bipartite (version 0.90)

nestedness.corso: Calculates the (weighted) nestedness of a network according to the method proposed by Corso et al. (2008), with weighting option by Galeano et al. (2008).

Description

Calculates a nestedness value (not unlike the matrix temperature returned by nestedness, but in the interval [0,1] (0 means no nesting, 1 perfect nesting). Nestedness according to this function differs fundamentally in the way it is calculated. Roughly, it describes the observed distances between links in the network matrix, and compares that to what is possible under the given connectance. The weighted version builds on the fact that at some point during the calculations of Corso et al.'s nestedness index the Manhattan distance is used to calculate distances between cells. Here, we can slot in a simple weight (in this case the respective dependencies) and hence weight the distance by the number of observations (or rather the dependencies).

Usage

nestedness.corso(web, weighted=FALSE, reps=500)

Arguments

web

A matrix with lower trophic level species as rows, higher trophic level species as columns and number of interactions as entries.

weighted

Should the quantitative version, using number of observations to calculate weights, be used? Defaults to FALSE.

reps

Number of replicates for constructing random networks (used in the weighted version to find the minimum nestedness). Defaults to 5000. Anything less than 1000 would be very unsensible, while 10000 and more will take up time (only a few seconds per 1000).

Value

• The nestedness value, ranging between 0 (perfect nesting) and 1 (chaos).

encoding

latin1

Details

The logic and descriptions are available from the two references. However, it may be useful to point out that while there is a straightforward way to calculate observed, maximum and minimum nestedness for the unweighted version, the weighted version has an element of heuristics (i.e. fiddling). In principle, both versions sort the matrix by arranging rows and columns to densest packing, then calculate distances between (occupied) cells and sum those. Then the same is done for the minimally and maximally nested matrix with the same dimensions and number of links. For the weighted version, however, only the maximally nested can be identified uniquely, not the unnested maximum. Hence, we resorted to using the shuffle.web function to produce random, high-entropy webs, that serve to delimit the lowest possible nestedness. Furthermore, because the real maximum chaos cannot be derived (to my knowledge) algorithmically, we use the 95% quantile of 500 randomisations as maximum. This will lead to a consistently overestimated nestedness, but it is less sensitive to the number of replicates than the max.

References

Corso G, de Ara�jo AIL, de Almeida AM (2008) A new nestedness estimator in community networks. arXiv 0803.0007v1 [physics.bio-ph] Galeano J, Pastor JM, Iriondo JM (2008) Weighted-Interaction Nestedness Estimator (WINE): A new estimator to calculate over frequency matrices. arXiv 0808.3397v1 [physics.bio-ph] Ulrich, W. and Gotelli, N.J. (2007) Null model analysis of species nestedness patterns. Ecology 88, 1824--1831

See Also

See also as nestedness and discrepancy

Examples

data(Safariland)
nestedness.corso(Safariland, weighted=TRUE, reps=1000)