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The robustness of ecosystems to species losses is a central question in ecology, given the current pace of extinctions and the many species threatened by human impacts, including habitat destruction and climate change. Robustness from the perspective of secondary extinctions has been addressed in the context of food webs to consider the complex network of species interactions that underlie responses to perturbations. In-silico removal experiments have examined the structural properties of food webs that enhance or hamper the robustness of ecosystems to species losses, with a focus on the role of hubs, the most connected species. Here we take a different approach and focus on the role of the connections themselves. We show that trophic links can be divided into functional and redundant based on their contribution to robustness. The analysis of empirical webs shows that hubs are not necessarily the most important species as they may hold many redundant links. Furthermore, the fraction of functional connections is high and constant across systems regardless of size and interconnectedness. The main consequence of this scaling pattern is that ecosystem robustness can be considerably reduced by species extinctions even when these do not result in any secondary extinctions. This introduces the possibility of tipping points in the collapse of ecosystems.

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In this paper we investigate ecological flow networks via graph theory in search of the real sequential chains through which energy passes from producers to consumers in complex food webs. We obtain such fundamental pathways by identifying strongly connected components (SCCs), subsystems that groups species that take part in cycling, and performing topological sorting on the acyclic graphs that are obtained. Topological sorting identifies preferential directions for energy to flow from sources to sinks, while recycling remains confined within each SCC. Resolving food web networks for SCC highlights the possibility that compartments can be found in ecosystems, but this does not seem a general rule. The four aquatic food webs described in detail show a rather clear subdivision between benthic and pelagic subcommunities, a result that is discussed in the light of other studies. Should further research confirm these results, new insight into the way ecosystems use energy will be provided, with implications on cycling, reciprocal dependency of variables and indirect effects.