IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0024200.html
   My bibliography  Save this article

Structural Perturbations to Population Skeletons: Transient Dynamics, Coexistence of Attractors and the Rarity of Chaos

Author

Listed:
  • Brajendra K Singh
  • Paul E Parham
  • Chin-Kun Hu

Abstract

Background: Simple models of insect populations with non-overlapping generations have been instrumental in understanding the mechanisms behind population cycles, including wild (chaotic) fluctuations. The presence of deterministic chaos in natural populations, however, has never been unequivocally accepted. Recently, it has been proposed that the application of chaos control theory can be useful in unravelling the complexity observed in real population data. This approach is based on structural perturbations to simple population models (population skeletons). The mechanism behind such perturbations to control chaotic dynamics thus far is model dependent and constant (in size and direction) through time. In addition, the outcome of such structurally perturbed models is [almost] always equilibrium type, which fails to commensurate with the patterns observed in population data. Methodology/Principal Findings: We present a proportional feedback mechanism that is independent of model formulation and capable of perturbing population skeletons in an evolutionary way, as opposed to requiring constant feedbacks. We observe the same repertoire of patterns, from equilibrium states to non-chaotic aperiodic oscillations to chaotic behaviour, across different population models, in agreement with observations in real population data. Model outputs also indicate the existence of multiple attractors in some parameter regimes and this coexistence is found to depend on initial population densities or the duration of transient dynamics. Our results suggest that such a feedback mechanism may enable a better understanding of the regulatory processes in natural populations.

Suggested Citation

  • Brajendra K Singh & Paul E Parham & Chin-Kun Hu, 2011. "Structural Perturbations to Population Skeletons: Transient Dynamics, Coexistence of Attractors and the Rarity of Chaos," PLOS ONE, Public Library of Science, vol. 6(9), pages 1-9, September.
    • Handle: RePEc:plo:pone00:0024200
    DOI: 10.1371/journal.pone.0024200
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0024200
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0024200&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0024200?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
    ---><---

    References listed on IDEAS

    as
    1. Brett A. Melbourne & Alan Hastings, 2008. "Extinction risk depends strongly on factors contributing to stochasticity," Nature, Nature, vol. 454(7200), pages 100-103, July.
    2. John M. Drake & Blaine D. Griffen, 2010. "Early warning signals of extinction in deteriorating environments," Nature, Nature, vol. 467(7314), pages 456-459, September.
    3. Marten Scheffer & Jordi Bascompte & William A. Brock & Victor Brovkin & Stephen R. Carpenter & Vasilis Dakos & Hermann Held & Egbert H. van Nes & Max Rietkerk & George Sugihara, 2009. "Early-warning signals for critical transitions," Nature, Nature, vol. 461(7260), pages 53-59, September.
    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. Richter, Andries & Dakos, Vasilis, 2015. "Profit fluctuations signal eroding resilience of natural resources," Ecological Economics, Elsevier, vol. 117(C), pages 12-21.
    2. Martin Lindegren & Vasilis Dakos & Joachim P Gröger & Anna Gårdmark & Georgs Kornilovs & Saskia A Otto & Christian Möllmann, 2012. "Early Detection of Ecosystem Regime Shifts: A Multiple Method Evaluation for Management Application," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-9, July.
    3. Vasilis Dakos & Stephen R Carpenter & William A Brock & Aaron M Ellison & Vishwesha Guttal & Anthony R Ives & Sonia Kéfi & Valerie Livina & David A Seekell & Egbert H van Nes & Marten Scheffer, 2012. "Methods for Detecting Early Warnings of Critical Transitions in Time Series Illustrated Using Simulated Ecological Data," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-20, July.
    4. Christian Meisel & Andreas Klaus & Christian Kuehn & Dietmar Plenz, 2015. "Critical Slowing Down Governs the Transition to Neuron Spiking," PLOS Computational Biology, Public Library of Science, vol. 11(2), pages 1-20, February.
    5. Maarten C Boerlijst & Thomas Oudman & André M de Roos, 2013. "Catastrophic Collapse Can Occur without Early Warning: Examples of Silent Catastrophes in Structured Ecological Models," PLOS ONE, Public Library of Science, vol. 8(4), pages 1-6, April.
    6. Manfred Füllsack & Daniel Reisinger & Marie Kapeller & Georg Jäger, 2022. "Early warning signals from the periphery," Journal of Computational Social Science, Springer, vol. 5(1), pages 665-685, May.
    7. William A Brock & Stephen R Carpenter, 2012. "Early Warnings of Regime Shift When the Ecosystem Structure Is Unknown," PLOS ONE, Public Library of Science, vol. 7(9), pages 1-10, September.
    8. Tatiana Baumuratova & Simona Dobre & Thierry Bastogne & Thomas Sauter, 2013. "Switch of Sensitivity Dynamics Revealed with DyGloSA Toolbox for Dynamical Global Sensitivity Analysis as an Early Warning for System's Critical Transition," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-12, December.
    9. William A. Brock & Steven N. Durlauf, 2015. "On Sturdy Policy Evaluation," The Journal of Legal Studies, University of Chicago Press, vol. 44(S2), pages 447-473.
    10. Kiran D’Souza & Bogdan I Epureanu & Mercedes Pascual, 2015. "Forecasting Bifurcations from Large Perturbation Recoveries in Feedback Ecosystems," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-19, September.
    11. Yang, Anji & Wang, Hao & Yuan, Sanling, 2023. "Tipping time in a stochastic Leslie predator–prey model," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    12. Orozco-Fuentes, S. & Griffiths, G. & Holmes, M.J. & Ettelaie, R. & Smith, J. & Baggaley, A.W. & Parker, N.G., 2019. "Early warning signals in plant disease outbreaks," Ecological Modelling, Elsevier, vol. 393(C), pages 12-19.
    13. Tobias Brett & Marco Ajelli & Quan-Hui Liu & Mary G Krauland & John J Grefenstette & Willem G van Panhuis & Alessandro Vespignani & John M Drake & Pejman Rohani, 2020. "Detecting critical slowing down in high-dimensional epidemiological systems," PLOS Computational Biology, Public Library of Science, vol. 16(3), pages 1-19, March.
    14. Bhowmick, Amiya Ranjan & Saha, Bapi & Chattopadhyay, Joydev & Ray, Santanu & Bhattacharya, Sabyasachi, 2015. "Cooperation in species: Interplay of population regulation and extinction through global population dynamics database," Ecological Modelling, Elsevier, vol. 312(C), pages 150-165.
    15. Tobias S Brett & Eamon B O’Dea & Éric Marty & Paige B Miller & Andrew W Park & John M Drake & Pejman Rohani, 2018. "Anticipating epidemic transitions with imperfect data," PLOS Computational Biology, Public Library of Science, vol. 14(6), pages 1-18, June.
    16. Ryan D Batt & Tarsha Eason & Ahjond Garmestani, 2019. "Time scale of resilience loss: Implications for managing critical transitions in water quality," PLOS ONE, Public Library of Science, vol. 14(10), pages 1-19, October.
    17. Mohammed, M.M.A. & Landi, P. & Minoarivelo, H.O. & Hui, C., 2018. "Frugivory and seed dispersal: Extended bi-stable persistence and reduced clustering of plants," Ecological Modelling, Elsevier, vol. 380(C), pages 31-39.
    18. Méndez, Vicenç & Llopis, Isaac & Campos, Daniel & Horsthemke, Werner, 2010. "Extinction conditions for isolated populations affected by environmental stochasticity," Theoretical Population Biology, Elsevier, vol. 77(4), pages 250-256.
    19. Karimi Rahjerdi, Bahareh & Ramamoorthy, Ramesh & Nazarimehr, Fahimeh & Rajagopal, Karthikeyan & Jafari, Sajad, 2022. "Indicating the synchronization bifurcation points using the early warning signals in two case studies: Continuous and explosive synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    20. John M Drake & Tobias S Brett & Shiyang Chen & Bogdan I Epureanu & Matthew J Ferrari & Éric Marty & Paige B Miller & Eamon B O’Dea & Suzanne M O’Regan & Andrew W Park & Pejman Rohani, 2019. "The statistics of epidemic transitions," PLOS Computational Biology, Public Library of Science, vol. 15(5), pages 1-14, May.

    More about this item

    Statistics

    Access and download statistics

    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:plo:pone00:0024200. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.