Lévy flights search patterns of biological organisms

We discuss recent findings suggesting that an inverse square probability density distribution P(ℓ) ℓ−2 of step lengths ℓ leads to an optimal random search strategy for organisms that can search efficiently for randomly located objects that can only be detected in the limited vicinity of the searcher and can be revisited any number of times. We explore the extent to which these findings may be dependent on the dimensionality of the search space and the presence of short-range correlations in the step lengths and directions.