Optimal scale-free searching strategies for the location of moving targets: New insights on visually cued mate location behaviour in insects

The most efficient random Lévy-flight (scale-free) searching strategies for the location of moving targets are identified. Brownian targets are best caught using ballistic (long straight-line) searches, and vice versa. Brownian searches and ballistic searches are close to being optimal for the capture of a Lévy-flyer whose flight-segment lengths are distributed according to an inverse-square law. The movement patterns of some foragers are characterised by such an inverse-square law and these are known to constitute an optimal searching strategy for the location of randomly and sparsely distributed stationary resources. It is suggested that visually cued mate location behaviour in butterflies and in some other insects can be understood within the context of optimal scale-free searching strategies for the location of moving targets.