Improvements in the statistical approach to random Levy flight searches

Recently it has been shown that the most efficient strategy for searching r andomly located objects, when the sites are randomly distributed and can be revisited any number of times, leads to a power law distribution P(l) = l( -mu) of the flights l, with mu = 2. We show analytically that the incorpora tion of energy considerations limits the possible range for the Levy expone nt mu, however, mu =2 still emerges as the optimal foraging condition. Furt hermore, we show that the probability distribution of flight lengths for th e short and intermediate flight length regimes depends on the details of th e system. (C) 2001 Elsevier Science B.V, All rights reserved.