Lévy flights and superdiffusion in the context of biological encounters and random searches

We review the general problem of random searches in the context of biological encounters. We analyze deterministic and stochastic aspects of searching in general and address the destructive and nondestructive cases specifically. We discuss the concepts of Lévy walks as adaptive strategies and explore possible examples. We also review Lévy searches in other media and spaces, including lattices and networks as opposed to continuous environments. We analyze empirical evidence supporting the Lévy flight foraging hypothesis, as well as the more general idea of superdiffusive foraging. We compare these hypothesis with alternative theories of random searches. Finally, we comment on several issues relevant to the practical application of models of Lévy and superdiffusive strategies to the general question of biological foraging.