Quantifying the control laws governing terminal attack in lions

In the last seconds of a chase, lions rely on steering more than speed.

Most descriptions of a chase treat it as a race: the predator is faster, the gap closes, and the hunt ends. But a prey animal does not usually need to outrun a predator. It needs to turn more tightly than the predator can.

The reason is mechanical. To turn, a running animal has to push sideways against the ground, and there is a limit to how hard it can push before its feet slip or its legs cannot take the load. That limit is set by the animal's body and does not change with speed. The size of the turn does. The tightest turn an animal can make gets wider in proportion to the square of its speed, so an animal running twice as fast needs a turn four times as wide. A slower animal can therefore make a corner that a faster one cannot follow.

This makes the end of a chase a control problem rather than a speed problem. At every stride, the lion has to decide which way to point and how much speed it can carry into the next turn.

My colleague Hadleigh Frost and I measured how lions make both decisions. We filmed six lions from a drone as they chased a lure that was pulled along unpredictable routes across their enclosure. We recorded 67 chases and reconstructed each one stride by stride.

The steering followed a rule that engineers use for intercepting moving targets. There are two standard versions. In proportional pursuit, the pursuer keeps itself pointed at the target and turns harder the further the target drifts off its heading. In proportional navigation, the pursuer watches how the target moves across its field of view and turns to hold that drift at zero. This is the same principle as the rule for predicting a collision at sea: if another vessel stays at a fixed bearing, the two are on a collision course. Proportional navigation is the rule used by most homing missiles.

The lions used a combination of the two. This combination had previously been reported in one other animal, the Harris's hawk, which hunts rabbits and other prey that change direction suddenly. Peregrine falcons, dragonflies, bats and predatory flies have each been shown to use one rule or the other. A large mammal running on the ground turns out to use the same steering rule as a hawk hunting in the air.

The lions also adjusted their speed in a consistent way. They slowed when a turn was sharp, and they slowed over roughly the last five metres before reaching the lure, which reduced the risk of overshooting it.

None of this requires the lion to compute anything. A guidance law is a compact description of how what the animal sees is converted into what it does, and natural selection arrived at these rules long before engineers formalised them. The point is that a chase, which looks too fast and too variable to analyse, can be described by a short equation with a few parameters.

Because those parameters have physical meaning, the same measurements can be made in any predator. With a drone and video-tracking software, it is now possible to ask whether cheetahs, wolves or hawks use the same rule, and whether the strategy an animal uses is set by its evolutionary ancestry.

Ongoing thread. More from Isla C. Duporge to follow.