vaznull {bipartite}

Null model with constrained connectance and moderately constrained marginal totals

Description

Implements Diego Vazquez proposal of a null model for pollination networks

Usage

 vaznull(N, web) 

Arguments

N

Number of desired null model webs.

web

An interaction matrix.

Details

This function produces a null model network with the main constraint of a connectance that is the same as in the original network. In the process of producing this null model, marginal totals will turn out to be different from the original network, less so for large, dense webs than for small, sparse webs. vaznull is our implementation of the algorithm proposed by Diego Vazquez, hence its name. vaznull differs from swap.web in that marginal totals are not strictly constrained! The algorithm used as well as the null model it outputs are different.

The algorithm was described as follows: "The algorithm randomized the total number of individual interactions observed in the original interaction matrix, F. To this end, the algorithm first created a binary matrix, assigning interspecific interactions according to species-specific probabilities, requiring that each species had at least one interaction. As in Vazquez et al. (2005b), the species-specific probabilities were proportional to species' relative abundances (probabilities are in fact approximately proportional and not equal to relative abundances because of the requirement that each species receives at least one interaction; this requirement causes probabilities to deviate from relative abundances, especially for rare species). Once the number of filled cells in the original matrix was reached, the remaining interactions were distributed among the filled cells, so that connectance in the original and randomized matrices was the same." (Vazquez et al. 2007, page 1122-1123).

Value

A list of N randomised matrices with the same dimensions and connectivity as the initial web.

Author(s)

Bernd Gruber <[e-mail]> & Carsten F. Dormann <[e-mail]>

References

Vázquez, D. P., C. J. Melian, N. M. Williams, N. Blüthgen, B. R. Krasnov, and R. Poulin. 2007. Species abundance and asymmetric interaction strength in ecological networks. Oikos 116: 1120-1127.

See Also

r2dtable, swap.web

Examples

	## Not run: 
		data(Safariland)
		networklevel(Safariland, index="info")
		networklevel(vaznull(1, Safariland)[[1]], index="info")
		system.time(vaznull(10, Safariland))
		system.time(swap.web(10, Safariland))
	
## End(Not run)