Nested interaction network enhances responsiveness in collective behavior

Survival in dynamic and complex environments requires groups to exhibit a high level of responsiveness to rapidly changing circumstances. Recent studies have shown the role of selective social interactions in driving responsive collective behavior at the individual-level decision making. However, much less effort has been devoted to understanding how structures of interaction networks shape collective responses. Here we show that the highly nested structures enhance responsiveness in schooling fish and swarm robotics. First, analysis of trajectories from schooling Hemigrammus rhodostomus reveals that the high nestedness, quantified through the nestedness metric based on overlap and decreasing fill (NODF), emerges as a key interaction structure feature in maneuverable movements. Using a general contagion model, we then show that the perfectly nested interaction network (PNIN) achieves the optimal information transfer efficiency. Furthermore, we integrate the PNIN into the self-propelled system and demonstrate the advantages of PNIN in facilitating efficient and robust collective responses through semi-physical simulations and 50 real robots. Our study provides a modeling perspective to elucidate collective responses through structural arrangements of interaction networks. Survival in dynamic and complex environments requires groups to exhibit a high level of responsiveness to rapidly changing circumstances. Using empirical data from Hemigrammus rhodostomus fish schools and experiments with swarm robotics, the study demonstrates that perfectly nested interaction networks enhance information flow and shape highly responsive collective behavior in both collective hovering and following tasks.