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Colaço JR, Araújo HA, da Luz MGE, Viswanathan GM, Bartumeus F, Raposo EP. Effect of the search space dimensionality for finding close and faraway targets in random searches. Phys Rev E 2022; 106:034124. [PMID: 36266792 DOI: 10.1103/physreve.106.034124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2022] [Accepted: 09/01/2022] [Indexed: 06/16/2023]
Abstract
We investigate the dependence on the search space dimension of statistical properties of random searches with Lévy α-stable and power-law distributions of step lengths. We find that the probabilities to return to the last target found (P_{0}) and to encounter faraway targets (P_{L}), as well as the associated Shannon entropy S, behave as a function of α quite differently in one (1D) and two (2D) dimensions, a somewhat surprising result not reported until now. While in 1D one always has P_{0}≥P_{L}, an interesting crossover takes place in 2D that separates the search regimes with P_{0}>P_{L} for higher α and P_{0}<P_{L} for lower α, depending on the initial distance to the last target found. We also obtain in 2D a maximum in the entropy S for α∈(0,2], not observed in 1D apart from the trivial α→0 ballistic limit. Improving the understanding of the role of dimensionality in random searches is relevant in diverse contexts, as in the problem of encounter rates in biology and ecology.
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Affiliation(s)
- J R Colaço
- Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, Recife-PE, 50670-901, Brazil
| | - H A Araújo
- Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, Recife-PE, 50670-901, Brazil
- Departamento de Matemática, Universidade Federal de Pernambuco, Recife-PE, 50670-901, Brazil
| | - M G E da Luz
- Departamento de Física, Universidade Federal do Paraná, Curitiba-PR, 81531-980, Brazil
| | - G M Viswanathan
- Department of Physics and National Institute of Science and Technology of Complex Systems, Federal University of Rio Grande do Norte, Natal-RN, 59078-970, Brazil
| | - F Bartumeus
- Centre d'Estudis Avançats de Blanes-CEAB-CSIC, Girona, 17300, Spain
- CREAF, Universitat Autònoma de Barcelona, Cerdanyola del Vallés, 08193, Spain
- Institució Catalana de Recerca i Estudis Avançats-ICREA, Barcelona, 08010, Spain
| | - E P Raposo
- Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, Recife-PE, 50670-901, Brazil
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Garg K, Kello CT, Smaldino PE. Individual exploration and selective social learning: balancing exploration-exploitation trade-offs in collective foraging. J R Soc Interface 2022; 19:20210915. [PMID: 35472271 PMCID: PMC9042579 DOI: 10.1098/rsif.2021.0915] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Search requires balancing exploring for more options and exploiting the ones previously found. Individuals foraging in a group face another trade-off: whether to engage in social learning to exploit the solutions found by others or to solitarily search for unexplored solutions. Social learning can better exploit learned information and decrease the costs of finding new resources, but excessive social learning can lead to over-exploitation and too little exploration for new solutions. We study how these two trade-offs interact to influence search efficiency in a model of collective foraging under conditions of varying resource abundance, resource density and group size. We modelled individual search strategies as Lévy walks, where a power-law exponent (μ) controlled the trade-off between exploitative and explorative movements in individual search. We modulated the trade-off between individual search and social learning using a selectivity parameter that determined how agents responded to social cues in terms of distance and likely opportunity costs. Our results show that social learning is favoured in rich and clustered environments, but also that the benefits of exploiting social information are maximized by engaging in high levels of individual exploration. We show that selective use of social information can modulate the disadvantages of excessive social learning, especially in larger groups and when individual exploration is limited. Finally, we found that the optimal combination of individual exploration and social learning gave rise to trajectories with μ ≈ 2 and provide support for the general optimality of such patterns in search. Our work sheds light on the interplay between individual search and social learning, and has broader implications for collective search and problem-solving.
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Affiliation(s)
- Ketika Garg
- Department of Cognitive and Information Sciences, University of California, Merced, CA, USA
| | - Christopher T Kello
- Department of Cognitive and Information Sciences, University of California, Merced, CA, USA
| | - Paul E Smaldino
- Department of Cognitive and Information Sciences, University of California, Merced, CA, USA
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Campos D, Cristín J, Méndez V. Optimal escape-and-feeding dynamics of random walkers: Rethinking the convenience of ballistic strategies. Phys Rev E 2021; 103:052109. [PMID: 34134199 DOI: 10.1103/physreve.103.052109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2020] [Accepted: 04/13/2021] [Indexed: 11/07/2022]
Abstract
Excited random walks represent a convenient model to study food intake in a media which is progressively depleted by the walker. Trajectories in the model alternate between (i) feeding and (ii) escape (when food is missed and so it must be found again) periods, each governed by different movement rules. Here, we explore the case where the escape dynamics is adaptive, so at short times an area-restricted search is carried out, and a switch to extensive or ballistic motion occurs later if necessary. We derive for this case explicit analytical expressions of the mean escape time and the asymptotic growth of the depleted region in one dimension. These, together with numerical results in two dimensions, provide surprising evidence that ballistic searches are detrimental in such scenarios, a result which could explain why ballistic movement is barely observed in animal searches at microscopic and millimetric scales, therefore providing significant implications for biological foraging.
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Affiliation(s)
- Daniel Campos
- Grup de Física Estadística, Departament de Física. Facultat de Ciències, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
| | - Javier Cristín
- Grup de Física Estadística, Departament de Física. Facultat de Ciències, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
| | - Vicenç Méndez
- Grup de Física Estadística, Departament de Física. Facultat de Ciències, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
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