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

Abstract

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.

Keywords:

• motif analysis
• food webs
• cannibalism
• node ordering
• body mass
• niche model

Acknowledgements

We are grateful to Ulrich Brose and Christoph Digel for providing the experimental data on food-web structures.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The collaboration on this project was supported by Research Unit FOR 1748 funded by the DFG. Christian Guill was supported by the Leopoldina Fellowship Programme [grant number LPDS 2012-07]. Pavel Paulau was supported by Volkswagenstiftung [grant number 85 183] and DFG [grant number BL 772/2-1].