metacom (version 1.5.1)

Modularity: Calculates Barber's Bipartite Modularity

Description

Modularity, community formation, boundary clumping. Call it what you want, there is a fair amount of overlap in definition here. As such, we posit that modularity statistics may be able to detect boundary clumping better than Morisita's index. We offer a function here to calculate modularity. Specifically, this function calculates Barber's Q statistic, and compares it relative to null model randomizations.

Usage

Modularity(comm, method = "tswap", sims = 1000, scores = 1,
  order = TRUE, c = length(comm), nstarts = 100, returnModules = FALSE)

Arguments

comm

community data in the form of a presence absence matrix

method

null model randomization method used by NullMaker. See details below (and the help file of fucntion NullMaker) for more information.

sims

number of simulated null matrices to use in analysis

scores

axis scores to ordinate matrix. 1: primary axis scores (default) 2: secondary axis scores

order

logical argument indicating whether to ordinate the interaction matrix or not. See details.

c

starting guess for the number of modules present. Defaults to the maximum number of modules possible.

nstarts

number of starts. Default is 100. More will both slow the function down, and increase the likelihood of converging on the true modularity value.

returnModules

logical argument indicating whether to return a vector of module IDs

Value

A vector containing Barber's modularity statistic (Q), the z statistic comparing observed modularity against null matrices (z), p-value (pval), and mean (simulatedMean) and variance (simulatedVariance) from null model simulations

Details

method is an argument handed to functions in the vegan package. Leibold & Mikkelson advocated the use of equiprobable rows and columns (provided that rows and columns had at least one entry). This method is called r00. Methods maintaining row (site) frequencies include r0,r1, and r2. The default method argument is r1, which maintains the species richness of a site (row totals) and fills species ranges (columns) based on their marginal probabilities. Arguably the most conservative null algorithm is the fixed row - fixed column total null, which can be attained using many of swap algorithms described in the vegan package (sequential methods like tswap, swap, and non-sequential quasiswap and backtracking). See the help file for commsim or Wright et al. 1998 for more information.

If order is FALSE, the interaction matrix is not ordinated, allowing the user to order the matrix based on site characteristics or other biologically relevant characteristics.

References

Barber, M. J. 2007. Modularity and community detection in bipartite networks. Physical Review E, 76(6), 066102.

Leibold, M.A. and G.M. Mikkelson. 2002. Coherence, species turnover, and boundary clumping: elements of meta-community structure. Oikos 97: 237 - 250.

Wright, D.H., Patterson, B.D., Mikkelson, G.M., Cutler, A. & Atmar, W. (1998). A comparative analysis of nested subset patterns of species composition. Oecologia 113, 1-20.

Examples

# NOT RUN {
#define an interaction matrix
data(TestMatrices)
intmat <- TestMatrices[[3]]

#determine Barber"s modularity
mod.intmat <- Modularity(intmat, method="r1", sims=5,
 scores=1, order=TRUE, nstarts=10)

#return results
mod.intmat

# }