Optimal Random Searches: Lévy Walks and Animal Movement

We review the general process of random search and discuss its main ingredients, potential goals, as well as ways to quantity search efficiency. We address Lévy walk search models, with emphasis on how they are widely applicable to simple yet concrete phenomena. Moreover, since search strategies can alter encounter rates, it is natural to expect that how animals move must have a bearing on ecological and evolutionary phenomena. We discuss some examples of empirical studies in the latter context. We also present a theoretical analysis of an idealized model in one and two spatial dimensions. A different open question relates to the extent to which the empirically observed Lévy walk patterns are related to the optimization of the search efficiency conferred by Lévy walks, since the latter fact does not logically imply the former. A major development in this context was a study of Drosophila larvae that showed the existence of intrinsic neurophysiological mechanisms for generating patterns similar to Lévy walks. Finally, as a digression, we briefly comment on how search is inherent in human nature.