Disentangling the co-structure of multilayer interaction networks: degree distribution and module composition in two-layer bipartite networks.

Species establish different interactions (e.g. antagonistic, mutualistic) with multiple species, forming multilayer ecological networks. Disentangling network co-structure in multilayer networks is crucial to predict how biodiversity loss may affect the persistence of multispecies assemblages. Existing methods to analyse multilayer networks often fail to consider network co-structure. We present a new method to evaluate the modular co-structure of multilayer networks through the assessment of species degree co-distribution and network module composition. We focus on modular structure because of its high prevalence among ecological networks. We apply our method to two Lepidoptera-plant networks, one describing caterpillar-plant herbivory interactions and one representing adult Lepidoptera nectaring on flowers, thereby possibly pollinating them. More than 50% of the species established either herbivory or visitation interactions, but not both. These species were over-represented among plants and lepidopterans, and were present in most modules in both networks. Similarity in module composition between networks was high but not different from random expectations. Our method clearly delineates the importance of interpreting multilayer module composition similarity in the light of the constraints imposed by network structure to predict the potential indirect effects of species loss through interconnected modular networks.