Functional duality in group criticality via ambiguous interactions

Abstract

Critical phenomena are wildly observed in living systems. If the system is at criticality, it can quickly transfer information and achieve optimal response to external stimuli. Especially, animal collective behavior has numerous critical properties, which are related to other research regions, such as the brain system. Although the critical phenomena influencing collective behavior have been extensively studied, two important aspects require clarification. First, these critical phenomena never occur on a single scale but are instead nested from the micro- to macro-levels (e.g., from a Lévy walk to scale-free correlation). Second, the functional role of group criticality is unclear. To elucidate these aspects, the ambiguous interaction model is constructed in this study; this model has a common framework and is a natural extension of previous representative models (such as the Boids and Vicsek models). We demonstrate that our model can explain the nested criticality of collective behavior across several scales (considering scale-free correlation, super diffusion, Lévy walks, and 1/f fluctuation for relative velocities). Our model can also explain the relationship between scale-free correlation and group turns. To examine this relation, we propose a new method, applying partial information decomposition (PID) to two scale-free induced subgroups. Using PID, we construct information flows between two scale-free induced subgroups and find that coupling of the group morphology (i.e., the velocity distributions) and its fluctuation power (i.e., the fluctuation distributions) likely enable rapid group turning. Thus, the flock morphology may help its internal fluctuation convert to dynamic behavior. Our result sheds new light on the role of group morphology, which is relatively unheeded, retaining the importance of fluctuation dynamics in group criticality. Author summary To investigate the critical phenomena influencing collective behavior, we propose the ambiguous interaction model as a natural extension of the Boids model. Our proposed model exhibits various critical properties with respect to real-world collective behavior depending on the parameter settings (scale-free correlation, Lévy-walk behavior, and 1/f fluctuations in the center-of-mass frame). The results show that individual and group criticalities originate from the single algorithm employed by our model. Furthermore, we determine the functional duality for different input types (velocity and fluctuation) using a scale-free induced correlated domain inside a flock. The information flow between sub-domains within the flock is found to be bidirectional rather than unidirectional. This means that, contrary to appearances, a flock does not have a leader-follower information structure. Moreover, our analysis suggests a strong relationship between group morphology (i.e., velocity distributions) and its fluctuation power (i.e., fluctuation distributions) for rapid group turning. Our result also sheds new light on the role of group morphology, which has not been thoroughly investigated, retaining the importance of fluctuation dynamics in group criticality.