Prohibition rules for three-node substructures in ordered food webs with cannibalistic species

We evaluate the spectrum of ordered three-node substructures in food webs taking self-links (cannibalism) into account. If the order of nodes in the network cannot be neglected, 512 substructures can be distinguished. Simple statistical models of networks impose constraints on the structure that prohibit a large number of substructures completely. We analyse two variants of the widely used niche model, the original niche model and the generalised niche model, and show analytically and numerically that they exclude 344 and 320 substructures, respectively. The prohibition rules for three-node substructures in the two niche-model variants are further contrasted with a large set of empirical food webs, which reveals that up to about 30% of the three-node substructures that occur in empirical food webs are prohibited by the model algorithms.