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Charles Z Firestone, William H Warren; Why does the rabbit escape the fox on a zig-zag path? Predator-prey dynamics and the constant bearing strategy. Journal of Vision 2010;10(7):1049. doi: https://doi.org/10.1167/10.7.1049.
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It is frequently observed that prey often evade predators by darting back and forth on a zig-zag path, rather than simply outrunning them on a straight path. What might account for this behavior? Previous work has shown that humans, dragonflies, and bats intercept moving targets by nulling change in the bearing angle of the target. The present research investigated whether a zig-zag escape path may be an effective countermeasure to this constant bearing strategy. Computer simulations randomly generated hundreds of thousands of ‘prey’ escape paths, each of which was tested against Fajen & Warren's (2007) dynamical model of the ‘predator's’ constant bearing strategy. Parameters included the angle and frequency of turns in the escape path, initial distance between predator and prey, relative speed of predator and prey, and the predator's visual-motor delay. Performance was measured as ground gained by ‘prey’ over ‘predator.’ Zig-zag paths emerged as the most effective escape route, and succeeded even when the prey was slower than the predator and a straight path would have failed. Analysis revealed a strong positive correlation between the variability in the bearing angle and the ground gained by the prey, suggesting that zig-zag paths succeed by disrupting the predator's efforts to hold the bearing angle constant. A rule of thumb for prey also emerged from the data: When the predator ‘zigs,’ you should ‘zag.’ We are currently collecting data on human ‘predators’ pursuing virtual ‘prey’ in an ambulatory virtual environment, to test the simulation predictions and to determine whether humans maintain the constant bearing strategy. Future work will test an interactive escape strategy in which the prey's ‘zags’ are contingent upon the predator's ‘zigs.’ The results suggest that zig-zag escape paths are common because they are effective countermeasures to the constant bearing strategy.
Acknowledgments: NIH R01 EY10923
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