Animals use power laws to minimize the time they spend searching for hidden objects, according to a group of physicists in France. Olivier Bénichou and colleagues at the University of Paris 6 and the Curie Institute, also in Paris, came to their conclusion by developing a mathematical model of animal searching patterns. They found that their model agrees with previous observations made by biologists and say that it could be used to speed up human searching (Phys. Rev. Lett. 94 198101).
Bénichou and colleagues created the model by assuming that foraging animals exhibit two distinct phases of behaviour. In the first phase they move quickly on a single trajectory from one location to another. Then in the second phase they search the new location by moving around more slowly and randomly — akin to molecules undergoing diffusion. They carry on this two-phase process until they find the object. Pet owners routinely see this type of behaviour in their dog, for example, when it looks for an object in the garden (see figure).
The physicists varied the time spent in each phase over a range of different search scenarios. They found that in order to minimize the search period, the time spent in the first phase is equal to the time spent in the second raised to a certain power. This relationship is also seen in actual animal behaviour.
Bénichou told PhysicsWeb that the results could be extended to human activities, such as searching for a lost object or perhaps even a victim in an avalanche. Doing so would require spending the appropriate amount of time carrying out each phase of the search.