# A calculated pursuit

## A mathematical model based on the ‘homicidal chauffeur game’ describes the turning strategies used by prey as they attempt to outrun a predator.

A pursuit between a predator and its prey involves complex strategies. Prey often make sudden sharp turns when running to evade a predator. Any predator that cannot turn quickly enough will have to run further to catch up with the prey again, thus potentially allowing the prey to pull away from the predator. The timing of these turns is crucial; if the prey turns when the predator is too far away, the predator can cut the corner off the turn and catch up with the prey more easily.

The speed at which animals can turn depends on the forces involved in cornering, and larger animals need to produce greater forces for any given turn. However, larger animals can apply relatively less force than smaller animals for turns and so cannot turn as rapidly. The effect of the relationship between mass and turning ability on the strategies used during land-based pursuits had not been investigated.

Rory Wilson and co-workers have now created a mathematical model that considers how the mass of a predator and its prey influences the course and strategies used in a land-based pursuit. The model is based in part on a mathematical problem called the ‘homicidal chauffeur game’, where a car driver attempts to run over a pedestrian. Wilson and colleagues’ model predicts that chases between large predators and smaller prey should feature frequent sharp turns, as the prey try to exploit their superior turning ability. However, when the predators and prey are of similar size, the prey gain little or no advantage from executing high-speed turns. Indeed, as turning slows the prey down, turning may often be disadvantageous, and so fewer turns should be seen during a pursuit.

The predictions of the model were compared with the pursuit strategies of wild cheetahs, which were studied using collars equipped with tags to measure acceleration as the predators chased prey of different sizes — from hares to large antelopes called gemsboks. The tracking data confirmed the predictions of the model; thereby revealing that body mass and the ability of animals to choose when best to turn strongly determine the outcome of predator-prey pursuits.

### To find out more

Listen to Rory Wilson talk about predators and prey in episode 24 of the eLife podcast.
Read the eLife research paper on which this eLife digest is based: “Mass enhances speed but diminishes turn capacity in terrestrial pursuit predators” (August 7, 2015)
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