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Some Comments on Fisher's α Index of Diversity and on the Kazwini Cosmography

In: Statistical Inference, Econometric Analysis and Matrix Algebra

Author

Listed:
  • Oskar Maria Baksalary

    (Adam Mickiewicz University, ul. Umultowska 85, Faculty of Physics)

  • Ka Lok Chu

    (Dawson College, 3040 ouest, rue Sherbrooke, Department of Mathematics)

  • Simo Puntanen

    (University of Tampere, Department of Mathematics and Statistics)

  • George P.H. Styan

    (McGill University, Department of Mathematics and Statistics)

Abstract

Biodiversity, or biological diversity, is “the variety of life on our planet, measurable as the variety within species, between species, and the variety of ecosystems” [12, 41] and the most widely applied index of biodiversity is surely Fisher's α, defined implicitly by S = αloge{1+(n/α)}, where n is the number of individuals and S is the number of species. This index αwas first proposed over 60 years ago by R. A. Fisher in a three-part joint paper with A. Steven Corbet and C. B. Williams [14]. We also present some comments on the diversity of the paintings by Johannes Vermeer (1632–1675) depicted on postage stamps updating our findings in [3]. The earliest study of biodiversity seems to be that reported in the Kazwini Cosmography c. 1283; this study involved 72 different kinds of papillons that were collected in what we believe was Baghdad in c. 900 AD. We also found some magic squares in the Kazwini Cosmography. Our list of references is annotated and contains hyperlinks to open-access and restricted-access files on the internet.

Suggested Citation

  • Oskar Maria Baksalary & Ka Lok Chu & Simo Puntanen & George P.H. Styan, 2009. "Some Comments on Fisher's α Index of Diversity and on the Kazwini Cosmography," Springer Books, in: Bernhard Schipp & Walter Kräer (ed.), Statistical Inference, Econometric Analysis and Matrix Algebra, pages 369-394, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7908-2121-5_26
    DOI: 10.1007/978-3-7908-2121-5_26
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