Multiple preferred escape trajectories are explained by a geometric model incorporating prey's turn and predator attack endpoint.

ABSTRACT

The escape trajectory (ET) of prey - measured as the angle relative to the predator's approach path - plays a major role in avoiding predation. Previous geometric models predict a single ET; however, many species show highly variable ETs with multiple preferred directions. Although such a high ET variability may confer unpredictability to avoid predation, the reasons why animals prefer specific multiple ETs remain unclear. Here, we constructed a novel geometric model that incorporates the time required for prey to turn and the predator's position at the end of its attack. The optimal ET was determined by maximizing the time difference of arrival at the edge of the safety zone between the prey and predator. By fitting the model to the experimental data of fish Pagrus major, we show that the model can clearly explain the observed multiple preferred ETs. By changing the parameters of the same model within a realistic range, we were able to produce various patterns of ETs empirically observed in other species (e.g., insects and frogs) a single preferred ET and multiple preferred ETs at small (20-50°) and large (150-180°) angles from the predator. Our results open new avenues of investigation for understanding how animals choose their ETs from behavioral and neurosensory perspectives.

When a prey spots a predator about to pounce, it turns swiftly and accelerates away to avoid being captured. The initial direction the prey chooses to take ­ known as its escape trajectory ­ can greatly impact their chance of survival. Previous models were able to predict the optimal direction an animal should take to maximize its chances of evading the predator. However, experimental data suggest that prey actually tend to escape via multiple specific directions, although why animals use this approach has not been clarified. To investigate this puzzle, Kawabata et al. built a new mathematical model that better represents how prey and predators interact with one another in the real world. Unlike past models, Kawabata et al. incorporated the time required for prey to change direction and only allowed the predators to move toward the prey for a limited distance. By including these two factors, they were able to reproduce the escape trajectories of real animals, including a species of fish, as well as species from other taxa such as frogs and insects. The new model suggests that prey escape along one of two directions either by moving directly away from the predator in order to outrun its attack, or by dodging sideways to avoid being captured. Which strategy the prey chooses has some elements of unpredictability, which makes it more difficult for predators to adjust their capturing method. These findings shed light on why escaping in multiple specific directions makes prey harder to catch. The model could also be extended to test the escape trajectories of a wider variety of predator and prey species, which may avoid capture via different routes. This could help researchers better understand how predators and prey interact with one another. The findings could also reveal how sensory information (such as sound and sight) associated with the threat of an approaching predator is processed and stimulates the muscle activity required to escape in multiple different directions.