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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.

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Movement is fundamental to the ecology of animals, and an animal's choice of movement speed determines the duration, energetic costs, and probability of success of any given activity. It is often assumed that animals should use maximum speeds when escaping from predators, but an increasing number of studies find animals rarely move as fast as they can in nature because faster speeds come with a greater chance of mistakes. Mathematical modelling suggests that, when escaping predators, prey animals should optimise speeds to simultaneously outrun their pursuer and minimise their probability of slipping. This can be particularly important when running along narrow structures like branches. When foraging, however, animals should avoid moving at high speeds, which are often energetically costly and decrease the ability to detect food or predators. In this study, we examined how trade‐offs between speed and probability of slipping influenced the speed choice of wild antechinus (Antechinus mysticus) during escaping and foraging behaviours. We also examined how this trade‐off affected foraging behaviour. Antechinus ran significantly faster when escaping (1.207 ± 0.033 m/s) than foraging (0.145 ± 0.002 m/s), and slipped 37% more often during escapes. However, foraging antechinus still slipped frequently on narrow branches, despite running an order of magnitude more slowly than they did on wide branches. Furthermore, antechinus slipped at lower speeds when foraging than they did when escaping, suggesting that avoiding mistakes is less highly prioritized when foraging. Antechinus visited the feeding station accessed by a wide branch more frequently (and ate more while there) compared with feeding stations accessed by narrow branches, even when those branches were 33% or 67% shorter. This suggests that foraging decisions may be based on potential limitations to speed and the probability of slipping over distance to cover. Though activities such as running can be fundamental to animals’ fitness, a general framework to understand how animals select speeds in nature is still being developed. We test the assumption that animals choose running speeds to minimise their motor mistakes, and demonstrate the cost of mistakes is likely to be different across ecological and behavioural contexts. A http://onlinelibrary.wiley.com/doi/10.1111/1365-2435.13036/suppinfo is available for this article.

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