Improvements in the statistical approach to random Lévy flight searches

Recently it has been shown that the most efficient strategy for searching randomly 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−μ of the flights ℓ, with μ=2. We show analytically that the incorporation of energy considerations limits the possible range for the Lévy exponent μ, however, μ=2 still emerges as the optimal foraging condition. Furthermore, we show that the probability distribution of flight lengths for the short and intermediate flight length regimes depends on the details of the system.