Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
162 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Hypochaos prevents tragedy of the commons in discrete-time eco-evolutionary game dynamics (2401.12245v1)

Published 20 Jan 2024 in q-bio.PE and nlin.AO

Abstract: While quite a few papers have explored game-resource feedback using the framework of evolutionary game theory, almost all the studies are confined to using time-continuous dynamical equations. Moreover, in such literature, the effect of ubiquitous chaos in the resulting eco-evolutionary dynamics is rather missing. Here, we present a deterministic eco-evolutionary discrete-time dynamics in generation-wise non-overlapping population of two types of harvesters, one harvesting at a faster rate than the other, consuming a self-renewing resource capable of showing chaotic dynamics. In the light of our finding that sometimes chaos is confined exclusively to either the dynamics of the resource or that of the consumer fractions, an interesting scenario is realized: The resource state can keep oscillating chaotically, and hence, it does not vanish to result in the tragedy of the commons, extinction of the resource due to selfish indiscriminate exploitation, and yet the consumer population, whose dynamics depends directly on the state of the resource, may end up being composed exclusively of defectors, i.e., high harvesters. This appears non-intuitive because it is well known that prevention of tragedy of the commons usually requires substantial cooperation to be present.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (60)
  1. T. Malthus and G. Gilbert, An Essay on the Principle of Population, Oxford world’s classics (Oxford University Press, 1999).
  2. W. Lloyd, Two Lectures on the Checks to Population (S. Collingwood, 1833).
  3. G. Hardin, “The tragedy of the commons,” Science 162, 1243 (1968).
  4. E. Ostrom, “Coping with tragedies of the commons,” Ann. Rev. Pol. Sci. 2, 493 (1999).
  5. I. A. Shiklomanov, “Appraisal and assessment of world water resources,” Water Int. 25, 11 (2000).
  6. S. F. Pires and W. D. Moreto, “Preventing wildlife crimes: Solutions that can overcome the ‘tragedy of the commons’,” Eur. J. Crim. Pol. Res. 17, 101 (2011).
  7. Y. Maaravi, A. Levy, T. Gur, D. Confino, and S. Segal, ““the tragedy of the commons”: How individualism and collectivism affected the spread of the covid-19 pandemic,” Front. Public Health 9, 2296 (2021).
  8. M. Schuster, E. Foxall, D. Finch, H. Smith, and P. De Leenheer, “Tragedy of the commons in the chemostat,” PLoS ONE 12, 12 (2017).
  9. P. Smith and M. Schuster, “Public goods and cheating in microbes,” Curr. Biol. 29, R442 (2019).
  10. D. J. Rankin and H. Kokko, “Sex, death and tragedy,” Trends. Ecol. Evol. 21, 225 (2006).
  11. Anna Melbinger, J. Cremer, and E. Frey, “Evolutionary game theory in growing populations,” Phys. Rev. Lett. 105, 178101 (2010).
  12. J. Cremer, A. Melbinger, and E. Frey, ‘‘Evolutionary and population dynamics: A coupled approach,” Phys. Rev. E. 84, 051921 (2011).
  13. Karl Wienand, M. Lechner, F. Becker, H. Jung, and E. Frey, “Non-selective evolution of growing populations,” PLoS ONE 10, 8 (2015).
  14. S. N. Chowdhury, S. Kundu, M. Perc, and D. Ghosh, “Complex evolutionary dynamics due to punishment and free space in ecological multigames,” Proc. R. Soc. A: Math. Phys. Eng. Sci. 477, 20210397 (2021).
  15. S. Nag Chowdhury, S. Kundu, J. Banerjee, M. Perc, and D. Ghosh, “Eco-evolutionary dynamics of cooperation in the presence of policing,” J. Theor. Biol. 518, 110606 (2021).
  16. S. Roy, S. Nag Chowdhury, P. C. Mali, M. Perc, and D. Ghosh, “Eco-evolutionary dynamics of multigames with mutations,” PLoS ONE 17, 8 (2022).
  17. S. Nag Chowdhury, J. Banerjee, M. Perc, and D. Ghosh, “Eco-evolutionary cyclic dominance among predators, prey, and parasites,” J. Theor. Biol. 564, 111446 (2023).
  18. K. Wienand, E. Frey, and M. Mobilia, ‘‘Evolution of a fluctuating population in a randomly switching environment,” Phys. Rev. Lett. 119, 158301 (2017).
  19. K. Wienand, E. Frey, and M. Mobilia, “Eco-evolutionary dynamics of a population with randomly switching carrying capacity,” J. R. Soc. Interface 15, 20180343 (2018).
  20. J. S. Weitz, C. Eksin, K. Paarporn, S. P. Brown, and W. C. Ratcliff, “An oscillating tragedy of the commons in replicator dynamics with game-environment feedback,” Proc. Natl. Acad. Sci. U.S.A. 113, E7518 (2016).
  21. X. Chen and A. Szolnoki, ‘‘Punishment and inspection for governing the commons in a feedback-evolving game,” PLoS Comput. Biol. 14, 7 (2018).
  22. Y.-H. Lin and J. S. Weitz, “Spatial interactions and oscillatory tragedies of the commons,” Phys. Rev. Lett. 122, 148102 (2019).
  23. A. R. Tilman, J. B. Plotkin, and E. Akcay, “Evolutionary games with environmental feedbacks,” Nat. Commun. 11, 915 (2020).
  24. J. D. Bairagya, S. S. Mondal, D. Chowdhury, and S. Chakraborty, “Game-environment feedback dynamics in growing population: Effect of finite carrying capacity,” Phys. Rev. E 104, 044407 (2021).
  25. F. Yan, X. Chen, Z. Qiu, and A. Szolnoki, “Cooperator driven oscillation in a time-delayed feedback-evolving game,” New J. Phys. 23, 053017 (2021).
  26. S. S. Mondal, M. Pathak, and S. Chakraborty, “Reward versus punishment: averting the tragedy of the commons in eco-evolutionary dynamics,” J. phys. Complex 3, 025005 (2022).
  27. L. Liu, X. Chen, and A. Szolnoki, “Coevolutionary dynamics via adaptive feedback in collective-risk social dilemma game,” Elife 12, e82954 (2023).
  28. J. D. Bairagya, S. S. Mondal, D. Chowdhury, and S. Chakraborty, “Eco-evolutionary games for harvesting self-renewing common resource: effect of growing harvester population,” J. phys. Complex 4, 025002 (2023).
  29. C. Xia, J. Wang, M. Perc, and Z. Wang, “Reputation and reciprocity,” Phys. Life Rev. 46, 8 (2023).
  30. M. Perc, J. Gómez-Gardeñes, A. Szolnoki, L. M. Floría, and Y. Moreno, “Evolutionary dynamics of group interactions on structured populations: a review,” J. R. Soc. Interface 10, 20120997 (2013).
  31. B. Fernández-Marín, R. Milla, N. Martín-Robles, E. Arc, I. Kranner, J. M. Becerril, and J. I. García-Plazaola, “Side-effects of domestication: cultivated legume seeds contain similar tocopherols and fatty acids but less carotenoids than their wild counterparts,” BMC Plant Biol. 14, 1599 (2014).
  32. H. C. J. Godfray and M. P. Hassell, “Discrete and continuous insect populations in tropical environments,” J. Anim. Ecol. 58, 153 (1989).
  33. R. M. May, “Regulation of populations with nonoverlapping generations by microparasites: A purely chaotic system,” Am. Nat. 125, 573 (1985).
  34. R. Boonstra, “Life history variation in maturation in fluctuating meadow vole populations (microtus pennsylvanicus),” Oikos 54, 265 (1989).
  35. O. Rossler, “An equation for hyperchaos,” Phys. Lett. A 71, 155 (1979).
  36. T. Matsumoto, L. O. Chua, and K. Kobayashi, “Hyper chaos: Laboratory experiment and numerical confirmation,” IEEE Trans. Circuits Syst. 33, 1143 (1986).
  37. G. Baier and M. Klein, “Maximum hyperchaos in generalized Hénon maps,” Phys. Lett. A 151, 281 (1990).
  38. P. Frederickson, J. L. Kaplan, E. D. Yorke, and J. A. Yorke, “The liapunov dimension of strange attractors,” J. Differ. Equ. 49, 185 (1983).
  39. A. Rapoport and A. Chammah, Prisoner’s Dilemma (University of Michigan Press, 1965).
  40. J. F. Nash, “Equilibrium points in n-person games,” Proc. Natl. Acad. Sci. U.S.A. 36, 48 (1950).
  41. E. Wagner, “The explanatory relevance of nash equilibrium: One-dimensional chaos in boundedly rational learning,” Philos. Sci. 80, 783 (2013).
  42. V. Pareto, Cours d’Économie Politique. Professé a l’Université de Lausanne. (F. Rouge, 1896).
  43. K. L. Cooke and M. Witten, “One-dimensional linear and logistic harvesting models,” Math. Model. 7, 301 (1986).
  44. J. D. Murray, Mathematical Biology (Springer Berlin Heidelberg, 1993).
  45. W. Ricker and F. R. B. of Canada, Handbook of Computations for Biological Statistics of Fish Populations, Canada. Fisheries Research Board. Bulletin (Queen’s Printer and Controller of Stationery, 1963).
  46. R. J. H. Beverton and S. J. Holt, On the Dynamics of Exploited Fish Populations (Springer Netherlands, 1993).
  47. M. P. Hassell, “Density-dependence in single-species populations,” J. Anim. Ecol. 44, 283 (1975).
  48. M. P. Hassell, J. H. Lawton, and R. M. May, “Patterns of dynamical behaviour in single-species populations,” J. Anim. Ecol. 45, 471 (1976).
  49. D. J. Rankin, K. Bargum, and H. Kokko, “The tragedy of the commons in evolutionary biology,” Trends. Ecol. Evol. 22, 643 (2007).
  50. R. Cressman and Y. Tao, “The replicator equation and other game dynamics,” Proc. Natl. Acad. Sci. U.S.A. 111, 10810 (2014).
  51. A. Mukhopadhyay and S. Chakraborty, “Replicator equations induced by microscopic processes in nonoverlapping population playing bimatrix games,” Chaos 31, 023123 (2021).
  52. A. Mukhopadhyay and S. Chakraborty, ‘‘Deciphering chaos in evolutionary games,” Chaos 30, 121104 (2020a).
  53. V. Pandit, A. Mukhopadhyay, and S. Chakraborty, “Weight of fitness deviation governs strict physical chaos in replicator dynamics,” Chaos 28, 033104 (2018).
  54. S. Hummert, K. Bohl, D. Basanta, A. Deutsch, S. Werner, G. Theißen, A. Schroeter, and S. Schuster, “Evolutionary game theory: cells as players,” Mol. BioSyst. 10, 3044 (2014).
  55. A. Mukhopadhyay and S. Chakraborty, “Periodic orbit can be evolutionarily stable: Case study of discrete replicator dynamics,” J. Theor. Biol. 497, 110288 (2020b).
  56. W. Huang, C. Hauert, and A. Traulsen, “Stochastic game dynamics under demographic fluctuations,” Proc. Natl. Acad. Sci. U.S.A. 112, 9064 (2015).
  57. F. Stollmeier and J. Nagler, “Unfair and anomalous evolutionary dynamics from fluctuating payoffs,” Phys. Rev. Lett. 120, 058101 (2018).
  58. R. A. Fisher, The genetical theory of natural selection (Oxford University Press: Clarendon, 1930).
  59. S. Wright, “Evolution in Mendelian populations,” Genetics 16, 97 (1931).
  60. P. A. P. Moran, “Random processes in genetics,” Math. Proc. Camb. Philos. Soc. 54, 60 (1958).
Citations (3)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets