Conditions under which a superdiffusive random-search strategy is necessary

Intuitively, lower target densities and lower detection capabilities should demand more sophisticated search strategies for a random search reasonable outcome. In contrast, when targets are easily found, a simple Brownian random walk strategy is enough. But where is the threshold between these two scenarios and when is optimization really necessary? We address this considering the interplay between two essential scales in random search, the average distance between neighbor targets l(o) and the detection capability r(v). In the limit cases the ratio beta = r(v)/l(o) suffices to characterize the problem. For low (high) beta a superdiffusive behavior is (is not) crucial for the process optimization. However, there is a crossover range, which is a nontrivial function of r(v) and l(o), separating the two regimes. We analyze this intermediate region, common in nature, and discuss the often overlooked important trade between resources availability and the searcher location power. Our results highlight contexts where efficient random search is a key factor for survival, such as in animal foraging.