title: Search in patchy media: Exploitation-exploration tradeoff.
abstract: How to best exploit patchy resources? We introduce a minimal exploitation-migration model that incorporates the coupling between a searcher's trajectory, modeled by a random walk, and ensuing depletion of the environment by the searcher's consumption of resources. The searcher also migrates to a new patch when it takes S consecutive steps without finding resources. We compute the distribution of consumed resources F_{t} at time t for this non-Markovian searcher and show that consumption is maximized by exploring multiple patches. In one dimension, we derive the optimal strategy to maximize F_{t}. This strategy is robust with respect to the distribution of resources within patches and the criterion for leaving the current patch. We also show that F_{t} has an optimum in the ecologically relevant case of two-dimensional patchy environments.
authors.affiliation: Laboratoire de Physique Théorique et Modèles Statistiques (UMR 8626), Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France.|Laboratoire de Physique Théorique de la Matière Condensée (UMR 7600), Université Pierre et Marie Curie, 4 Place Jussieu, 75255 Paris Cedex, France.
authors.forename: M
authors.initials: M
authors.lastname: Chupeau
authors.affiliation: Laboratoire de Physique Théorique de la Matière Condensée (UMR 7600), Université Pierre et Marie Curie, 4 Place Jussieu, 75255 Paris Cedex, France.
authors.forename: O
authors.initials: O
authors.lastname: Bénichou
authors.affiliation: Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.|Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
authors.forename: S
authors.initials: S
authors.lastname: Redner