Calculates the maximum NODF that be achieved in a network with a given number of rows, columns and links.
maxnodf(web, quality = 0)
Either a numeric matrix describing a bipartite network (a bipartite incidence matrix where elements are positive numbers if nodes interact, and 0 otherwise) or a numeric vector of length 3 of the form web = c(#Rows, #Columns, #Links).
An optional quality parameter to control the tradeoff between computation time and result quality. Can be 0, 1 or 2.
For a given network,
maxnodf calculates the maximum nestedness that can be achieved in a network with a given number of rows, columns and links, subject to the constraint that all rows and columns must have at least one link (i.e. marginal totals must always be >= 1).
This allows nestedness values to be normalised as NODF/max(NODF) following Song et al (2017). To control for connectance and network size, Song et al. (2017) suggest an additional normalisation that
can be used: (NODF/max(NODF))/(C * log(S)) where C is the network connectance and S is the geometric mean of the number of plants and pollinators in the network.
maxnodf has three algorithms for finding the maximum nestedness of a bipartite network. These can be set using the
quality argument. Lower quality settings are faster, but find worse optima. Higher quality settings
are slower, but find better optima.
quality = 0, uses a greedy algorithm.
quality = 1, uses a greedy algorithm plus hillclimbing.
quality = 2, uses a simulated annealing algorithm, with the greedy algorithm output as the start point. Best results, but requires the most computation time.
Returns a list of length 2, where the first element ('max_nodf') is the maximum nestedness of the network and the second element ('max_nodf_mtx') is the incidence matrix corresponding to this maximum nestedness.
Song, C., Rohr, R.P. and Saavedra, S., 2017. Why are some plant–pollinator networks more nested than others? Journal of Animal Ecology, 86(6), pp.1417-1424
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