ILSM: A package for analyzing the interconnection structure of tripartite interaction networks

In natural or human-disturbed ecosystems, ecological networks often comprise multiple interaction types, which have been often represented by multipartite ecological networks. One important aspect of their network architecture is how different interaction types or subnetworks are interconnected by shared species, here defined as the interconnection structure. Previous studies have proposed various indices of shared species to characterize macro-scale interconnection patterns and micro-scale centrality, but the meso-scale interconnection structures (here defined as interconnection motifs) remain largely unexplored. Furthermore, there is no package available in the R programming language for conducting analyses of various interconnection structures. Within a tripartite network with two interaction subnetworks, we define the forms of interconnection motifs and unique roles within these motifs. Then we introduce the R package ILSM for analyzing interconnection patterns, interconnection centrality, and interconnection motif. Specifically, we derive mathematical expressions for the frequencies of interconnection motifs and species roles within motifs. We describe the main functions in the package and demonstrate their uses with an example pollinator-plant-herbivore network. ILSM will help ecologists understand how different types of interactions are interconnected together by shared species using interconnection pattern, centrality and motif.