title: 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.
authors.affiliation: Departamento de Física, Universidade Federal do Paraná, C.P. 19044, 81531-980 Curitiba-PR, Brazil.
authors.forename: M E
authors.initials: ME
authors.lastname: Wosniack
authors.affiliation: Departamento de Física, Universidade Federal do Paraná, C.P. 19044, 81531-980 Curitiba-PR, Brazil.
authors.forename: M C
authors.initials: MC
authors.lastname: Santos
authors.affiliation: Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife-PE, Brazil.
authors.forename: E P
authors.initials: EP
authors.lastname: Raposo
authors.affiliation: Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, 59078-970 Natal-RN, Brazil.|National Institute of Science and Technology of Complex Systems, Universidade Federal do Rio Grande do Norte, 59078-970 Natal-RN, Brazil.
authors.forename: G M
authors.initials: GM
authors.lastname: Viswanathan
authors.affiliation: Departamento de Física, Universidade Federal do Paraná, C.P. 19044, 81531-980 Curitiba-PR, Brazil.
authors.forename: M G E
authors.initials: MG
authors.lastname: da Luz