Levy flights in random searches

We review the general search problem of how to find randomly located object s that can only be detected in the limited vicinity of a forager, and discu ss its quantitative description using the theory of random walks. We illust rate Levy flight foraging by comparison to Brownian random walks and discus s experimental observations of Levy flights in biological foraging. We revi ew recent findings suggesting that an inverse square probability density di stribution P(l) similar to l(-2) Of step lengths l can lead to optimal sear ches. Finally, we survey the explanations put forth to account for these un expected findings. (C) 2000 Published by Elsevier Science B.V. All rights r eserved.