http://iet.metastore.ingenta.com
1887

Wright–Fisher dynamics on adaptive landscape

Wright–Fisher dynamics on adaptive landscape

For access to this article, please select a purchase option:

Buy article PDF
£12.50
(plus tax if applicable)
Buy Knowledge Pack
10 articles for £75.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IET Systems Biology — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

Adaptive landscape, proposed by Sewall Wright, has provided a conceptual framework to describe dynamical behaviours. However, it is still a challenge to explicitly construct such a landscape, and apply it to quantify interesting evolutionary processes. This is particularly true for neutral evolution. In this work, the authors study one-dimensional Wright Fisher process, and analytically obtain an adaptive landscape as a potential function. They provide the complete characterisation for dynamical behaviours of all possible mutation rates under the influence of mutation and random drift. This same analysis has been applied to situations with additive selection and random drift for all possible selection rates. The critical state dividing the basins of two stable states is directly obtained by the landscape. In addition, the landscape is able to handle situations with pure random drift, which would be non-normalisable for its stationary distribution. The nature of non-normalisation is from the singularity of adaptive landscape. In addition, they propose a new type of neutral evolution. It has the same probability for all possible states. The new type of neutral evolution describes the non-neutral alleles with 0%. They take the equal effect of mutation and random drift as an example.

References

    1. 1)
      • P. Ao .
        1. Ao, P.: ‘Global view of bionetwork dynamics: adaptive landscape’, J. Genet. Genomics, 2009, 36, (2), pp. 6373 (doi: 10.1016/S1673-8527(08)60093-4).
        . J. Genet. Genomics , 2 , 63 - 73
    2. 2)
      • R.S. Yuan , P. Ao .
        2. Yuan, R.S., Ao, P.: ‘Beyond Ito and Stratonovich’, J. Stat. Mech.: Theor. Exp., 2012, 2012, (7), pp. 07010 (doi: 10.1088/1742-5468/2012/07/P07010).
        . J. Stat. Mech.: Theor. Exp. , 7 , 07010
    3. 3)
      • P. Ao .
        3. Ao, P.: ‘Laws in Darwinian evolutionary theory’, Phys. Life Rev., 2005, 2, (2), pp. 117156 (doi: 10.1016/j.plrev.2005.03.002).
        . Phys. Life Rev. , 2 , 117 - 156
    4. 4)
      • D.M. McCandlish .
        4. McCandlish, D.M.: ‘Visualizing fitness landscapes’, Evolution, 2011, 65, (6), pp. 15441558 (doi: 10.1111/j.1558-5646.2011.01236.x).
        . Evolution , 6 , 1544 - 1558
    5. 5)
      • D.M. Weinreich , S. Sindi , R.A. Watson .
        5. Weinreich, D.M., Sindi, S., Watson, R.A.: ‘Finding the boundary between evolutionary basins of attraction, and implications for Wrights fitness landscape analogy’, J. Stat. Mech. Theor. Exp., 2013, 01, pp. 01001 (doi: 10.1088/1742-5468/2013/01/P01001).
        . J. Stat. Mech. Theor. Exp. , 01001
    6. 6)
      • A. Prugel-Bennett .
        6. Prugel-Bennett, A.: ‘Modelling evolving populations’, J. Theor. Biol., 1997, 185, (1), pp. 8195 (doi: 10.1006/jtbi.1996.0295).
        . J. Theor. Biol. , 1 , 81 - 95
    7. 7)
      • M. Rattray , J.L. Shapiro .
        7. Rattray, M., Shapiro, J.L.: ‘Cumulant dynamics of a population under multiplicative selection, mutation, and drift’, Theor. Popul. Biol., 2001, 60, (1), pp. 1731 (doi: 10.1006/tpbi.2001.1531).
        . Theor. Popul. Biol. , 1 , 17 - 31
    8. 8)
      • N.H. Barton , J.B. Coe .
        8. Barton, N.H., Coe, J.B.: ‘On the application of statistical physics to evolutionary biology’, J. Theor. Biol., 2009, 259, (2), pp. 317324 (doi: 10.1016/j.jtbi.2009.03.019).
        . J. Theor. Biol. , 2 , 317 - 324
    9. 9)
      • N.H. Barton , H.P. de Vladar .
        9. Barton, N.H., de Vladar, H.P.: ‘Statistical mechanics and the evolution of polygenic quantitative traits’, Genetics, 2009, 181, (3), pp. 9971011 (doi: 10.1534/genetics.108.099309).
        . Genetics , 3 , 997 - 1011
    10. 10)
      • A.J. McKane , D. Waxman .
        10. McKane, A.J., Waxman, D.: ‘Singular solutions of the diffusion equation of population genetics’, J. Theor. Biol., 2007, 247, (4), pp. 849858 (doi: 10.1016/j.jtbi.2007.04.016).
        . J. Theor. Biol. , 4 , 849 - 858
    11. 11)
      • D. Zhou , H. Qian .
        11. Zhou, D., Qian, H.: ‘Fixation, transient landscape and diffusion's dilemma in stochastic evolutionary game dynamics’, Phys. Rev. E, 2011, 84, (3), pp. 031907(14 pages) (doi: 10.1103/PhysRevE.84.031907).
        . Phys. Rev. E , 3 , 031907
    12. 12)
      • F.J. Poelwijk , D.J. Kiviet , D.M. Weinreich , S.J. Tans .
        12. Poelwijk, F.J., Kiviet, D.J., Weinreich, D.M., Tans, S.J.: ‘Empirical fitness landscapes reveal accessible evolutionary paths’, Nature, 2007, 445, (7126), pp. 383386 (doi: 10.1038/nature05451).
        . Nature , 7126 , 383 - 386
    13. 13)
      • T. Aita , Y. Husimi .
        13. Aita, T., Husimi, Y.: ‘Biophysical connection between evolutionary dynamics and thermodynamics in in vitro evolution’, J. Theor. Biol., 2012, 294, (7), pp. 122129 (doi: 10.1016/j.jtbi.2011.10.036).
        . J. Theor. Biol. , 7 , 122 - 129
    14. 14)
      • P. Ao .
        14. Ao, P.: ‘Emerging of stochastic dynamical equalities and steady state thermodynamics from Darwinian dynamics’, Commun. Theor. Phys., 2008, 49, (5), pp. 10731090 (doi: 10.1088/0253-6102/49/5/01).
        . Commun. Theor. Phys. , 5 , 1073 - 1090
    15. 15)
      • M. Carneiro , D.L. Hartl .
        15. Carneiro, M., Hartl, D.L.: ‘Adaptive landscapes and protein evolution’. Proc. National Academy of Science USA, 2010, vol. 107, no. (suppl. 1), pp. 17471751.
        . Proc. National Academy of Science USA , 1747 - 1751
    16. 16)
      • R.A. Fisher . (1930)
        16. Fisher, R.A.: ‘The genetical theory of natural selection’ (Clarendon Press, Oxford, 1930, 1st edn.), pp. 2098.
        .
    17. 17)
      • S. Wright .
        17. Wright, S.: ‘Evolution in Mendelian populations’, Genetics, 1931, 16, (2), pp. 97159.
        . Genetics , 2 , 97 - 159
    18. 18)
      • R.A. Blythe , A.J. McKane .
        18. Blythe, R.A., McKane, A.J.: ‘Stochastic models of evolution in genetics, ecology and linguistics’, J. Stat. Mech: Theor. Exp., 2007, 2007, (7), pp. P07018 (doi: 10.1088/1742-5468/2007/07/P07018).
        . J. Stat. Mech: Theor. Exp. , 7 , P07018
    19. 19)
      • D. Waxman , L. Loewe .
        19. Waxman, D., Loewe, L.: ‘A stochastic model for a single click of Muller's ratchet’, J. Theor. Biol., 2010, 264, (4), pp. 11201132 (doi: 10.1016/j.jtbi.2010.03.014).
        . J. Theor. Biol. , 4 , 1120 - 1132
    20. 20)
      • P. Ao .
        20. Ao, P.: ‘Potential in stochatic differential equation: novel construction’, J. Phys. Math. Gen., 2004, 37, (3), pp. 2530 (doi: 10.1088/0305-4470/37/3/L01).
        . J. Phys. Math. Gen. , 3 , 25 - 30
    21. 21)
      • W.J. Ewens .
        21. Ewens, W.J.: ‘Mathematics, genetics and evolution’, Quantum Biol., 2013, 1, (3), pp. 931 (doi: 10.1007/s40484-013-0003-5).
        . Quantum Biol. , 3 , 9 - 31
    22. 22)
      • J.H. Gillespie .
        22. Gillespie, J.H.: ‘Population genetics: a concise guide’ (The Johns Hopkins University Press, 2nd edn. 2004), pp. 2098.
        .
    23. 23)
      • X.M. Zhu , L. Yin , L. Hood , P. Ao .
        23. Zhu, X.M., Yin, L., Hood, L., Ao, P.: ‘Robustness, stability and efficiency of phage lambda genetic switch: dynamical structure analysis’, J. Bioinf. Comput. Biol., 2004, 2, (4), pp. 785817 (doi: 10.1142/S0219720004000946).
        . J. Bioinf. Comput. Biol. , 4 , 785 - 817
    24. 24)
      • Y.F. Cao , H.M. Lu , J. Liang .
        24. Cao, Y.F., Lu, H.M., Liang, J.: ‘Probability landscape of heritable and robust epigenetic state of lysogeny in phage lambda’. Proc. National Academy of Sci. USA, 2010, vol. 107, no. 43, pp. 1844518450.
        . Proc. National Academy of Sci. USA , 43 , 18445 - 18450
    25. 25)
      • W. Feller .
        25. Feller, W.: ‘Diffusion processes in one dimension’, Trans. Am. Math. Soc., 1954, 77, (1), pp. 131 (doi: 10.1090/S0002-9947-1954-0063607-6).
        . Trans. Am. Math. Soc. , 1 , 1 - 31
    26. 26)
      • E. van Nimwegen , J.P. Crutchfield , M. Huynen .
        26. van Nimwegen, E., Crutchfield, J.P., Huynen, M.: ‘Neutral evolution of mutational robustness’. Proc. National Academy of Sci. USA, 1999, vol. 96, no. 17, pp. 97169720.
        . Proc. National Academy of Sci. USA , 17 , 9716 - 9720
    27. 27)
      • D.C. Krakauer , J.B. Plotkin .
        27. Krakauer, D.C., Plotkin, J.B.: ‘Redundancy, antiredundancy, and the robustness of genomes’. Proc. National Academy of Sci. USA, 2002, vol. 99, no. 3, pp. 14051409.
        . Proc. National Academy of Sci. USA , 3 , 1405 - 1409
    28. 28)
      • C.C. Li . (1955)
        28. Li, C.C.: ‘Population genetics’ (The University of Chicago Press, 1955, 1st edn.), pp. 1090.
        .
    29. 29)
      • S.Y. Jiao , P. Ao .
        29. Jiao, S.Y., Ao, P.: ‘Absorbing phenomena and escaping time for Muller's ratchet in adaptive landscape’, BMC Syst. Biol., 2012, 6, (suppl.), pp. S10(13 pages) (doi: 10.1186/1752-0509-6-S1-S10).
        . BMC Syst. Biol. , S10
    30. 30)
      • S. Wright .
        30. Wright, S.: ‘The role of mutation, inbreeding, crossbreeding and selection in evolution’. Proc. Sixth Int. Congr. of Genetics, Wisconsin, America, 1932, pp. 356366.
        . Proc. Sixth Int. Congr. of Genetics , 356 - 366
    31. 31)
      • H.A. Kramers .
        31. Kramers, H.A.: ‘Brownian motion in a field of force and the diffusion model of chemical reactions’, Physica, 1940, 7, (4), pp. 284304 (doi: 10.1016/S0031-8914(40)90098-2).
        . Physica , 4 , 284 - 304
    32. 32)
      • N.G. van Kampen .
        32. van Kampen, N.G.: ‘Ito versus stratonovich’, J. Stat. Phys., 1981, 24, (1), pp. 175187 (doi: 10.1007/BF01007642).
        . J. Stat. Phys. , 1 , 175 - 187
    33. 33)
      • M. Pigliucci , J.M. Kaplan . (2006)
        33. Pigliucci, M., Kaplan, J.M.: ‘Making sense of evolution: the conceptual foundations of evolutionary biology’ (University of Chicago Press, 20061st edn.), pp. 1120.
        .
    34. 34)
      • S. Gavrilets .
        34. Gavrilets, S.: ‘Evolution and speciation on holey adaptive landscapes’, Trends Ecol. Evol., 1997, 12, (8), pp. 307312 (doi: 10.1016/S0169-5347(97)01098-7).
        . Trends Ecol. Evol. , 8 , 307 - 312
    35. 35)
      • P. Ao .
        35. Ao, P.: ‘Darwinian dynamics implies developmental ascendency’, Biol. Theor., 2007, 2, (1), pp. 113115 (doi: 10.1162/biot.2007.2.1.113).
        . Biol. Theor. , 1 , 113 - 115
    36. 36)
      • J.H. Shi , T.Q. Chen , R.S. Yuan , B. Yuan , P. Ao .
        36. Shi, J.H., Chen, T.Q., Yuan, R.S., Yuan, B., Ao, P.: ‘Relation of a new interpretation of stochastic differential equations to Ito process’, J. Stat. Phys., 2012, 148, (3), pp. 579590 (doi: 10.1007/s10955-012-0532-8).
        . J. Stat. Phys. , 3 , 579 - 590
    37. 37)
      • M. Kimura .
        37. Kimura, M.: ‘Diffusion models in population genetics’, J. Appl. Probab., 1964, 1, (2), pp. 177232 (doi: 10.2307/3211856).
        . J. Appl. Probab. , 2 , 177 - 232
    38. 38)
      • S.J. Arnold , M.E. Pfrender , A.G. Jones .
        38. Arnold, S.J., Pfrender, M.E., Jones, A.G.: ‘The adaptive landscape as a conceptual bridge between micro-and macroevolution’, Genetica, 2001, 112, (1), pp. 932 (doi: 10.1023/A:1013373907708).
        . Genetica , 1 , 9 - 32
    39. 39)
      • F. Zhang , L. Xu , K. Zhang , E.K. Wang , J. Wang .
        39. Zhang, F., Xu, L., Zhang, K., Wang, E.K., Wang, J.: ‘The potential and flux landscape theory of evolution’, J. Chem. Phys., 2012, 137, (6), pp. 065102(19 pages) (doi: 10.1063/1.4734305).
        . J. Chem. Phys. , 6 , 065102
    40. 40)
      • J. Wang , L. Xu , E.K. Wang .
        40. Wang, J., Xu, L., Wang, E.K.: ‘Probability landscape and flux framework of non-equilibrium networks: robustness, dissipation and coherence of biochemical oscillations’. Proc. National Academy of Sci. USA, 2008, vol. 105, no. 34, pp. 1227112276.
        . Proc. National Academy of Sci. USA , 34 , 12271 - 12276
    41. 41)
      • J. Wang , K. Zhang , E.K. Wang .
        41. Wang, J., Zhang, K., Wang, E.K.: ‘Kinetic paths, time scale, and underlying landscape: a path integral framework to study global natures of nonequilibrium systems and networks’, J. Chem. Phys., 2010, 133, (12), pp. 125103(13 pages) (doi: 10.1063/1.3478547).
        . J. Chem. Phys. , 12 , 125103
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-syb.2012.0058
Loading

Related content

content/journals/10.1049/iet-syb.2012.0058
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address