Calculates the NODF_c metric proposed by Song et al (2017) for a bipartite incidence matrix
NODFc(web, quality = 0)A numeric matrix describing a bipartite network (a bipartite incidence matrix where elements are positive numbers if nodes interact, and 0 otherwise).
An optional quality parameter to control the tradeoff between computation time and result quality. Can be 0, 1 or 2.
Returns the value of NODF_c as a single number.
For a given network, NODFc calculates the NODF_c metric proposed by Song et al (2017), defined as \((NODF/max(NODF))/(C * log(S))\) where C is the network connectance, S is the geometric mean of the number of plants and pollinators in the network,
NODF is the raw NODF of the network and max(NODF) is the maximum nestedness that can be achieved in a network with the same number of rows, columns and links as web, subject to the constraint that all rows and columns must have at least one link (i.e. marginal totals must always be >= 1).
NODFc 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.
Song, C., Rohr, R.P. and Saavedra, S., 2017. Why are some plant<U+2013>pollinator networks more nested than others? Journal of Animal Ecology, 86(6), pp.1417-1424
# NOT RUN {
set.seed(123)
NODFc(matrix(sample(x = 0:1, size = 100, replace = TRUE),10,10), quality = 0)
# }
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