Influence of differently shaped behavioral zones on the shape and structure of fish schools

Agent-based models have shown that local interactions between identical agents can, through self-organizational processes, give rise to patterns at a group level that resemble those in animal groups, such as mocking birds or schooling and milling fish. Flocking or schooling is achieved in most models by surrounding the individuals with behavioral (response) zones which induce the individual to avoid agents that are close-by, align with those at mid-range and are attracted to others that are further away. Previous models have shown that circular (2D) and spherical (3D) behavioral zones give rise to elongated schools. There are, however, physiological indications that circular or spherical behavioral zones do not accurately reflect the sensory capabilities of real fish. In addition, the width-height ratios of schools brought about by spherical behavioral zones do not suficiently resemble empirical measurements of real fish schools. The present study investigates the effects on school shape and structure of differently shaped behavioral zones in a model of schooling fish. It was found that the school shape in general adopts the shape of the behavioral zone and is additionally influenced by group size and density of the schools. School structure is expressed in terms of the position of the nearest neighbors with respect to the individuals. For stronger attraction the positions of the nearest neighbors are mainly determined by the individuals' blind angle, whereas for weaker attraction the nearest neighbors are most often found at position where the behavioral zones are smallest. Furthermore, this study explains how these spatial structures emerge through measurements of the direction and magnitude of the repulsion and attraction forces experienced by the individuals. This study is the first to show schools with realistic school structures, i.e. angles towards positions of the nearest neighbors, and school shapes that resemble empirical data in all three dimensions. The schools which most resemble those of real fish result from behavioral zones which extend less in the vertical direction. This might indicate that fish respond more to, or can more easily perceive, conspecifics swimming on the movement plane.