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).