IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v165y2022ip2s0960077922009961.html
   My bibliography  Save this article

General non-linear imitation leads to limit cycles in eco-evolutionary dynamics

Author

Listed:
  • Liu, Yuan
  • Cao, Lixuan
  • Wu, Bin

Abstract

Eco-evolutionary dynamics is crucial to understand how individuals’ behaviors and the surrounding environment interplay with each other. Typically, it is assumed that individuals update their behaviors via linear imitation function, i.e., the replicator dynamics. It has been proved that there cannot be limit circles in such eco-evolutionary dynamics. It suggests that eco-evolutionary dynamics alone is not sufficient to explain the widely observed fluctuating behavior in both the biological and social systems. We extrapolate from the linear imitation function to general imitation function, which can be non-linear. It is shown that the general imitation does not change the internal equilibrium and its local stability. It however leads to limit cycles, which are never present in classical eco-evolutionary dynamics. Moreover, the average cooperation level and average environment state agree with the first and the second component of the internal fixed point. Furthermore, we estimate the location of the emergent limit cycle. On the one hand, our results provide an alternative mechanism to make cooperators and defectors coexist in a periodic way in the “tragedy of the commons” and indicates the global eco-evolutionary dynamics is sensitive to the imitation function. Our work indicates that the way of imitation, i.e., the imitation function, is crucial in eco-evolutionary dynamics, which is not true for evolutionary dynamics with a static environment.

Suggested Citation

  • Liu, Yuan & Cao, Lixuan & Wu, Bin, 2022. "General non-linear imitation leads to limit cycles in eco-evolutionary dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
  • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p2:s0960077922009961
    DOI: 10.1016/j.chaos.2022.112817
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922009961
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2022.112817?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. Apesteguia, Jose & Huck, Steffen & Oechssler, Jorg, 2007. "Imitation--theory and experimental evidence," Journal of Economic Theory, Elsevier, vol. 136(1), pages 217-235, September.
    2. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2012. "Unbeatable imitation," Games and Economic Behavior, Elsevier, vol. 76(1), pages 88-96.
    3. Martin A. Nowak & Corina E. Tarnita & Edward O. Wilson, 2010. "The evolution of eusociality," Nature, Nature, vol. 466(7310), pages 1057-1062, August.
    4. Liu, Fanglin & Wu, Bin, 2022. "Environmental quality and population welfare in Markovian eco-evolutionary dynamics," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    5. Andy Hector & Robert Bagchi, 2007. "Biodiversity and ecosystem multifunctionality," Nature, Nature, vol. 448(7150), pages 188-190, July.
    6. Paul B. Rainey & Katrina Rainey, 2003. "Evolution of cooperation and conflict in experimental bacterial populations," Nature, Nature, vol. 425(6953), pages 72-74, September.
    7. Zhao, Jinhua & Wang, Xianjia & Niu, Lei & Gu, Cuiling, 2021. "Environmental feedback and cooperation in climate change dilemma," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    8. Jeff Gore & Hyun Youk & Alexander van Oudenaarden, 2009. "Snowdrift game dynamics and facultative cheating in yeast," Nature, Nature, vol. 459(7244), pages 253-256, May.
    9. Joung-Hun Lee & Yoh Iwasa & Ulf Dieckmann & Karl Sigmund, 2019. "Social evolution leads to persistent corruption," Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, vol. 116(27), pages 13276-13281, July.
    10. Alex McAvoy & Christoph Hauert, 2015. "Asymmetric Evolutionary Games," PLOS Computational Biology, Public Library of Science, vol. 11(8), pages 1-26, August.
    11. Cao, Lixuan & Wu, Bin, 2021. "Eco-evolutionary dynamics with payoff-dependent environmental feedback," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    12. Hauert, Christoph & Wakano, Joe Yuichiro & Doebeli, Michael, 2008. "Ecological public goods games: Cooperation and bifurcation," Theoretical Population Biology, Elsevier, vol. 73(2), pages 257-263.
    13. Shu, Gang & Du, Xia & Li, Ya, 2016. "Surrounding information consideration promotes cooperation in Prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 689-694.
    14. Martin A. Nowak & Karl Sigmund, 1998. "Evolution of indirect reciprocity by image scoring," Nature, Nature, vol. 393(6685), pages 573-577, June.
    15. Martin A. Nowak & Akira Sasaki & Christine Taylor & Drew Fudenberg, 2004. "Emergence of cooperation and evolutionary stability in finite populations," Nature, Nature, vol. 428(6983), pages 646-650, April.
    16. M.A. Nowak & K. Sigmund, 1998. "Evolution of Indirect Reciprocity by Image Scoring/ The Dynamics of Indirect Reciprocity," Working Papers ir98040, International Institute for Applied Systems Analysis.
    17. Martin A. Nowak & Karl Sigmund, 2005. "Evolution of indirect reciprocity," Nature, Nature, vol. 437(7063), pages 1291-1298, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Quan, Ji & Li, Haoze & Zhang, Man & Wang, Xianjia, 2024. "Cooperation dynamics in nonlinear spatial public goods games with endogenous synergy and discounting feedback," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    2. Ma, Xiaojian & Quan, Ji & Wang, Xianjia, 2023. "Evolution of cooperation with nonlinear environment feedback in repeated public goods game," Applied Mathematics and Computation, Elsevier, vol. 452(C).

    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. Cao, Lixuan & Wu, Bin, 2021. "Eco-evolutionary dynamics with payoff-dependent environmental feedback," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    2. Du, Faqi & Fu, Feng, 2013. "Quantifying the impact of noise on macroscopic organization of cooperation in spatial games," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 35-44.
    3. Ma, Xiaojian & Quan, Ji & Wang, Xianjia, 2023. "Evolution of cooperation with nonlinear environment feedback in repeated public goods game," Applied Mathematics and Computation, Elsevier, vol. 452(C).
    4. Qi Su & Lei Zhou & Long Wang, 2019. "Evolutionary multiplayer games on graphs with edge diversity," PLOS Computational Biology, Public Library of Science, vol. 15(4), pages 1-22, April.
    5. Quan, Ji & Zhang, Xiyue & Chen, Wenman & Tang, Caixia & Wang, Xianjia, 2024. "Reputation-dependent social learning on the evolution of cooperation in spatial public goods games," Applied Mathematics and Computation, Elsevier, vol. 475(C).
    6. Fernando P Santos & Francisco C Santos & Jorge M Pacheco, 2016. "Social Norms of Cooperation in Small-Scale Societies," PLOS Computational Biology, Public Library of Science, vol. 12(1), pages 1-13, January.
    7. Swami Iyer & Timothy Killingback, 2020. "Evolution of Cooperation in Social Dilemmas with Assortative Interactions," Games, MDPI, vol. 11(4), pages 1-31, September.
    8. Xiaojie Chen & Alana Schick & Michael Doebeli & Alistair Blachford & Long Wang, 2012. "Reputation-Based Conditional Interaction Supports Cooperation in Well-Mixed Prisoner’s Dilemmas," PLOS ONE, Public Library of Science, vol. 7(5), pages 1-7, May.
    9. Gao, Yan & Li, Minlan & Hu, Yuanyuan & Wang, Rui-Wu & Wang, Chao, 2024. "Evolutionary dynamics in voluntary prisoner’s dilemma game with environmental feedbacks," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    10. Qu, Xinglong & Zhou, Changli & Cao, Zhigang & Yang, Xiaoguang, 2016. "Conditional dissociation as a punishment mechanism in the evolution of cooperation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 449(C), pages 215-223.
    11. Manapat, Michael L. & Nowak, Martin A. & Rand, David G., 2013. "Information, irrationality, and the evolution of trust," Journal of Economic Behavior & Organization, Elsevier, vol. 90(S), pages 57-75.
    12. Jorge M Pacheco & Flávio L Pinheiro & Francisco C Santos, 2009. "Population Structure Induces a Symmetry Breaking Favoring the Emergence of Cooperation," PLOS Computational Biology, Public Library of Science, vol. 5(12), pages 1-7, December.
    13. Faqi Du & Feng Fu, 2011. "Partner Selection Shapes the Strategic and Topological Evolution of Cooperation," Dynamic Games and Applications, Springer, vol. 1(3), pages 354-369, September.
    14. Yao Meng & Sean P. Cornelius & Yang-Yu Liu & Aming Li, 2024. "Dynamics of collective cooperation under personalised strategy updates," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    15. Liang, Pinghan & Meng, Juanjuan, 2016. "Favor transmission and social image concern: An experimental study," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 63(C), pages 14-21.
    16. Lv, Shaojie & Wang, Xianjia, 2020. "The impact of heterogeneous investments on the evolution of cooperation in public goods game with exclusion," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    17. Jason Delaney & Sarah Jacobson, 2016. "Payments or Persuasion: Common Pool Resource Management with Price and Non-price Measures," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 65(4), pages 747-772, December.
    18. Laura Schmid & Farbod Ekbatani & Christian Hilbe & Krishnendu Chatterjee, 2023. "Quantitative assessment can stabilize indirect reciprocity under imperfect information," Nature Communications, Nature, vol. 14(1), pages 1-14, December.
    19. Quan, Ji & Nie, Jiacheng & Chen, Wenman & Wang, Xianjia, 2022. "Keeping or reversing social norms promote cooperation by enhancing indirect reciprocity," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    20. Hu, Qi & Jin, Tao & Jiang, Yulian & Liu, Xingwen, 2024. "Reputation incentives with public supervision promote cooperation in evolutionary games," Applied Mathematics and Computation, Elsevier, vol. 466(C).

    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:chsofr:v:165:y:2022:i:p2:s0960077922009961. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.