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Adaptive Landscape with Singularity in Evolutionary Processes

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Nonlinear Dynamics and Complexity

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 8))

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Abstract

Adaptive landscape, proposed by Sewall Wright, has been used to find optimized solutions of a system. The optimized solution of an evolutionary system is when evolution maximizes or minimizes the value of some function of the trait under consideration, thus providing an absolute measure of fixation for a biological process in a probabilistic sense. We survey the role of adaptive landscape and give some general results concerning the question of infinite potential escaping. The results presented include complex dynamical behaviors manifested by adaptive landscape with singularity in all parameters regimes. In addition, both metaphoric and quantitative description of many complex biological phenomena is provided by adaptive landscape, such as the rare event of transition between different stable states.

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Acknowledgements

The critical discussion with Prof. Zhu Xiaomei is appreciated. We also thank Jiang Pengyao, Wang Yanbo, and other members in the lab for their constructive comments.

Author information

Authors and Affiliations

  1. Shanghai Center for Systems Biomedicine, Department of Mathematics, Shanghai Jiao Tong University, Shanghai, China

    Shuyun Jiao

  2. Xinyang Normal University, Henan, China

    Shuyun Jiao

  3. Department of Biomathematiccs, University of California, Los Angeles, USA

    Song Xu

  4. Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, Shanghai, China

    Ping Ao

Authors
  1. Shuyun Jiao
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  2. Song Xu
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  3. Ping Ao
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Corresponding author

Correspondence to Ping Ao .

Editor information

Editors and Affiliations

  1. San Luis Potosi University, San Luis Potosi, Mexico

    Valentin Afraimovich

  2. School of Engineering Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, Illinois, USA

    Albert C. J. Luo

  3. Shandong Normal University, Ji’nan, People's Republic of China

    Xilin Fu

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Jiao, S., Xu, S., Ao, P. (2014). Adaptive Landscape with Singularity in Evolutionary Processes. In: Afraimovich, V., Luo, A., Fu, X. (eds) Nonlinear Dynamics and Complexity. Nonlinear Systems and Complexity, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-02353-3_6

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  • DOI: https://doi.org/10.1007/978-3-319-02353-3_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-02352-6

  • Online ISBN: 978-3-319-02353-3

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