The influence of the environment on Lévy random search efficiency: Fractality and memory effects

An open problem in the field of random searches relates to optimizing the search efficiency in fractal environments. Here we address this issue through a systematic study of Levy searches in landscapes encompassing several degrees of target aggregation and fractality. For scarce resources, non-destructive searches with unrestricted revisits to targets are shown to present universal optimal behavior irrespective of the general scaling properties of the spatial distribution of targets. In contrast, no such universal behavior occurs in the destructive case with forbidden revisits, in which the optimal strategy strongly depends on the degree of target aggregation. We also investigate how the presence of memory and learning skills of the searcher affect the search efficiency. By considering a limiting model in which the searcher learns through recent experience to recognize food-rich areas, we find that a statistical memory of previous encounters does not necessarily increase the rate of target findings in random searches. Instead, there is an optimal extent of memory, dependent on specific details of the search space and stochastic dynamics, which maximizes the search efficiency. This finding suggests a more general result, namely that in some instances there are actual advantages to ignoring certain pieces of partial information while searching for objects.