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Quasi-species model for host-parasite coevolution with a frequency-dependent fitness landscape

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Abstract

We investigate the host-parasite coevolution by using the quasi-species model with a frequencydependent fitness landscape. We propose a quasi-species model for the host-parasite coevolution and find the phase diagram for a given set of dynamics parameters by means of a linear stability analysis and numerical solutions. There are four trivial equilibrium points, which are stable or unstable, and one internal equilibrium point, which is unstable or a center-fixed point enclosed by limit cycles, depending on the dynamics parameters. By starting from a random initial condition, we determine the separatrix and the basins of attraction. We also present the corresponding stochastic model for the host-parasite coevolution, and by computer simulation, we find that the stochastic simulation results are consistent with those of the quasi-species model.

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References

  1. R. M. May and R. M. Anderson, Parasitology 100, S59 (1990).

    Article  Google Scholar 

  2. V. Apanius, D. Penn, P. R. Slev, L. R. Ruff and W. K. Potts, Crit. Rev. Immunol. 17, 179 (1997).

    Article  Google Scholar 

  3. A. V. S. Hill, Annu. Rev. Genomics Hum. Genet. 2, 373 (2001).

    Article  Google Scholar 

  4. R. K. Grosberg and M. W. Hart, Science 289, 2111 (2000).

    Article  ADS  Google Scholar 

  5. P. H. Thrall, J. J. Burdon and A. Young, J. Ecol. 89, 736 (2001).

    Google Scholar 

  6. M. M. Palomino, B. C. Meyers, R. W. Michelmore and B. S. Gaut, Genome Res. 12, 1305 (2002).

    Article  Google Scholar 

  7. H. H. Flor, Adv. Genet. 8, 29 (1956).

    Article  Google Scholar 

  8. J. L. Dangl and J. D. G. Jones, Nature 411, 826 (2001).

    Article  ADS  Google Scholar 

  9. J. Bergelson, G. Dwyer and J. J. Emerson, Annu. Rev. Genet. 35, 469 (2001).

    Article  Google Scholar 

  10. E. B. Holub, Nat. Rev. Genet. 2, 516 (2001).

    Article  Google Scholar 

  11. A. Sasaki, Proc. R. Soc. Lond. Ser. B Biol. Sci. 267, 2183 (2000).

    Article  Google Scholar 

  12. J. Segarra, Phytopathology 95, 728 (2005).

    Article  Google Scholar 

  13. A. Tellier and J. K. M. Brown, Proc. R. Soc. Lond. Ser. B Biol. Sci. 274, 809 (2007).

    Article  Google Scholar 

  14. S. D. Jayakar, Theor. Popul. Biol. 1, 140 (1970).

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Computer Engineering, Hanshin University, Osan, 447-791, Korea

    Yung-Gyung Kang

  2. Department of Physics, The Catholic University of Korea, Bucheon, 420-743, Korea

    Jeong-Man Park

Authors
  1. Yung-Gyung Kang
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  2. Jeong-Man Park
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Correspondence to Jeong-Man Park.

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Kang, YG., Park, JM. Quasi-species model for host-parasite coevolution with a frequency-dependent fitness landscape. Journal of the Korean Physical Society 64, 322–327 (2014). https://doi.org/10.3938/jkps.64.322

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  • DOI: https://doi.org/10.3938/jkps.64.322

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