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Consolidating Birth-Death and Death-Birth Processes in Structured Populations

Author

Listed:
  • Joshua Zukewich
  • Venu Kurella
  • Michael Doebeli
  • Christoph Hauert
Abstract
Network models extend evolutionary game theory to settings with spatial or social structure and have provided key insights on the mechanisms underlying the evolution of cooperation. However, network models have also proven sensitive to seemingly small details of the model architecture. Here we investigate two popular biologically motivated models of evolution in finite populations: Death-Birth (DB) and Birth-Death (BD) processes. In both cases reproduction is proportional to fitness and death is random; the only difference is the order of the two events at each time step. Although superficially similar, under DB cooperation may be favoured in structured populations, while under BD it never is. This is especially troubling as natural populations do not follow a strict one birth then one death regimen (or vice versa); such constraints are introduced to make models more tractable. Whether structure can promote the evolution of cooperation should not hinge on a simplifying assumption. Here, we propose a mixed rule where in each time step DB is used with probability and BD is used with probability . We derive the conditions for selection favouring cooperation under the mixed rule for all social dilemmas. We find that the only qualitatively different outcome occurs when using just BD (). This case admits a natural interpretation in terms of kin competition counterbalancing the effect of kin selection. Finally we show that, for any mixed BD-DB update and under weak selection, cooperation is never inhibited by population structure for any social dilemma, including the Snowdrift Game.

Suggested Citation

  • Joshua Zukewich & Venu Kurella & Michael Doebeli & Christoph Hauert, 2013. "Consolidating Birth-Death and Death-Birth Processes in Structured Populations," PLOS ONE, Public Library of Science, vol. 8(1), pages 1-7, January.
    • Handle: RePEc:plo:pone00:0054639
    DOI: 10.1371/journal.pone.0054639
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    References listed on IDEAS

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    1. Christoph Hauert & Michael Doebeli, 2004. "Spatial structure often inhibits the evolution of cooperation in the snowdrift game," Nature, Nature, vol. 428(6983), pages 643-646, April.
    2. Peter D. Taylor & Troy Day & Geoff Wild, 2007. "Evolution of cooperation in a finite homogeneous graph," Nature, Nature, vol. 447(7143), pages 469-472, May.
    3. 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.
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    Cited by:

    1. Mark Broom & Igor V. Erovenko & Jan Rychtář, 2021. "Modelling Evolution in Structured Populations Involving Multiplayer Interactions," Dynamic Games and Applications, Springer, vol. 11(2), pages 270-293, June.
    2. Yang Wang & Binghong Wang, 2015. "Evolution of Cooperation on Spatial Network with Limited Resource," PLOS ONE, Public Library of Science, vol. 10(8), pages 1-9, August.
    3. Szolnoki, Attila & Danku, Zsuzsa, 2018. "Dynamic-sensitive cooperation in the presence of multiple strategy updating rules," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 371-377.
    4. Sarkar, Bijan, 2021. "The cooperation–defection evolution on social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 584(C).
    5. Wes Maciejewski & Feng Fu & Christoph Hauert, 2014. "Evolutionary Game Dynamics in Populations with Heterogenous Structures," PLOS Computational Biology, Public Library of Science, vol. 10(4), pages 1-16, April.
    6. Laura Hindersin & Arne Traulsen, 2015. "Most Undirected Random Graphs Are Amplifiers of Selection for Birth-Death Dynamics, but Suppressors of Selection for Death-Birth Dynamics," PLOS Computational Biology, Public Library of Science, vol. 11(11), pages 1-14, November.
    7. Lin, Jingyan & Huang, Changwei & Dai, Qionglin & Yang, Junzhong, 2020. "Evolutionary game dynamics of combining the payoff-driven and conformity-driven update rules," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    8. Takesue, Hirofumi, 2019. "Effects of updating rules on the coevolving prisoner’s dilemma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 399-408.
    9. Josef Tkadlec & Andreas Pavlogiannis & Krishnendu Chatterjee & Martin A Nowak, 2020. "Limits on amplifiers of natural selection under death-Birth updating," PLOS Computational Biology, Public Library of Science, vol. 16(1), pages 1-13, January.
    10. Sarkar, Bijan, 2018. "Moran-evolution of cooperation: From well-mixed to heterogeneous complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 319-334.
    11. Christian Hilbe & Maria Kleshnina & Kateřina Staňková, 2023. "Evolutionary Games and Applications: Fifty Years of ‘The Logic of Animal Conflict’," Dynamic Games and Applications, Springer, vol. 13(4), pages 1035-1048, December.
    12. Lv, Shaojie & Zhao, Changheng & Li, Jiaying, 2022. "Generosity in public goods game with the aspiration-driven rule," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    13. Fulin Guo, 2023. "Experience-weighted attraction learning in network coordination games," Papers 2310.18835, arXiv.org.

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