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Stochastic Optimal Foraging: Tuning Intensive and Extensive Dynamics in Random Searches

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  • Frederic Bartumeus
  • Ernesto P Raposo
  • Gandhimohan M Viswanathan
  • Marcos G E da Luz

Abstract

Recent theoretical developments had laid down the proper mathematical means to understand how the structural complexity of search patterns may improve foraging efficiency. Under information-deprived scenarios and specific landscape configurations, Lévy walks and flights are known to lead to high search efficiencies. Based on a one-dimensional comparative analysis we show a mechanism by which, at random, a searcher can optimize the encounter with close and distant targets. The mechanism consists of combining an optimal diffusivity (optimally enhanced diffusion) with a minimal diffusion constant. In such a way the search dynamics adequately balances the tension between finding close and distant targets, while, at the same time, shifts the optimal balance towards relatively larger close-to-distant target encounter ratios. We find that introducing a multiscale set of reorientations ensures both a thorough local space exploration without oversampling and a fast spreading dynamics at the large scale. Lévy reorientation patterns account for these properties but other reorientation strategies providing similar statistical signatures can mimic or achieve comparable efficiencies. Hence, the present work unveils general mechanisms underlying efficient random search, beyond the Lévy model. Our results suggest that animals could tune key statistical movement properties (e.g. enhanced diffusivity, minimal diffusion constant) to cope with the very general problem of balancing out intensive and extensive random searching. We believe that theoretical developments to mechanistically understand stochastic search strategies, such as the one here proposed, are crucial to develop an empirically verifiable and comprehensive animal foraging theory.

Suggested Citation

  • Frederic Bartumeus & Ernesto P Raposo & Gandhimohan M Viswanathan & Marcos G E da Luz, 2014. "Stochastic Optimal Foraging: Tuning Intensive and Extensive Dynamics in Random Searches," PLOS ONE, Public Library of Science, vol. 9(9), pages 1-11, September.
  • Handle: RePEc:plo:pone00:0106373
    DOI: 10.1371/journal.pone.0106373
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    Cited by:

    1. Sakiyama, Tomoko, 2023. "Spatial inconsistency of memorized positions produces different types of movements," Ecological Modelling, Elsevier, vol. 481(C).
    2. Marina E Wosniack & Marcos C Santos & Ernesto P Raposo & Gandhi M Viswanathan & Marcos G E da Luz, 2017. "The evolutionary origins of Lévy walk foraging," PLOS Computational Biology, Public Library of Science, vol. 13(10), pages 1-31, October.
    3. Bao, Xiaomei & Tian, Canrong, 2019. "Delay driven vegetation patterns of a plankton system on a network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 74-88.
    4. Alves, Samuel B. & de Oliveira, Gilson F. & de Oliveira, Luimar C. & Passerat de Silans, Thierry & Chevrollier, Martine & Oriá, Marcos & de S. Cavalcante, Hugo L.D., 2016. "Characterization of diffusion processes: Normal and anomalous regimes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 392-401.

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