Collective States, Multistability and Transitional Behavior in Schooling Fish

The spontaneous emergence of pattern formation is ubiquitous in nature, often arising as a collective phenomenon from interactions among a large number of individual constituents or sub-systems. Understanding, and controlling, collective behavior is dependent on determining the low-level dynamical principles from which spatial and temporal patterns emerge; a key question is whether different group-level patterns result from all components of a system responding to the same external factor, individual components changing behavior but in a distributed self-organized way, or whether multiple collective states co-exist for the same individual behaviors. Using schooling fish (golden shiners, in groups of 30 to 300 fish) as a model system, we demonstrate that collective motion can be effectively mapped onto a set of order parameters describing the macroscopic group structure, revealing the existence of at least three dynamically-stable collective states; swarm, milling and polarized groups. Swarms are characterized by slow individual motion and a relatively dense, disordered structure. Increasing swim speed is associated with a transition to one of two locally-ordered states, milling or highly-mobile polarized groups. The stability of the discrete collective behaviors exhibited by a group depends on the number of group members. Transitions between states are influenced by both external (boundary-driven) and internal (changing motion of group members) factors. Whereas transitions between locally-disordered and locally-ordered group states are speed dependent, analysis of local and global properties of groups suggests that, congruent with theory, milling and polarized states co-exist in a bistable regime with transitions largely driven by perturbations. Our study allows us to relate theoretical and empirical understanding of animal group behavior and emphasizes dynamic changes in the structure of such groups. Author Summary: The patterns exhibited by moving animal groups like flocks of birds and schools of fish are typical of self-organizing systems in which global structural and dynamical properties arise from local interactions between individuals. Despite their apparent complexity, such systems can often be described, and understood, in terms of these emergent properties, rather than the detailed low-level description needed for depicting the individual dynamics. Here we show that schooling fish (in groups of 30 to 300 golden shiners) can be described in terms of the degree of alignment and degree of rotation among group members. We demonstrate that shiner schools exhibit three distinct behaviors: a swarm state with low speeds and little order; a strongly aligned state where the fish move with higher speeds; and a milling state, where each fish moves around the center of the group. Simulations have previously predicted this type of behavior, and we relate our findings to a well-known model of collective motion to help highlight similarities and differences between models and animal groups. Our results give insight into the regulation of group structure among animals, and also inform us generally about how global structures arise naturally from interactions among components of dynamical systems.