IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v637y2024ics0378437124000360.html
   My bibliography  Save this article

Modeling ants’ walks in patrolling multiple resources using stochastic approximation partial momentum refreshment

Author

Listed:
  • Cao, Jiajia
  • Zhou, Yanbin
  • Wei, Kun

Abstract

In the realm of ant foraging studies, researchers commonly map the movement of ant colonies to Markov Chain Monte Carlo (MCMC) models based on the probability matching strategy, aiming to achieve optimal foraging outcomes. When faced with multiple resources, ants often exhibit remarkable flexibility by patrolling over the foraging area and maximizing resource utilization. However, the regular MCMC models face challenges when resources are multimodally distributed as they struggle to efficiently explore the state space, particularly when modes are distantly separated. Building upon the existing partial momentum refreshment model, we propose a stochastic approximation partial momentum refreshment (SAPMR) model that not only performs equally well as regular MCMC models in bimodal distributions featuring two closely located modes but also overcomes energy barriers associated with multimodal distributions characterized by distantly separated modes. The synthetic data generated using SAPMR exhibits characteristics reminiscent of ants’ behavior such as Lévy-like patterns and maintaining a constant scaling function (≈1) when examining the relationship between the rescaled event speed and the rescaled time.

Suggested Citation

  • Cao, Jiajia & Zhou, Yanbin & Wei, Kun, 2024. "Modeling ants’ walks in patrolling multiple resources using stochastic approximation partial momentum refreshment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    • Handle: RePEc:eee:phsmap:v:637:y:2024:i:c:s0378437124000360
    DOI: 10.1016/j.physa.2024.129528
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437124000360
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2024.129528?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Liang, Faming & Liu, Chuanhai & Carroll, Raymond J., 2007. "Stochastic Approximation in Monte Carlo Computation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 305-320, March.
    2. David W. Sims & Emily J. Southall & Nicolas E. Humphries & Graeme C. Hays & Corey J. A. Bradshaw & Jonathan W. Pitchford & Alex James & Mohammed Z. Ahmed & Andrew S. Brierley & Mark A. Hindell & David, 2008. "Scaling laws of marine predator search behaviour," Nature, Nature, vol. 451(7182), pages 1098-1102, February.
    3. Liang, Faming, 2009. "On the use of stochastic approximation Monte Carlo for Monte Carlo integration," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 581-587, March.
    4. Nicolas E. Humphries & Nuno Queiroz & Jennifer R. M. Dyer & Nicolas G. Pade & Michael K. Musyl & Kurt M. Schaefer & Daniel W. Fuller & Juerg M. Brunnschweiler & Thomas K. Doyle & Jonathan D. R. Hought, 2010. "Environmental context explains Lévy and Brownian movement patterns of marine predators," Nature, Nature, vol. 465(7301), pages 1066-1069, June.
    5. Liang, Faming, 2005. "A Generalized WangLandau Algorithm for Monte Carlo Computation," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1311-1327, December.
    6. Ghaemi, Mehrdad & Zabihinpour, Zahra & Asgari, Yazdan, 2009. "Computer simulation study of the Levy flight process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1509-1514.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Faming Liang & Momiao Xiong, 2013. "Bayesian Detection of Causal Rare Variants under Posterior Consistency," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-16, July.
    2. Bi, Zhimin & Liu, Shutang & Ouyang, Miao, 2022. "Spatial dynamics of a fractional predator-prey system with time delay and Allee effect," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    3. Toman, Kellan & Voulgarakis, Nikolaos K., 2022. "Stochastic pursuit-evasion curves for foraging dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    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. Yukito Iba & Nen Saito & Akimasa Kitajima, 2014. "Multicanonical MCMC for sampling rare events: an illustrative review," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(3), pages 611-645, June.
    6. Bi, Zhimin & Liu, Shutang & Ouyang, Miao, 2022. "Three-dimensional pattern dynamics of a fractional predator-prey model with cross-diffusion and herd behavior," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    7. Muhammad Irfan & Abdul Wadood & Tahir Khurshaid & Bakht Muhammad Khan & Ki-Chai Kim & Seung-Ryle Oh & Sang-Bong Rhee, 2021. "An Optimized Adaptive Protection Scheme for Numerical and Directional Overcurrent Relay Coordination Using Harris Hawk Optimization," Energies, MDPI, vol. 14(18), pages 1-21, September.
    8. Shinohara, Shuji & Okamoto, Hiroshi & Manome, Nobuhito & Gunji, Pegio-Yukio & Nakajima, Yoshihiro & Moriyama, Toru & Chung, Ung-il, 2022. "Simulation of foraging behavior using a decision-making agent with Bayesian and inverse Bayesian inference: Temporal correlations and power laws in displacement patterns," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    9. 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.
    10. Jaehee Kim & Sooyoung Cheon, 2010. "A Bayesian regime‐switching time‐series model," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 365-378, September.
    11. Andy Reynolds & Eliane Ceccon & Cristina Baldauf & Tassia Karina Medeiros & Octavio Miramontes, 2018. "Lévy foraging patterns of rural humans," PLOS ONE, Public Library of Science, vol. 13(6), pages 1-16, June.
    12. Pereira, A.P.P. & Fernandes, J.P. & Atman, A.P.F. & Acebal, J.L., 2018. "Parameter calibration between models and simulations: Connecting linear and non-linear descriptions of anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 369-382.
    13. Pauline Formaglio & Marina E. Wosniack & Raphael M. Tromer & Jaderson G. Polli & Yuri B. Matos & Hang Zhong & Ernesto P. Raposo & Marcos G. E. Luz & Rogerio Amino, 2023. "Plasmodium sporozoite search strategy to locate hotspots of blood vessel invasion," Nature Communications, Nature, vol. 14(1), pages 1-11, December.
    14. LaScala-Gruenewald, Diana E. & Mehta, Rohan S. & Liu, Yu & Denny, Mark W., 2019. "Sensory perception plays a larger role in foraging efficiency than heavy-tailed movement strategies," Ecological Modelling, Elsevier, vol. 404(C), pages 69-82.
    15. Hao, Mengli & Jia, Wantao & Wang, Liang & Li, Fuxiao, 2022. "Most probable trajectory of a tumor model with immune response subjected to asymmetric Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    16. Danish A. Ahmed & Sergei V. Petrovskii & Paulo F. C. Tilles, 2018. "The “Lévy or Diffusion” Controversy: How Important Is the Movement Pattern in the Context of Trapping?," Mathematics, MDPI, vol. 6(5), pages 1-27, May.
    17. E P Raposo & F Bartumeus & M G E da Luz & P J Ribeiro-Neto & T A Souza & G M Viswanathan, 2011. "How Landscape Heterogeneity Frames Optimal Diffusivity in Searching Processes," PLOS Computational Biology, Public Library of Science, vol. 7(11), pages 1-8, November.
    18. Andrea Censi & Andrew D Straw & Rosalyn W Sayaman & Richard M Murray & Michael H Dickinson, 2013. "Discriminating External and Internal Causes for Heading Changes in Freely Flying Drosophila," PLOS Computational Biology, Public Library of Science, vol. 9(2), pages 1-14, February.
    19. Pierpaolo Andriani & Bill McKelvey, 2009. "Perspective ---From Gaussian to Paretian Thinking: Causes and Implications of Power Laws in Organizations," Organization Science, INFORMS, vol. 20(6), pages 1053-1071, December.
    20. Franziska Matthäus & Mario S Mommer & Tine Curk & Jure Dobnikar, 2011. "On the Origin and Characteristics of Noise-Induced Lévy Walks of E. Coli," PLOS ONE, Public Library of Science, vol. 6(4), pages 1-8, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:637:y:2024:i:c:s0378437124000360. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.