# [R] rarefaction variance

Ben Bolker ben at zoo.ufl.edu
Wed Nov 14 11:47:34 CET 2001

``` This isn't a direct answer to your question, but

documents a program by Steven Holland, and says:

The program uses the rarefaction equations for E given by Hurlbert (1971)
and for Var given by Heck et al. (1975). These are the same equations used
by Raup (1975) and Tipper (1979). In particular, this program uses the
formulation of Tipper (1979), as his equations (1) and (2) are easy to
program and avoid the overflow errors associated with the large
combinatorials.

The Tipper reference is:

Tipper, J.C., 1979. Rarefaction and rarefiction - the use and abuse of a
method in paleontology. Paleobiology 5: 423-434.

Sounds like this might help fix your problem.

Ben Bolker

On Tue, 13 Nov 2001, Michael Camann wrote:

> Here's a question for ecologists on the r-help list-- I'm addressing this
> to ecologists in particular because they're most likely to be familiar
> with the equation in question but I'll be happy to discuss the problem
> with anyone who's willing to take a whack at it.
>
> I'm trying to write a function to calculate the large sample variance of
> species richness estimates by rarefaction using the Heck et al (1975)
> equation.  I won't try to reproduce the equation here because it's complex
> and I don't know how to render it readibly in ASCII characters, but if
> anyone wishes a faxed copy I'll gladly provide one.  If you have Krebs
> _Ecological_Methodology_ it's on page 415 of the second edition.  It's on
> page 27 of Gotelli and Graves _Null_Models_in_Ecology_, and in lots of
> other references as well.
>
> The problem is not the calculations of binary coefficients
> (combinatorials) per se-- I use lgamma(x+1) to do it with logs of
> factorials-- but rather the 1-(quotient of combinatorials) term in the
> first summation which forces me to exp() the log terms before the
> calculation is complete.  This invariably causes an overflow (Inf) with
> all but the most unrealistically small data sets.
>
> So, my questions are: 1) has anyone written an R function to calculate
> this variance and would they be willing to share it, and 2) failing #1, is
> anyone familiar with this equation willing to take a whack at helping me
> write such a function?  As I said, I'll be happy to fax a copy of the
> equation to anyone who does not have it handy but who wants to help solve
> this problem.
>
>
> --Mike C.
>
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> Michael A. Camann                                  Voice: 707-826-3676
> Associate Professor of Zoology                       Fax: 707-826-3201
> Institute for Forest Canopy Research     Email: mac24 at axe.humboldt.edu
> Department of Biology                            ifcr at axe.humboldt.edu
> Humboldt State University
> Arcata, CA 95521
>
>                  URL:http://www.humboldt.edu/~mac24/
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>
>
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