logkda: Etienne's K(D,A)

Description

Calculates Etienne's $K(D,A)$ using a variety of different methods

Usage

logkda.R(a, use.brob=TRUE)
logkda.a11(a)
logkda.pari(a, numerical=TRUE)
logkda(a, method="pari", ...)

Arguments

Count object

use.brob

In function logkda.R(), Boolean, with default TRUE meaning to use Brobdingnagian numbers for the calculation. This is slower but allows one to analyze larger datasets

numerical

In function logkda.pari(), Boolean, with default TRUE meaning to return a numerical vector and FALSE meaning to return the string produced by pari/gp

method

In function logkda(), a string specifying which method to use. Takes R, a11, or pari

...

In function logkda(), further arguments which are passed to the other functions

Details

The user should use function logkda(), which is a wrapper for the other functions. Note that the default method, pari, requires the pari/gp system to be installed. This is the preferred option because it is much faster than the other methods. Functions logkda.R() and logkda.pari() calculate $K(D,A)$ using the method appearing in Etienne (2005), supplementary online material; they use R and pari/gp respectively. Function logkda.a11 is a direct implementation of formula A11 in Etienne (2005). The formula is

$$K(D,A)= \sum_{\left{a_1,\ldots,a_S|\sum a_i=A\right}} \prod_{i=1}^S\frac{ \overline{s}\left(n_i, a_i\right) \overline{s}\left(a_i, 1\right) }{ \overline{s}\left(n_i,1\right)}$$ where $\overline{s}\left(n_i,a_i\right)$ are Stirling numbers of the first kind (see logS1).

References

R. S. Etienne 2005. A New Sampling Formula for Neutral Biodiversity. Ecology Letters, volume 8, pp253--260. doi: 10.111/j.1461-0248.2004.00717.x

C. Batut and K. Belabas and D. Bernardi and H. Cohen and M. Olivier 2000. User's guide to PARI/GP. http://www.parigp-home.de/

Examples

Run this code

a <- count(c(dogs=7,pigs=3,crabs=1,hogs=1,slugs=1))

logkda(a)

logkda.R(a)
logkda.R(a, use.brob=FALSE)
logkda.a11(a)
# All four should be the same up to numerical errors