A framework for hierarchical compound topologies in species interaction networks

Hierarchical compound topologies of interaction networks that are segmented into internally nested modules have received scant attention, compared to simple nested and modular topologies. This is due to the lack of a theoretical model that encompasses all relevant alternative topologies, and an effective method to differentiate compound from simple topologies. Here we present a framework to address compound topologies in ecological networks. We propose a mechanistic schema of processes that generate modular, nested and compound topologies, based on differences in availability and preferences among species. We show that, in combination, these processes produce a unique signature in the structure of compound topologies. Then, we propose a procedure to identify this signature and hence discriminate among simple and compound topologies. We test the efficiency of this procedure in a set of synthetic matrices and then apply it to an actual plant-herbivore network (Asteraceae and their flowehead feeders in Brazil). In this case, the compound topology is clearly substantiated, demonstrating that these advances are applicable to empirical ecological networks and that compound patterns decidedly belong to the array of topologies to be probed in interaction assemblages at various scales. By including extramodular structures in the analysis of compound topologies, we enhance our understanding of how community-wide networks are organized and their responses to various drivers.