# [R-sig-eco] slope for rarefaction curve

Jari Oksanen jari.oksanen at oulu.fi
Mon May 11 11:09:41 CEST 2015

```Basic algebrra seems to lead to this function:

rarederatk <-
function (x, k)
{
x <- x[x>0]
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-bounces at r-project.org> on behalf of Zoltan Botta-Dukat <botta-dukat.zoltan at okologia.mta.hu>
Sent: 11 May 2015 08:49
To: r-sig-ecology at 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
>
> _______________________________________________
> R-sig-ecology mailing list
> R-sig-ecology at r-project.org
> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology

--
Botta-Dukát Zoltán
--------------------------------
Ökológiai és Botanikai Intézet
Ökológiai Kutatóközpont
--------------------------------
2163. Vácrátót, Alkotmány u. 2-4.
tel: +36 28 360122/157
fax: +36 28 360110
botta-dukat.zoltan at okologia.mta.hu
www.okologia.mta.hu

Zoltán BOTTA-Dukát
--------------------------------
Institute of Ecology and Botany
Centre for Ecological Research
--------------------------------
H-2163 Vácrátót, Alkomány u. 2-4.
HUNGARY
Phone: +36 28 360122/157
Fax..: +36 28 360110
botta-dukat.zoltan at okologia.mta.hu
www.okologia.mta.hu

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