untb (version 1.2-5)

logkda: Etienne's K(D,A)

Description

Calculates Etienne's $K(D,A)$

Usage

logkda(a)
logkda.a11(a)

Arguments

a

Count object

Details

Function logkda() calculates $K(D,A)$ using the method appearing in Etienne (2005), supplementary online material. 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

See Also

etienne,logS1

Examples

a <- count(c(dogs=7,pigs=3,crabs=1,hogs=1,slugs=1))
logkda(a)
logkda.a11(a)