Just for your information: new version of vegan (2.3-0) is now available on
CRAN, and it has function rareslope() that finds the slope of the rarefaction
curve at given sample size. It can also calculate the slope at at intermediate
non-integer sample sizes. Together with this, the latest vegan also adds
similar slope calculations for analytic species accumulation models (exact,
rarefaction, coleman) plus all non-linear regression models in
fitspecaccum() (function specslope()).
Cheers, Jari Oksanen
On 11/05/2015, at 12:09 PM, Jari Oksanen wrote:
Basic algebrra seems to lead to this function:
rarederatk -
function (x, k)
{
x - x[x0]
J - sum(x)
d - digamma(J-k+1) -digamma(J-x-k+1)
g - lgamma(J-x+1) + lgamma(J-k+1) - lgamma(J-x-k+1)-lgamma(J+1)
d - d*exp(g)
sum(d[is.finite(d)])
}
Here 'x' must be a vector of species abundances for a single site, and 'k'
the sample site at which the
derivative is evaluate. Here a simple test that this seems to work (but
please check):
library(vegan)
data(mite)
rarecurve(mite[1,]) # first sampling point
sum(rarecurve(mite[1,]) # 140, evaluate at 126 individuals
y - rarefy(mite[1,], 126) # 19.47011
b - rarederatk(mite[1,], 126) # derivetive 0.04032 (with warnings)
abline(y-126*b, b) # matches the rarecurve plot
Cheers, Jari Oksanen
From: R-sig-ecology r-sig-ecology-boun...@r-project.org on behalf of Zoltan
Botta-Dukat botta-dukat.zol...@okologia.mta.hu
Sent: 11 May 2015 08:49
To: r-sig-ecology@r-project.org
Subject: Re: [R-sig-eco] slope for rarefaction curve
Dear Simone,
Function rarefy uses the function developed by Hurlbert, thus if you
need slope in a certain point (as your graph suggests) you can calculate
the derivative of this function. It is not an easy job, because
factorials should be derived. See cues here how it can be done:
http://math.stackexchange.com/questions/300526/derivative-of-a-factorial
If you need mean slope in an interval, simply calculate the difference
in the calculated values for the beginning and end of the interval, and
divide the difference by the length of the interval.
Zoltan
2015.05.10. 23:57 keltezéssel, Simone Ruzza írta:
Dear all,
apologies for the total beginner's question. I was wondering if anyone
can give some advice on how to calculate the slope for the last 10% of
the records of a rarefaction curve computed with rarefy from vegan.
Here is a graphic representation of what I would like to do:
https://dl.dropboxusercontent.com/u/33966347/figure.JPG
I have seen that this has been done in a recent paper and I was
wondering if anyone may have any code snippet to do that. Sorry, maybe
this is something really obvious but I have not quite understood how
to do it.
thanks!
Simone
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Botta-Dukát Zoltán
Ökológiai és Botanikai Intézet
Magyar Tudományos Akadémia
Ökológiai Kutatóközpont
2163. Vácrátót, Alkotmány u. 2-4.
tel: +36 28 360122/157
fax: +36 28 360110
botta-dukat.zol...@okologia.mta.hu
www.okologia.mta.hu
Zoltán BOTTA-Dukát
Institute of Ecology and Botany
Hungarian Academy of Sciences
Centre for Ecological Research
H-2163 Vácrátót, Alkomány u. 2-4.
HUNGARY
Phone: +36 28 360122/157
Fax..: +36 28 360110
botta-dukat.zol...@okologia.mta.hu
www.okologia.mta.hu
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