Measuring biological diversity using Euclidean metrics
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We study the complementary use of Rao's theory of diversity (1986) and Euclidean metrics. The first outcome is a Euclidean diversity coefficient. This index allows to measure the diversity in a set of species beyond their relative abundances using biological information about the dissimilarity between the species. It also involves geometrical interpretations and graphical representations. Moreover, several populations (e.g., different sites) can be compared using a Euclidean dissimilarity coefficient derived from the Euclidean diversity coefficient. These proposals are used to compare breeding bird communities living in comparable habitat gradients in different parts of the world.
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- d'Aubigny, G. (1988) The additive decomposition of some entropy functions and (constrained-) ordination methods. Proceedings of the XVIth International Biometric Conference, Namur, 1988.Google Scholar
- Blondel, J., Vuillermier, F., Marcus, L.F., and Terouanne, E. (1984) Is there ecomorphological convergence among mediterranean bird communities of Chile, California and France? In: Evolutionary Biology, M.K. Hecht, B. Wallace, and R.J. MacIntyre (eds), Plenum Press, New York, pp. 141–213.Google Scholar
- Gower, J.C. (1966) Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika, 53, 325–88.Google Scholar
- Gower, J.C. (1982) Euclidean distance geometry. Mathematical Scientist, 7, 1–14.Google Scholar
- Gower, J.C. and Legendre, P. (1986) Metric and Euclidean properties of dissimilary coefficients. Journal of Classification, 3, 5–48.Google Scholar
- Patil, G.P. and Taillie, C. (1982) Diversity as a concept and its measurement. Journal of the American Statistical Association, 77, 548–61.Google Scholar
- Rao, C.R. (1982) Diversity and dissimilarity coefficients: a unified approach. Theoretical Population Biology, 21, 24–43.Google Scholar
- Rao, C.R. (1986) Rao's axiomatization of diversity measures. In: Encyclopedia of Statistical Sciences Volume 7, S. Kotz, N.L. Johnson, and C.R. Read (eds), pp. 614–17.Google Scholar
- Rosen, J.B. (1960) The gradient projection method for nonlinear programming. Part I: linear constraints. Journal of the Society for Industrial and Applied Mathematics, 8, 181–217.Google Scholar
- Solow, A.R. and Polasky, S. (1994) Measuring biological diversity. Environmental and Ecological Statistics, 1, 95–107.Google Scholar
- Thioulouse, J., Chessel, D., Dolédec, S., and Olivier, J.-M. (1997) ADE-4: a multivariate analysis and graphical display software. Statistics and Computing, 7, 75–83.Google Scholar