Journal of the Korean Society for Industrial and Applied Mathematics

  • 제24권4호
  • /
  • Pages.351-362
  • /
  • 2020
  • /
  • 1226-9433(pISSN)
  • /
  • 1229-0645(eISSN)
한국산업응용수학회 (Korean Society for Industrial and Applied Mathematics)
권호 표지
DOI QR코드

DOI QR Code

RELATIVISTIC INTERPLAY BETWEEN ADAPTIVE MOVEMENT AND MOBILITY ON BIODIVERSITY IN THE ROCK-PAPER-SCISSORS GAME

  • PARK, JUNPYO (DEPARTMENT OF MATHEMATICAL SCIENCES, ULSAN NATIONAL INSTITUTE OF SCIENCE AND TECHNOLOGY) ;
  • JANG, BONGSOO (DEPARTMENT OF MATHEMATICAL SCIENCES, ULSAN NATIONAL INSTITUTE OF SCIENCE AND TECHNOLOGY)
  • 투고 : 2020.11.17
  • 심사 : 2020.12.07
  • 발행 : 2020.12.25
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Adaptive behaviors are one of ubiquitous features in evolutionary dynamics of populations, and certain adaptive behaviors can be witnessed by individuals' movements which are generally affected by local environments. In this paper, by revisiting the previous work, we investigate the sensitivity of species coexistence in the system of cyclic competition where species movement can be affected by local environments. By measuring the extinction probability through Monte-Carlo simulations, we find the relativistic effect of weights of local fitness and exchange rate for adaptive movement on species biodiversity which promotes species coexistence as the relativistic effect is intensified. In addition, by means of basins of initial conditions, we also found that adaptive movement can also affect species biodiversity with respect to the choice of initial conditions. The strong adaptive movement can eventually lead the coexistence as a globally stable state in the spatially extended system regardless of mobility.

키워드

과제정보

This work was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-2015S1A5A2A03049830)

참고문헌

  1. R. D. Holt, J. Grover, and D. Tilman, Simple rules for interspecific dominance in systems with exploitative and apparent competition, American Naturalist, 144 (1994), 741-771. https://doi.org/10.1086/285705
  2. A. Hastings, Can spatial variation alone lead to selection for dispersal?, Theoretical Population Biology, 24 (1983), 244-251. https://doi.org/10.1016/0040-5809(83)90027-8
  3. R. D. Holt and M. A. McPeek, Chaotic population-dynamics favors the evolution of dispersal, American Naturalist, 148 (1996), 709-718. https://doi.org/10.1086/285949
  4. M. A. Harrison, Y.-C. Lai, and R. D. Holt, A dynamical mechanism for coexistence of dispersing species without trade-offs in spatially extended ecological systems, Physical Review E, 63 (2001), 051905. https://doi.org/10.1103/PhysRevE.63.051905
  5. M. A. Harrison, Y.-C. Lai, and R. D. Holt, Dynamical mechanism for coexistence of dispersing species, Journal of Theoretical Biology, 213 (2001), 53-72. https://doi.org/10.1006/jtbi.2001.2404
  6. M. A. Nowak and R. M. May, Evolutionary games and spatial chaos, Nature, 359 (1992), 826-829. https://doi.org/10.1038/359826a0
  7. G. Szabo and C. Toke, Evolutionary prisoner's dilemma game on a square lattice, Physical Review E, 58 (1998), 69-73. https://doi.org/10.1103/physreve.58.69
  8. R. M. May and W. J. Leonard, Nonlinear aspects of competition between three species, SIAM Journal on Applied Mathematics, 29 (1975), 243-253. https://doi.org/10.1137/0129022
  9. J. Hofbauer and K. Sigmund, Evolutionary games and population dynamics, Cambridge University Press, Cambridge, 1998.
  10. T. Reichenbach, M. Mobilia, and E. Frey, Mobility promotes and jeopardizes biodiversity in rock-paperscissors games, Nature, 448 (2007), 1046-1049. https://doi.org/10.1038/nature06095
  11. T. Reichenbach, M. Mobilia, and E. Frey, Self-organization of mobile populations in cyclic competition, Journal of Theoretical Biology, 254 (2008), 368-383. https://doi.org/10.1016/j.jtbi.2008.05.014
  12. L. Frachebourg, P. L. Krapivsky, and E. Ben-Naim, Spatial organization in cyclic Lotka-Volterra systems, Physical Review E, 54 (1996), 6186-6200. https://doi.org/10.1103/PhysRevE.54.6186
  13. J. Knebel, T. Kruger, M. F. Weber, and E. Frey, Coexistence and survival in conservative Lotka-Volterra networks, Physical Review Letters, 110 (2013), 168106. https://doi.org/10.1103/physrevlett.110.168106
  14. M. Berr, T. Reichenbach, M. Schottenloher, and E. Frey, Zero-one survival behavior of cyclically competing species, Physical Review Letters, 102 (2009), 048102. https://doi.org/10.1103/PhysRevLett.102.048102
  15. A. Szolnoki and M. Perc, Zealots tame oscillations in the spatial rock-paper-scissors game, Physical Review E, 93 (2016), 062307. https://doi.org/10.1103/PhysRevE.93.062307
  16. A. Szolnoki, M. Mobilia, L. L. Jiang, B. Szczesny, A. M. Rucklidge, and M. Perc, Cyclic dominance in evolutionary games: a review Journal of The Royal Society Interface, 11 (2014), 20140735. https://doi.org/10.1098/rsif.2014.0735
  17. J. Park, Asymmetric interplay leads to robust coexistence by means of a global attractor in the spatial dynamics of cyclic competition Chaos, 28 (2018), 081103. https://doi.org/10.1063/1.5048468
  18. J. Park and B. Jang, Robust coexistence with alternative competition strategy in the spatial cyclic game of five species, Chaos, 29 (2019), 051105. https://doi.org/10.1063/1.5097003
  19. M. Mobilia, Oscillatory dynamics in rock-paper-scissors games with mutations, Journal of Theoretical Biology, 264 (2010), 1-10. https://doi.org/10.1016/j.jtbi.2010.01.008
  20. D. F. P. Toupo and S. H. Strogatz, Nonlinear dynamics of the rock-paper-scissors game with mutations, Physical Review E, 91 (2015), 052907. https://doi.org/10.1103/PhysRevE.91.052907
  21. J. Park, Biodiversity in the cyclic competition system of three species according to the emergence of mutant species, Chaos, 28 (2018), 053111. https://doi.org/10.1063/1.5021145
  22. J. Park, Nonlinear dynamics with Hopf bifurcations by targeted mutation in the system of rock-paper-scissors metaphor, Chaos, 29 (2019), 033102. https://doi.org/10.1063/1.5081966
  23. J. Park, Fitness-based mutation in the spatial rock-paper-scissors game: Shifting of critical mobility for extinction, EPL, 126 (2019), 38004. https://doi.org/10.1209/0295-5075/126/38004
  24. J. Park, Y. Do, Z.-G. Huang, and Y.-C. Lai, Persistent coexistence of cyclically competing species in spatially extended ecosystems, Chaos 23, 023128 (2013). https://doi.org/10.1063/1.4811298
  25. H. Shi, W.-X. Wang, R. Yang, and Y.-C. Lai, Basin of attraction for species extinction and coexistence in spatial rock-paper-scissors games, Physical Review E, 81 (2010), 030901(R).
  26. X. Ni, R. Yang, W.-X. Wang, Y.-C. Lai, and C. Grebogi, Basins of coexistence and extinction in spatially extended ecosystems of cyclically competing species, Chaos 20 (2010), 045116. https://doi.org/10.1063/1.3526993
  27. B. Kim and J. Park, Basins of distinct asymptotic states in the cyclically competing mobile five species game, Chaos 27, 103117 (2017). https://doi.org/10.1063/1.4998984
  28. R. Yang, W.-X. Wang, Y.-C. Lai, and C. Grebogi, Role of intraspecific competition in the coexistence of mobile populations in spatially extended ecosystems, Chaos, 20 (2010), 023113. https://doi.org/10.1063/1.3431629
  29. J. Park, Y. Do, B. Jang, and Y.-C. Lai, Emergence of unusual coexistence states in cyclic game systems, Scientific Reports, 7 (2017), 7465. https://doi.org/10.1038/s41598-017-07911-4
  30. J. Park, Balancedness among competitions for biodiversity in the cyclic structured three species system, Applied Mathematics and Computation, 320 (2018), 425-436. https://doi.org/10.1016/j.amc.2017.09.047
  31. J. Park, Y. Do, and B. Jang, Multistability in the cyclic competition system, Chaos, 28 (2018), 113110. https://doi.org/10.1063/1.5045366
  32. C. Hauert and O. Stenull, Simple Adaptive Strategy Wins the Prison's Dilemma, Journal of Theoretical Biology, 218 (2002), 261-272. https://doi.org/10.1006/jtbi.2002.3072
  33. B. J. McGill and J. S. Brown, Evolutionary Game Theory and Adaptive Dynamics of Continuous Traits, Annual Review of Ecology, Evolution, and Systematics, 38 (2007), 403-435. https://doi.org/10.1146/annurev.ecolsys.36.091704.175517
  34. R. Cressman and Y. Tao, The replicator equation and other game dynamics, Proceedings of the National Academy of Sciences of USA, 111 (2014), 10810-10817. https://doi.org/10.1073/pnas.1400823111
  35. P. D. Leenheer, A. Mohapatra, H. A. Ohms, D. A. Lytle, and J. M. Cushing, The puzzle of partial migration: Adaptive dynamics and evolutionary game theory perspectives, Journal of Theoretical Biology, 412 (2017), 172-185. https://doi.org/10.1016/j.jtbi.2016.10.011
  36. S. Redner, A Guide to First-Passage Processes, Cambridge University Press, Cambridge, 2001.

피인용 문헌

  1. Behavioural movement strategies in cyclic models vol.11, pp.1, 2020, https://doi.org/10.1038/s41598-021-85590-y