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We modify the deterministic Eigen model of species evolution into a randomized model in order to render the Eigen model more realistic for the description of species evolution. In the framework of the Eigen model, we regard the locus mutation rate of a genetic sequence as a Gaussian distributed random variable. Thus the Eigen model turns into a random model. In this randomized model, we can see that when the fluctuation strength of the mutation rate is small, the error threshold of the quasispecies changes slightly and still serves as a phase transition point. However, when the fluctuation strength becomes large, the error threshold shifts from a phase transition point into a crossover region. Since the error threshold in the real species evolution is a crossover region, we should consider the upper limit of the crossover region when dealing with practical problems.
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Keywords:
- Gaussian distributed random variable /
- mutation rate /
- quasispecies /
- error threshold
[1] Eigen M 1971 Naturwissenchaften 58 465
[2] Eigen M, McCaskill J, Schuster P 1989 Adv. Chem. Phys. 75 149
[3] Crow J F, Kimura M 1970 An Introduction to Population Genetics Theory (New York: Harper & Row) pp3-382
[4] Kimura M 1984 The Neutral Theory of Molecular Evolution (Cambridge: Cambridge University Press) pp34-50
[5] Kamp C, Bornholdt S 2002 Phys. Rev. Lett. 88 068104
[6] Kamp C 2003 Microbes Infect. 5 1397
[7] Tang F K, Wang Q, Hua N, Lu H, Tang X Z, Ma P 2011 Chin. Phys. B 20 010702
[8] Tang F K, Wang Q, Hua N, Tang X Z, Lu H, Ma P 2010 Chin. Phys. B 19 120601
[9] Deng S X, Cheng C, Ni G H, Meng Y D, Chen H 2010 Chin. Phys. B 19 105203
[10] Wang J, Ma Q L 2008 Chin. Phys. B 17 4424
[11] Li Z, Chen G H, Zhang L H, Yang Q S, Feng J 2006 Chin. Phys. 15 310
[12] Sheng L Y, Jia W Y 2005 Acta Phys. Sin. 54 5574 (in Chinese) [盛利元, 贾伟尧 2005 54 5574]
[13] Liu F M, Zhai H C, Yang X P 2003 Acta Phys. Sin. 52 2462 (in Chinese) [刘福民, 翟宏琛, 杨晓苹 2003 52 2462]
[14] Huang X G, Xu J X, Huang W, Zhu P C 2001 Acta Phys. Sin. 50 2296 (in Chinese) [黄显高, 徐健学, 黄伟, 朱甫臣 2001 50 2296]
[15] Feng X L, Gu J Z, Li Y X, Zhuo Y Z 2007 Commun. Theor. Phys. 48 763
[16] Feng X L, Li Y X, Gu J Z, Zhuo Y Z 2007 J. Theor. Biol. 246 28
[17] Muller H J 1922 Am. Nat. 56 32
[18] Drake J W, Holland J J 1999 Proc. Natl. Acad. Sci. 96 13910
[19] Eigen M, Schuster P 1977 Naturwissenchaften 64 541
[20] Eigen M 1986 Chem. Scrip. 26B 13
[21] Schuster P 1986 Chem. Scrip. 26B 27
[22] LeuthÄusser I 1987 J. Chem. Phys. 84 1884
[23] LeuthÄusser I 1987 J. Stat. Phys. 48 343
[24] Thompson C J, McBride J L 1974 Math. Biosci. 21 127
[25] Eigen M 2000 J. Biophys. Chem. 85 101
[26] Schuster P 2011 Theory Biosci. 130 71
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[1] Eigen M 1971 Naturwissenchaften 58 465
[2] Eigen M, McCaskill J, Schuster P 1989 Adv. Chem. Phys. 75 149
[3] Crow J F, Kimura M 1970 An Introduction to Population Genetics Theory (New York: Harper & Row) pp3-382
[4] Kimura M 1984 The Neutral Theory of Molecular Evolution (Cambridge: Cambridge University Press) pp34-50
[5] Kamp C, Bornholdt S 2002 Phys. Rev. Lett. 88 068104
[6] Kamp C 2003 Microbes Infect. 5 1397
[7] Tang F K, Wang Q, Hua N, Lu H, Tang X Z, Ma P 2011 Chin. Phys. B 20 010702
[8] Tang F K, Wang Q, Hua N, Tang X Z, Lu H, Ma P 2010 Chin. Phys. B 19 120601
[9] Deng S X, Cheng C, Ni G H, Meng Y D, Chen H 2010 Chin. Phys. B 19 105203
[10] Wang J, Ma Q L 2008 Chin. Phys. B 17 4424
[11] Li Z, Chen G H, Zhang L H, Yang Q S, Feng J 2006 Chin. Phys. 15 310
[12] Sheng L Y, Jia W Y 2005 Acta Phys. Sin. 54 5574 (in Chinese) [盛利元, 贾伟尧 2005 54 5574]
[13] Liu F M, Zhai H C, Yang X P 2003 Acta Phys. Sin. 52 2462 (in Chinese) [刘福民, 翟宏琛, 杨晓苹 2003 52 2462]
[14] Huang X G, Xu J X, Huang W, Zhu P C 2001 Acta Phys. Sin. 50 2296 (in Chinese) [黄显高, 徐健学, 黄伟, 朱甫臣 2001 50 2296]
[15] Feng X L, Gu J Z, Li Y X, Zhuo Y Z 2007 Commun. Theor. Phys. 48 763
[16] Feng X L, Li Y X, Gu J Z, Zhuo Y Z 2007 J. Theor. Biol. 246 28
[17] Muller H J 1922 Am. Nat. 56 32
[18] Drake J W, Holland J J 1999 Proc. Natl. Acad. Sci. 96 13910
[19] Eigen M, Schuster P 1977 Naturwissenchaften 64 541
[20] Eigen M 1986 Chem. Scrip. 26B 13
[21] Schuster P 1986 Chem. Scrip. 26B 27
[22] LeuthÄusser I 1987 J. Chem. Phys. 84 1884
[23] LeuthÄusser I 1987 J. Stat. Phys. 48 343
[24] Thompson C J, McBride J L 1974 Math. Biosci. 21 127
[25] Eigen M 2000 J. Biophys. Chem. 85 101
[26] Schuster P 2011 Theory Biosci. 130 71
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