also presented to measure evenness. These indices extend the usual univariate measures; they reflect not only the diversity of marginal distributions but also the dependence structure of abundance. The indices fulfill desirable measurement properties and are consistent with certain orderings of multivariate distributions. An order of concentration surfaces and a majorization order are also surveyed shortly.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Alatalo, R. and R. Alatalo. 1977. Components of diversity: Multivariate analysis with interaction. Ecology 58: 900–906.
Koshevoy, G. and K. Mosler. 1997. Multivariate Gini indices. J.Multivariate Analysis 60: 252–276.
Koshevoy, G. and K. Mosler. 1999. Measuring multidimensional concentration: A geometric approach. Allgemeines Statistisches Archiv 83: 173–189.
Loehle, C. and G. Wein. 1994. Landscape habitat diversity: A multiscale information theory approach. Ecol. Model. 73: 311–329.
Maasoumi, E. 1986. The measurement and decomposition of multidimensional inequality. Econometrica 54: 991–997.
Marshall, A.W. and I. Olkin. 1979. Inequalities: Theory of Majorization and its Applications. Academic Press, New York.
Mosler, K. 1994. Majorization in economic disparity measures. Linear Algebra and its Applications 199: 91–114.
Patil, G.P. and C. Taillie. 1982. Diversity as a concept and its measurement. JASA 77: 548–561.
Pielou, E.C. 1977. Mathematical Ecology. Wiley, New York.
Rao, C.R. 1982. Diversity and dissimilarity coefficients: A unified approach. Theoret. Popul. Biol. 21: 24–43.
Solomon, D.L. 1979. A comparative approach to species diversity. In: J.F. Grassle, G.P. Patil, W.K. Smith and C. Taillie (eds), Ecological Diversity in Theory and Practice. International Co-operative Publishing House, Fairland MD, pp 29–35.
Tong, Y.L. 1983. Some distribution properties of the sample species-diversity indices and their applications. Biometrics 39: 999–1008.
Tóthmérész, B. 1995. Comparison of different methods for diversity ordering. J. Veg Sci. 6: 283–290.
Whittaker, R.H. 1972. Evolution and measurement of species diversity. Taxon 21: 213–251.
Acknowledgements
thank Béla Tóthmérész, János Izsák and Frédéric Gosselin for helpful remarks.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Mosler, K. Multidimensional indices and orders of diversity. COMMUNITY ECOLOGY 2, 137–143 (2001). https://doi.org/10.1556/ComEc.2.2001.2.1
Published:
Issue Date:
DOI: https://doi.org/10.1556/ComEc.2.2001.2.1