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Order and flexibility in the motion of fish schools.

The coexistence of order and flexibility in the motion of fish schools was studied by using a simple numerical model and a computer simulation. The numerical model is based on behavioral rules for individuals in the school by considering attraction, repulsion, and parallel-orientation behavior. Each individual follows the same rules and makes school movements. The simulation results show that school order and flexibility are affected by the number of neighbors interacting with an individual in the school and by the randomness of individual motion. Increase in the number of interacting neighbors leads to high order, especially when the number increases from a low value (between one and three). An optimal number of interacting neighbors exists that is relatively low (two or three) for high flexibility, indicating that a fish needs only to pay attention to a few neighbors to realize both order and flexibility. The low randomness of individual motion benefits both order and flexibility. These results indicate that schooling fish have evolved specialized ability for establishing both school order and flexibility.