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.

Effects of support diameter and compliance on common marmoset (Callithrix jacchus) gait kinematics

“…Given that greater speed generally decreases agility (Hyams et al, 2012;Wheatley et al, 2015;Wynn et al, 2015), marmosets should decrease speed on narrow and compliant substrates.…”

“…Though faster speeds may facilitate dynamic stability, particularly in the rolling plane (Bruijn et al, 2009), fast travel also reduces agility (Hyams et al, 2012;Wheatley et al, 2015;Wynn et al, 2015) and increases peak force production (Weyand et al, 2000) -both of which may compromise stability when moving on a precariously narrow support. Indeed, substrate narrowness has previously been shown to be associated with slower travel speeds in many arboreal tetrapods, including tree frogs (Herrel et al, 2013), anoles (Losos and Sinervo, 1989; Losos and Irschick, 1996; Mattingly and Jayne, 2004;Hsieh, 2016), fence lizards (Sinervo and Losos, 1991), marsupial gliders (Karantanis et al, 2015), opossums (Lammers and Biknevicius, 2004;Shapiro et al, 2014), mice (Hyams et al, 2012), squirrels (Schmidt, 2011) and strepsirrhine primates (Stevens, 2007).…”

Optimal running speeds when there is a trade‐off between speed and the probability of mistakes

“…This is a common assumption in studies of animal performance, yet a recent mathematical model (Wheatley et al. Integrative and Comparative Biology , 55, 1166–1175; ) of escape behaviour predicts that animals should instead use speeds below their maximum capabilities even when running from predators. Fast speeds may compromise motor control and accuracy of limb placement, particularly as the animal runs along narrow structures like beams or branches.…”

“…Mistakes decrease speed and increase the probability of capture. We tested several key assumptions and predictions of Wheatley et al . 's () model using wild‐caught northern quolls ( Dasyurus hallucatus ), a squirrel‐sized marsupial carnivore. We quantified the speeds of quolls as they traversed beams of differing width and expected animals should balance the benefits of higher speeds against the increased probability of mistakes when selecting speeds. We first explored whether the probability of mistakes when running along a beam increased at faster running speeds (speed‐accuracy trade‐off) and when the difficulty of a task was greater (narrower beam).…”

“…narrower beams), thereby allowing them to decrease the total time it took to traverse the beam. Our data provide support for the assumptions and predictions of Wheatley et al . 's () model of optimal escape speeds, and suggest that animals optimize rather than simply maximize speeds when running along challenging substrates. Our work provides a foundation for understanding the movement behaviour of animals when their objective is to escape predatory attacks, and demonstrates that animals should select their escape strategy based on how both the speed of movement and motor control affect task success. A http://onlinelibrary.wiley.com/doi/10.1111/1365-2435.12902/suppinfo is available for this article.…”