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Biometrika 1975 62(3):697-699; doi:10.1093/biomet/62.3.697
© 1975 by Biometrika Trust
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A note on the geometric series as a species frequency model

STEINAR ENGEN *

Department of Biomathematics, University of Oxford

We consider a certain randomized geometric series of relative abundances and the limit, of the Dirichlet distribution used in the derivation of the logarithmic series distribution. When an individual is chosen at random from either of the populations, the abundance of the species it represents is shown to have the same distribution. The maximum likelihood estimate for the geometric series model with fixed abundances is evaluated, and a bias correction is proposed.

Key Words: Abundance of species • Ecology • Geometric series • Logarithmic series distribution • Maximum likelihood


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