Robustness of optimal random searches in fragmented environments

Abstract

The random search problem is a challenging and interdisciplinary topic of research in statistical physics. Realistic searches usually take place in nonuniform heterogeneous distributions of targets, e.g., patchy environments and fragmented habitats in ecological systems. Here we present a comprehensive numerical study of search efficiency in arbitrarily fragmented landscapes with unlimited visits to targets that can only be found within patches. We assume a random walker selecting uniformly distributed turning angles and step lengths from an inverse power-law tailed distribution with exponent μ. Our main finding is that for a large class of fragmented environments the optimal strategy corresponds approximately to the same value μ(opt)≈2. Moreover, this exponent is indistinguishable from the well-known exact optimal value μ(opt)=2 for the low-density limit of homogeneously distributed revisitable targets. Surprisingly, the best search strategies do not depend (or depend only weakly) on the specific details of the fragmentation. Finally, we discuss the mechanisms behind this observed robustness and comment on the relevance of our results to both the random search theory in general, as well as specifically to the foraging problem in the biological context.

And yet it optimizes

“…A limited account on the progress in this subject includes settling issues like the exact limits of low and high targets density and when an optimal strategy is indeed necessary [13], LWs as an alternative to the dilemma of behavior near starvation and species survival [14][15][16], proper (optimal) values of μ for the case of targets having regenerative times [17,18], the effect of small correlations in direction and the presence of partial cognitive power [19,20], to what extent superdiffusion could emerge from other distributions rather than Lévy [21], and finally, and perhaps more impressive, in which landscapes (fractal, patchy, lattice-like, etc.) LWs are able to optimize the random search efficiency, the answer being basically in all of them [20,22,23]. These works have shown that the Lévy is a very plastic strategy, leading to good solutions for the problem of adapting the random search strategy in distinct situations [24,25].…”

Hunters, busybodies, and the knowledge network building associated with curiosity

“…6B). Fractal movement patterns make Lévy flights particularly apt for efficiently searching for resources embedded in complex environments with hierarchical, lattice, patchy, or heterogeneous organizations [55][56][57] . Lévy flights have been observed in the movement trajectories of diverse systems, including cells, animals, and humans [58][59][60] .…”

Adaptive Autonomy in a Search and Rescue Scenario

“…Throughout the whole the simulation, agents perform continuous Levy walks in the generated 2D space, when in the idle state. The Levy walk algorithm was implemented as it has been considered an efficient strategy for search algorithms independent of the target distribution [25]. During these walks, agents publish their location to the environment node, and are able to detect fires/individuals if they are within a specified Euclidean distance (d v = 10% × grid w = 10% × grid h = 3).…”