Motif profile dynamics and transient species in a Boolean model of mutualistic ecological communities

Network motifs are generally studied to characterize the local interaction patterns of networks. Here, we apply the concept of a motif profile to a synchronous Boolean network model of the formation of mutualistic ecological communities, focusing on four-node subgraphs. We consider the process by which networks dynamically progress from a random initial condition to an attractor (steady state or limit cycle, collectively viewed in this context as a stable community). While the subgraphs are not classified as motifs in the usual sense of the term, we show that subgraphs with predominantly stabilizing (i.e. beneficial for species persistence) interactions are generally composed of species that are present in the attractor. The converse also holds: subgraphs with predominantly destabilizing (i.e. detrimental for species persistence) interactions are more commonly composed of species that are present in the community only transiently. We discuss our findings in the context of mutualistic ecological networks, and argue that the dynamic motif profile may provide a valuable analytical tool in other networks representing complex dynamic systems.