Pushing ecological networks over the edge: Hypergraph topology of trait-mediated effects
Unraveling the tremendous complexity of ecological systems is crucial for understanding their structure and function, despite challenges it poses. Ecologists have gained much insight in recent decades from studying the topologies of ecological networks: patterns of interactions between species. Almost universally, however, this work has involved networks consisting only of pairwise interactions. That approach is ill-suited for considering many ecologically important phenomena, which are fundamentally properties of more than two species. Prime examples include trait-mediated indirect interactions (TMIIs) and interaction modifications (IMs) associated with adaptive behaviors, which have repeatedly been shown to be crucial for the structure and function of ecological systems, provisioning of key system services, and recovery from disturbance. Hypergraphs are mathematical constructs capable of considering interactions between sets of three or more nodes, and have recently proven extremely valuable for the study of biomolecular networks. Here, we discuss the potential value of using hypergraphs to study the topology of ecological networks, as well as challenges associated with doing so. We demonstrate the approach using a real-world complex coffee agroecosystem, in which ants act as keystone species by imposing a large number of IMs, several of which are further modified by flies which parasitize the ants.
We demonstrate that a hypergraph representation of the system is able to successfully reflect both the significance of trait-mediated interactions for species' relative importance in the system, and also the context-dependency of that importance. In our example system, this is exemplified by parasitic phorid flies. These flies impose a large number of trait-mediated effects, but all represent modifications of other trait-mediated effects imposed by ants. Centrality metrics highlight phorid flies as one of the more important species in the hypergraph representation of the full system (with ants present), but not in the hypergraph representation of a system from which ants have been deleted. This represents an improvement over both the graph representation (in which phorid fly centralities are always low) and an alternative 'clique multigraph' representation (in which phorid fly centralities remain high even in the absence of ants). The prospect of topologically encoding such detail regarding the ways in which non-pairwise interactions are structured holds great promise for understanding their roles in complex ecological systems.