Optimal foraging theory shows how fitness-maximizing foragers can use information about patch quality to decide how to search within patches. It is amply supported by empirical studies. Nonetheless, the theory largely ignores the fact that foragers may need to search for patches as well as for the targets within them. Here, using an exact but simple mathematical argument, it is shown how foragers can use information about patch quality to facilitate the execution of Lévy walk movement patterns with μ = 2 at inter-patch scales. These movement patterns are advantageous when searching for patches that are not depleted or rejected once visited but instead remain profitable. The analytical results are verified by the results of numerical simulations. The findings bring forth an innovative theoretical synthesis of searching for and within patches and, suggest that foragers' memories may be adaptive under spatially heterogeneous reward schedules.
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