Hierarchical compound topology uncovers complex structure of species interaction networks.

Nestedness and modularity have been found in many species interaction networks. Despite being conceptually distinct, negatively correlated and having different causes, these patterns often co-occur. A realistic but seldom investigated alternative to these simple topologies is hierarchical compound networks, in which the entire network is modular, and modules are internally nested. In compound networks, nestedness is suppressed by modularity at higher network hierarchical levels, but prevails at lower levels, within modules. The aims of this study are (i) to evaluate the prevalence of simple and hierarchical compound topologies in binary and weighted networks describing different kinds of species interactions and (ii) to probe the relationships between modularity and nestedness at different network hierarchical levels. With a procedure that discriminates between simple and compound structures, we re-analysed the topology of 142 well-studied binary networks including seed dispersal, host-parasite, pollination and plant-herbivore interactions; 68 of these also had quantitative information. Additionally, we tested the relationship between robustness and topology of binary networks and compared the robustness of networks with compound topologies to different sequences of species removals. Compound topologies were detected in 34% of binary and 71% of weighted networks of all interaction kinds. These results establish the hierarchical compound topology as a widespread network architecture, often undetected without quantitative data. Furthermore, they disentangle an apparent paradox: despite conflicting with overall nestedness, modularity usually co-occurs with high values of low-level nestedness. Nestedness progressively decreased, while modularity increased, from seed dispersal to host-parasite, pollination and plant-herbivore networks. There were no consistent differences in the robustness of networks with nested and compound topologies. However, compound topologies were especially vulnerable to removal sequences that accelerate the exclusion of entire modules. Compound topologies improve the depiction of ecological networks and differentiate ecological and evolutionary processes that operate at different hierarchical levels, with the potential to advance our understanding of network dynamics, stability and response to species loss or change. Quantitative data often reveal specialization patterns that are indistinguishable in binary networks, strongly improving the detection of modular and compound topologies.