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Parrish, J. K., Viscido, S. V., & Grunbaum, D. (2002). Self-Organized Fish Schools: An Examination of Emergent Properties. Biol Bull, 202(3), 296–305.
Abstract: Heterogeneous, “aggregated” patterns in the spatial distributions of individuals are almost universal across living organisms, from bacteria to higher vertebrates. Whereas specific features of aggregations are often visually striking to human eyes, a heuristic analysis based on human vision is usually not sufficient to answer fundamental questions about how and why organisms aggregate. What are the individual-level behavioral traits that give rise to these features? When qualitatively similar spatial patterns arise from purely physical mechanisms, are these patterns in organisms biologically significant, or are they simply epiphenomena that are likely characteristics of any set of interacting autonomous individuals? If specific features of spatial aggregations do confer advantages or disadvantages in the fitness of group members, how has evolution operated to shape individual behavior in balancing costs and benefits at the individual and group levels? Mathematical models of social behaviors such as schooling in fishes provide a promising avenue to address some of these questions. However, the literature on schooling models has lacked a common framework to objectively and quantitatively characterize relationships between individual-level behaviors and group-level patterns. In this paper, we briefly survey similarities and differences in behavioral algorithms and aggregation statistics among existing schooling models. We present preliminary results of our efforts to develop a modeling framework that synthesizes much of this previous work, and to identify relationships between behavioral parameters and group-level statistics. N1 -
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Viscido, S. V., Miller, M., & Wethey, D. S. (2002). The dilemma of the selfish herd: the search for a realistic movement rule. J. Theor. Biol., 217(2), 183–194.
Abstract: The selfish herd hypothesis predicts that aggregations form because individuals move toward one another to minimize their own predation risk. The “dilemma of the selfish herd” is that movement rules that are easy for individuals to follow, fail to produce true aggregations, while rules that produce aggregations require individual behavior so complex that one may doubt most animals can follow them. If natural selection at the individual level is responsible for herding behavior, a solution to the dilemma must exist. Using computer simulations, we examined four different movement rules. Relative predation risk was different for all four movement rules (p<0.05). We defined three criteria for measuring the quality of a movement rule. A good movement rule should (a) be statistically likely to benefit an individual that follows it, (b) be something we can imagine most animals are capable of following, and (c) result in a centrally compact flock. The local crowded horizon rule, which allowed individuals to take the positions of many flock-mates into account, but decreased the influence of flock-mates with distance, best satisfied these criteria. The local crowded horizon rule was very sensitive to the animal's perceptive ability. Therefore, the animal's ability to detect its neighbors is an important factor in the dynamics of group formation.
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Viscido, S. V., Miller, M., & Wethey, D. S. (2001). The response of a selfish herd to an attack from outside the group perimeter. J. Theor. Biol., 208(3), 315–328.
Abstract: According to the selfish herd hypothesis, animals can decrease predation risk by moving toward one another if the predator can appear anywhere and will attack the nearest target. Previous studies have shown that aggregations can form using simple movement rules designed to decrease each animal's Domain of Danger. However, if the predator attacks from outside the group's perimeter, these simple movement rules might not lead to aggregation. To test whether simple selfish movement rules would decrease predation risk for those situations when the predator attacks from outside the flock perimeter, we constructed a computer model that allowed flocks of 75 simulated fiddler crabs to react to one another, and to a predator attacking from 7 m away. We attacked simulated crab flocks with predators of different sizes and attack speeds, and computed relative predation risk after 120 time steps. Final trajectories showed flight toward the center of the flock, but curving away from the predator. Path curvature depended on the predator's size and approach speed. The average crab experienced a greater decrease in predation risk when the predator was small or slow moving. Regardless of the predator's size and speed, however, predation risk always decreased as long as crabs took their flock-mates into account. We conclude that, even when flight away from an external predator occurs, the selfish avoidance of danger can lead to aggregation.
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