[R-sig-eco] unbiased estimator of Simpson's index

[Emili Garcia-Berthou]

Dear list:

I'll give a question and the answer this time, just in case it helps to
anybody in the future :-)

The standard formulae of Simpson's index of diversity (and other indices)
are available with the diversity function of the vegan package. For some
time, I wished to compute the unbiased estimator of Simpson's index (see
e.g. equation 5 in Hurlbert 1971 Ecology 52: 577-586 or page 115 of Magurran
2004's book "Measuring Biological Diversity")). I thought this was not
readily available in R and found no hints on mailing lists but Jari Oksanen
just suggested to me that it can be computed with something like

rarefy(x, 2) - 1

(You should take care of zero-richness samples, though).

I discovered afterwards at
vignette("diversity-vegan")

"the rarefied richness for two individuals is a finite sample variant of
Simpson's diversity index (or, more precisely of D1 + 1)"
 
Thanks to Jari (and the other vegan authors) for the answer and such a
useful package.

Cheers,


Emili GARCÍA-BERTHOU, Professor of Ecology
Institut d'Ecologia Aquàtica & Dept. Ciències Ambientals
Universitat de Girona, E-17071 GIRONA (Catalonia, Spain)

Tel.: +34 650 640 914 (dins UdG: 9221); Fax:  +34 972 418 150
Personal web page: http://invasiber.org/EGarcia/