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

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 , 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.