Secondary extinctions in ecological networks: bottlenecks unveiled

In ecosystems, a single extinction event could eventually precipitate in a mass extinction, involving species that may be several connections away from the target of the perturbation. This topic has been illuminated by recent studies on network mechanics, thanks to the concepts of hub, error and targeted removal, attack sensitivity, small world, and so forth. To forecast the effects of a species removal one can use an algorithm that unfolds a complex food web into a topologically simpler scheme, called its dominator tree. This structure is simple, elegant, and highly informative; all the bottlenecks and the effects of species removal are clearly traceable. While food web studies are mostly qualitative, in this paper the use of the dominator tree is extended to weighted food webs, in which link magnitude is specified. These structures were obtained from ecological flow networks. in eight of these food webs, the analysis consisted in removing links that were weaker than a threshold of magnitude and building the dominator tree associated to the remaining structure. By progressively increasing the threshold up to the value that would make the graph disconnected, we had the opportunity to investigate patterns of dominance as a function of link magnitude.