Correlates between inferred rules of interaction and group-level statistics of collective motion in small shoals of fish under different predator threat scenarios

Many species exhibit remarkable displays of coordinated collective motion. The broad hypothesis underpinning the theory of collective motion is that group-level patterns of movement emerge due to repeated interactions between individuals; these interactions are sometimes referred to as rules of interaction. Support for this hypothesis comes from a wide range of model-based studies of collective motion. Within the models, rules of interaction dictate how individuals adjust their velocity as a function of the relative positions and velocities of other members of the group. The rules of interaction usually include at least one of the following: (1) a rule for collision avoidance with neighbouring group members at short-range (a repulsion interaction); (2) a rule for aligning direction of motion with group members at intermediate distances (an orientation interaction); (3) a rule for moving toward group members at intermediate to longer distances (an attraction interaction). Adjusting the ranges over which repulsion, orientation and attraction interactions apply can affect emergent group-level patterns of movement, including the formation of swarms, mills, parallel movements and group fragmentation (Couzin et al. 2002, D’Orsogna et al. 2006).