Journal of the Korean Physical Society

  • 제73권9호
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  • Pages.1219-1224
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  • 2018
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  • 0374-4884(pISSN)
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  • 1976-8524(eISSN)
한국물리학회 (Korean Physical Society)
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Phase Transitions and Phase Diagram of the Island Model with Migration

  • Park, Jeong-Man (Department of Physics, The Catholic University of Korea)
  • 투고 : 2018.09.03
  • 심사 : 2018.09.06
  • 발행 : 2018.11.15
⟨ 이전 논문 다음 논문 ⟩

초록

We investigate the evolutionary dynamics and the phase transitions of the island model which consists of subdivided populations of individuals confined to two islands. In the island model, the population is subdivided so that migration acts to determine the evolutionary dynamics along with selection and genetic drift. The individuals are assumed to be haploid and to be one of two species, X or Y. They reproduce according to their fitness values, die at random, and migrate between the islands. The evolutionary dynamics of an individual based model is formulated in terms of a master equation and is approximated by using the diffusion method as the multidimensional Fokker-Planck equation (FPE) and the coupled non-linear stochastic differential equations (SDEs) with multiplicative noise. We analyze the infinite population limit to find the phase transitions from the monomorphic state of one type to the polymorphic state to the monomorphic state of the other type as we vary the ratio of the fitness values in two islands and complete the phase diagram of our island model.

키워드

과제정보

연구 과제 주관 기관 : National Research Foundation of Korea

참고문헌

  1. Y-G. Kang and J-M. Park, J. Korean Phys. Soc. 71, 528 (2017). https://doi.org/10.3938/jkps.71.528
  2. S. Wright, Genetics 16, 97 (1931).
  3. F. Rousset, Genetic Structure and Selection in Subdi-vided Populations (Princeton University Press, Oxford, 2004).
  4. G. W. A. Constable and A. J. McKane, Phys. Rev. E 89, 032141 (2014). https://doi.org/10.1103/PhysRevE.89.032141
  5. G. W. A. Constable and A. J. McKane, J. Theor. Biol. 358, 149 (2014). https://doi.org/10.1016/j.jtbi.2014.05.033
  6. G. W. A. Constable and A. J. McKane, Phys. Rev. Lett. 114, 038101 (2015). https://doi.org/10.1103/PhysRevLett.114.038101
  7. C. W. Gardiner, Handbook of Stochastic Methods, 4th ed. (Springer, Berlin, 2009).
  8. J. Grasman and O. A. van Herwaarden, Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in Application (Springer-Verlag, Berlin, 1999).
  9. N. G. Van Kampen, Stochastic Processes in Physics and Chemistry (Elsevier Science, Amsterdam, 1992).
  10. T. Biancalani, L. Dyson and A. J. McKane, Phys. Rev. Lett. 112, 038101 (2014). https://doi.org/10.1103/PhysRevLett.112.038101
  11. F. Jafarpour, T. Biancalani and N. Goldenfeld, Phys. Rev. Lett. 115, 158101 (2015). https://doi.org/10.1103/PhysRevLett.115.158101
  12. G. W. A. Constable, T. Rogers, A. J. McKane and C. E. Tarnita, Proc. Natl. Acad. Sci. U.S.A. 113, E4745 (2016). https://doi.org/10.1073/pnas.1603693113