Calculates Etienne's \(K(D,A)\) using a variety of different methods
logkda.R(a, use.brob=TRUE)
logkda.a11(a)
logkda.pari(a, numerical=TRUE, gp_binary = "gp")
logkda.polyn(a)
logkda(a, method="pari", ...)
logkda_pari_unix(a, numerical, pari_string, gp_binary)
logkda_pari_windows(a, numerical, pari_string)
Count object
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
Boolean, with default TRUE meaning to coerce
to a numerical vector (thereby losing precision), and FALSE
meaning to return the string produced by pari/gp
In function logkda(), a string specifying which
method to use. Takes “R”, “a11”, or “pari”
configuration variables (not intended to be changed by the user)
In function logkda(), further arguments which are
passed to the other functions
Robin K. S. Hankin; logkda() is an R transliteration of
pari/gp code appearing in Etienne 2005 (supplementary online
material) due to Chave.
Function logkda.polyn() provided by Francois Munoz.
Function .logkda.pari.windows() provided by Andrea Manica and
Francois Munoz.
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).
Function logkda.pari() dispatches to either
logkda_pari_unix() or logkda_pari_windows() but the
windows function is not guaranteed to work.
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/
etienne,logS1
a <- count(c(dogs=7,pigs=3,crabs=1,hogs=1,slugs=1))
if (FALSE) logkda(a)
logkda.R(a)
logkda.R(a, use.brob=FALSE)
logkda.a11(a)
# All four should be the same up to numerical errors
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