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Why does the rabbit escape the fox on a zig-zag path? Predator-prey dynamics and the constant bearing strategy



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
... Rabbits are foreleg short and long back legs, and they have strong muscles and tendons, which make them run faster. In addition, rabbits can also stop suddenly while running, turn sharply or run back to escape chase in a zigzag motion (Firestone and Warren, 2010). This survival strategy can easily confuse their enemies and help them escape tracking, which can effectively increase the survival probability of rabbits. ...
In this paper, a new bio-inspired meta-heuristic algorithm, named artificial rabbits optimization (ARO), is proposed and tested comprehensively. The inspiration of the ARO algorithm is the survival strategies of rabbits in nature, including detour foraging and random hiding. The detour foraging strategy enforces a rabbit to eat the grass near other rabbits’ nests, which can prevent its nest from being discovered by predators. The random hiding strategy enables a rabbit to randomly choose one burrow from its own burrows for hiding, which can decrease the possibility of being captured by its enemies. Besides, the energy shrink of rabbits will result in the transition from the detour foraging strategy to the random hiding strategy. This study mathematically models such survival strategies to develop a new optimizer. The effectiveness of ARO is tested by comparison with other well-known optimizers by solving a suite of 31 benchmark functions and five engineering problems. The results show that ARO generally outperforms the tested competitors for solving the benchmark functions and engineering problems. ARO is applied to the fault diagnosis of a rolling bearing, in which the back-propagation (BP) network optimized by ARO is developed. The case study results demonstrate the practicability of the ARO optimizer in solving challenging real-world problems. The source code of ARO is publicly available at and
... Canalization of individual lateral preference could, in turn, maximize an individual's speed potential. However, eluding attackers may also rely on endurance as well as the ability to turn both right and left (Firestone & Warren, 2010). Since in typical gallop sequences the inside fore leads on turns (Hildebrande, 1977: 142), individuals would benefit by being able to lead from either side. ...
We examined lateral biases in the asymmetrical gallop gaits of wild chimpanzees (Pan troglodytes) approaching trees to drum in Gombe National Park, Tanzania. This is the first study of chimpanzee fast gaits under natural conditions. Analyzing digital video recordings collected over a 12-year period, we were able to determine lateral bias in 153 gallop bouts for the eight most frequently sampled males. For 89 of these bouts, symmetry and duty factor measurements were also possible for at least one stride cycle. Seven of eight males were lateralized, and the eighth was ambi-preferent. The degree of lateralization was comparable to that reported for chimpanzee hand preference during complex, bi-manual object manipulation, and similar to that reported for galloping in domestic horses. No group-level directional bias was found. Although little is known about lateral biases in the asymmetrical gaits of mammals in the wild, we speculate that predator-prey dynamics would select against group-level lateral biases but for the ability to switch leads. The absence of lead switching by chimpanzees in this study may reflect selection for maximum speed to reach arboreal escape routes. We discuss the possibility that locomotor lateralization could constrain the emergence of grouplevel biases in hand preference in chimpanzees, and could be implicated in the development of limb long bone asymmetries.
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Although in real life people frequently perform visual search together, in lab experiments this social dimension is typically left out. Here, we investigate individual, collaborative and competitive visual search with visualization of search partners’ gaze. Participants were instructed to search a grid of Gabor patches while being eye tracked. For collaboration and competition, searchers were shown in real time at which element the paired searcher was looking. To promote collaboration or competition, points were rewarded or deducted for correct or incorrect answers. Early in collaboration trials, searchers rarely fixated the same elements. Reaction times of couples were roughly halved compared with individual search, although error rates did not increase. This indicates searchers formed an efficient collaboration strategy. Overlap, the proportion of dwells that landed on hexagons that the other searcher had already looked at, was lower than expected from simulated overlap of two searchers who are blind to the behavior of their partner. The proportion of overlapping dwells correlated positively with ratings of the quality of collaboration. During competition, overlap increased earlier in time, indicating that competitors divided space less efficiently. Analysis of the entropy of the dwell locations and scan paths revealed that in the competition condition, a less fixed looking pattern was exhibited than in the collaborate and individual search conditions. We conclude that participants can efficiently search together when provided only with information about their partner’s gaze position by dividing up the search space. Competing search exhibited more random gaze patterns, potentially reflecting increased interaction between searchers in this condition.
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