Factors influencing the structure and maintenance of fish schools

We explored the factors that contribute to fish school formation and maintenance using a series of computer simulation experiments. The factors we examined were mostly social, and included the functional form of attraction to – and repulsion from – neighbors, alignment with neighbors, regions of no social force (“neutral zones”), scaling of neighbor influence, random noise, and frictional drag. For each experiment, we compared the results from changing one factor with those of a “base case” that included a neutral zone 1 body length wide, linear attraction and repulsion forces, no alignment force, no scaling of neighbor influence, medium randomness, and no friction drag. We computed eight schooling metrics, two at the individual level (curvature and nearest-neighbor distance), four at the group level (group speed, polarity, group size, and expanse), and two at the population level (percent of stragglers and collision rate). For the parameter space we examined, all factors except random noise were important in determining the emergent properties of the group, as characterized by our schooling metrics. In some cases, schooling behavior was affected strongly by the presence or absence of a factor, but not to the value of the factor (e.g., drag) or its functional form (e.g., alignment force). In other cases, the results depended entirely on the functional form of the factor (e.g., attraction–repulsion; neighbor scaling). Our results indicate that a steep repulsion function is necessary to prevent collisions, and that this function must respond to local density. Second, a neutral zone must exist in which neither attraction nor repulsion operate. Third, to obtain polarity, there must be a modest alignment impulse, strong enough to induce polarity in the group, but weak enough to allow individual non-conformity. Fourth, the number and weighting of influential neighbors is crucially important in maintaining school structure. Fifth, the speed of motion is clearly important, leading to strong differences in school packing, individual path curvature, and polarization, between rapidly moving (with no drag present) and slow-moving (with high drag present) groups. Finally, individuality or non-conformity to group behavior, which most authors represent by randomness, likely plays a role in determining schooling behavior, although it was not a strong factor in our model. Each of these factors is important in determining the local interactions that give rise to emergent properties in fish schools.