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The influence of the environment on Lévy random search efficiency: Fractality and memory effects

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  • Ferreira, A.S.
  • Raposo, E.P.
  • Viswanathan, G.M.
  • da Luz, M.G.E.

Abstract

An open problem in the field of random searches relates to optimizing the search efficiency in fractal environments. Here we address this issue through a systematic study of Lévy searches in landscapes encompassing several degrees of target aggregation and fractality. For scarce resources, non-destructive searches with unrestricted revisits to targets are shown to present universal optimal behavior irrespective of the general scaling properties of the spatial distribution of targets. In contrast, no such universal behavior occurs in the destructive case with forbidden revisits, in which the optimal strategy strongly depends on the degree of target aggregation. We also investigate how the presence of memory and learning skills of the searcher affect the search efficiency. By considering a limiting model in which the searcher learns through recent experience to recognize food-rich areas, we find that a statistical memory of previous encounters does not necessarily increase the rate of target findings in random searches. Instead, there is an optimal extent of memory, dependent on specific details of the search space and stochastic dynamics, which maximizes the search efficiency. This finding suggests a more general result, namely that in some instances there are actual advantages to ignoring certain pieces of partial information while searching for objects.

Suggested Citation

  • Ferreira, A.S. & Raposo, E.P. & Viswanathan, G.M. & da Luz, M.G.E., 2012. "The influence of the environment on Lévy random search efficiency: Fractality and memory effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3234-3246.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:11:p:3234-3246
    DOI: 10.1016/j.physa.2012.01.028
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    References listed on IDEAS

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    Cited by:

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    2. Boschetti, Fabio & Vanderklift, Mathew A., 2015. "How the movement characteristics of large marine predators influence estimates of their abundance," Ecological Modelling, Elsevier, vol. 313(C), pages 223-236.
    3. Qi, Jie & Rong, Zhihai, 2013. "The emergence of scaling laws search dynamics in a particle swarm optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1522-1531.
    4. Nauta, Johannes & Simoens, Pieter & Khaluf, Yara, 2022. "Group size and resource fractality drive multimodal search strategies: A quantitative analysis on group foraging," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 590(C).
    5. 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.
    6. Ndibatya, Innocent & Booysen, M.J., 2021. "Characterizing the movement patterns of minibus taxis in Kampala's paratransit system," Journal of Transport Geography, Elsevier, vol. 92(C).

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