bipartite (version 2.16)

czvalues: Computes c and z for network modules

Description

Function to compute c and z values of module members according to Guimer<U+00E0> & Amaral (2005), with formulae taken from Olesen et al. (2007)

Usage

czvalues(moduleWebObject, weighted=FALSE, level="higher")

Arguments

moduleWebObject

A moduleWeb-class object as created by computeModules.

weighted

logical; if TRUE computes c and z from quantitative (=weighted) data; in this case, it will compute strength, rather than degrees for each species.

level

"higher" or "lower" trophic level to compute c and z values for; defaults to "higher"

Value

A list with two vectors, c and z, for all species of the selected trophic level.

Details

c = 1 - sum( (k.it/k.i)^2) # among-module connectivity = participation coefficient P in Guimer<U+00E0> & Amaral

z = (k.is - ks.bar) / SD.ks # within-module degree

k.is = number of links of i to other species in its own module s; ks.bar = average k.is of all species in module s; SD.ks = standard deviation of k.is of all species in module s; k.it = number of links of species i to module t; k.i = degree of species i

Note that for any species alone (in its level) in a module the z-value will be NaN, since then SD.ks is 0. This is a limitation of the way the z-value is defined (in multiples of degree/strength standard deviations).

Olesen et al. (2006) give critical c and z values of 0.62 and 2.6, respectively. Species exceeding these values are deemed connectors or hubs of a network. The justification of these thresholds remains unclear to me. They may also not apply for the quantitative version.

References

Guimer<U+00E0>, R. and Amaral, L.A.N. (2005) Functional cartography of complex metabolic networks. Nature 433, 895--900.

Olesen, J.M., Bascompte, J., Dupont, Y.L. and Jordano, P. (2007) The modularity of pollination networks. Proceedings of the National Academy of Sciences of the USA 104, 19891-19896.

Examples

# NOT RUN {
set.seed(2)
mod <- computeModules(memmott1999)
cz <- czvalues(mod)
plot(cz[[1]], cz[[2]], pch=16, xlab="c", ylab="z", cex=0.8, xlim=c(0,1), las=1)
abline(v=0.62) # threshold of Olesen et al. 2007
abline(h=2.5)   # dito
text(cz[[1]], cz[[2]], names(cz[[1]]), pos=4, cex=0.7)

# example for computing a c- or z-threshold:
mod <- computeModules(Safariland)
czobs <- czvalues(mod)
nulls <- nullmodel(Safariland, N=10) # this should be larger, of course
null.mod.list <- sapply(nulls, computeModules)
null.cz <- lapply(null.mod.list, czvalues)
# compute 95<!-- % CI for c and z: -->
null.cs <- sapply(null.cz, function(x) x$c) # c-values across all species in nulls
quantile(null.cs, 0.95) 
# this could now serve as thresholds for identifying particularly uncommonly high c-values
# and analogously for z, of course
# }