The effect of population size and number of influential neighbors on the emergent properties of fish schools

Fish schools and other animal aggregations are often highly coupled to emergent properties such as polarity, edges, and distinct shape. However, the relationship between an individual's behavior and the resulting group patterns is complex and poorly understood. Many previous theoretical investigations have assumed that population size and the number of neighbors influencing individual movement decisions do not exert an over-arching influence on emergent properties-clearly an unrealistic assumption for larger populations that frequently occur in nature. To understand how group patterns are affected by population size, we used an individual-based simulation model of fish movement in three dimensions with many individuals. We conducted simulation experiments over populations of 1-128 individuals and varied the number of influential neighbors from 4 to 24. We quantified the resulting movement and spatial distributions of our model fish at the individual, group, and population levels using a variety of metrics. Our results show that all group properties examined are strongly influenced both by population size, and by the number of influential neighbors. We also found a very strong interaction between the two factors: when the factors were similar, each individual responded to the exact same set of other animals, and fish schools remained relatively static, milling about in a disorganized fashion. When the local population size far exceeded the number of influential neighbors, each fish took cues from a different set of neighbors, which resulted in more mobile schools. With too many influential neighbors, group structure broke down, presumably because individuals were unable to solve the spatial problem of too many competing influences. Our results demonstrate that examination of a large state space with a wide array of metrics can shed light on the strength and combination of parameters necessary to induce specific types of gregarious patterns. Furthermore, our results suggest that, by regulating the number of influential neighbors to which they react, fish may be able to modulate group properties such as group size, speed, and polarity. (c) 2004 Elsevier B.V. All rights reserved.