How Fast Should an Animal Run When Escaping? An Optimality Model Based on the Trade-Off between Speed and Accuracy

Abstract

How fast should animals move when trying to survive? Although many studies have examined how fast animals can move, the fastest speed is not always best. For example, an individual escaping from a predator must run fast enough to escape, but not so fast that it slips and falls. To explore this idea, we developed a simple mathematical model that predicts the optimal speed for an individual running from a predator along a straight beam. A beam was used as a proxy for straight-line running with severe consequences for missteps. We assumed that success, defined as reaching the end of the beam, had two broad requirements: (1) running fast enough to escape a predator, and (2) minimizing the probability of making a mistake that would compromise speed. Our model can be tailored to different systems by revising the predator's maximal speed, the prey's stride length and motor coordination, and the dimensions of the beam. Our model predicts that animals should run slower when the beam is narrower or when coordination is worse.