bipartite (version 0.7)

discrepancy: Calculates discrepancy of a matrix

Description

Discrepancy is the number of mismatches between a packed (binary) matrix and the maximally packed matrix (with same row sums)

Usage

discrepancy(mat)

Arguments

mat

A matrix (or something that can be transformed into a matrix when as.matrix is called within the function) of species (in columns) on islands (in rows). If quantitative data are given (e.g. in a quantitative pollination network), these are in

Value

• Returns the number of mismatches, i.e. the discrepancy of the matrix from perfecct nestedness.

encoding

latin1

Details

Discrepancy is a way to measure the nestedness of a matrix. In a comparative study, Ulrich & Gotelli (2007) showed discrepancy to outperform all other measures and hence recommend its use (together with a fixed-columns, fixed-rows null model, such as implemented in commsimulator in vegan, see example). This function follows the logic laid out by Brualdi & Sanderson (1999), although, admittedly, I find their mathematical description highly confusing. Another implementation is given by the function nesteddisc in vegan. The reason to write a new function is simple: nesteddisc returns the wrong results, even when used on the simple example matrix given in Brualdi & Sanderson. This is very strange, because Jari Oksanen is a very meticulous and efficient programmer, and you (the user) may want to trust his version more than this one. Having said that, values don't differ much between the two implementations. (The real reason why I wrote discrepancy anew was that I wasn't aware of nesteddisc. I was sitting on a train and I wanted to use this measure later on, so I put it into a function consulting only the orignal paper. When looking for the swap algorithm to create null models, which I somehow knew to exist in vegan, I stumbled across nesteddisc. If you are interested in the swap algorithm and come across this help page, let me re-direct you to oecosimu in vegan.) So what does it do: The matrix is sorted by marginal totals, yielding a matrix A. Then, all 1s in A are pushed to the left to maximally compact the matrix, yielding P. Discrepancy is now simply the number of disagreements between A and P, divided by two (to correct for the fact that every wrong 1 will necessarily generate a wrong 0).

References

Brualdi, R.A. and Sanderson, J.G. (1999) Nested species subsets, gaps, and discrepancy. Oecologia 119, 256--264 Ulrich, W. and Gotelli, N.J. (2007) Disentangling community patterns of nestedness and species co-occurrence. Oikos 116, 2053--2061

See Also

nestedness for the most commonly used method to calculate nestedness, nestedness.corso for a new, unevaluated but very fast way to calculate nestedness; nestedtemp (another implementation of the same method used in our nestedness) and nestedn0 (calculating the number of missing species, which has been shown to be a poor measure of nestedness) in vegan

Examples

data(Safariland)
require(vegan)
nulls <- replicate(1000, discrepancy(commsimulator(Safariland, method="quasiswap")))
hist(nulls)
obs <- discrepancy(Safariland)
abline(v=obs, lwd=3, col="grey")
c("p value"=min(sum(nulls>obs), sum(nulls<obs))/length(nulls))
# calculate Brualdi & Sanderson's Na-value (i.e. the z-score):
c("N_a"=(unname(obs)-mean(nulls))/sd(nulls))