Who dominates whom in the ecosystem? Energy flow bottlenecks and cascading extinctions

In this paper, we investigate the problem of secondary extinction in food webs through the use of dominator trees, network topological structures that reduce food webs to linear pathways that are essential for energy delivery. Each species along these chains is responsible for passing energy to the taxa that follow it, and, as such, it is indispensable for their survival; because of this it is said to dominate them. The higher the number of species a node dominates, the greater the impact resulting from its removal. By computing dominator trees for 13 well-studied food webs we obtained for each of them the number of nodes dominated by a single species and the number of nodes that dominate each species. We illustrate the procedure for the Grassland Ecosystem showing the potential of this method for identifying species that play a major role in energy delivery and are likely to cause the greatest damage if removed. Finally, by means of two indices that measure error and attack sensitivity, we confirm a previous hypothesis that food webs are very robust to random loss of species but very fragile to the selective loss of the hubs.