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Breaking records in the evolutionary race

Author

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  • Krug, Joachim
  • Jain, Kavita

Abstract

We explore some aspects of the relationship between biological evolution processes and the mathematical theory of records. For Eigen's quasispecies model with an uncorrelated fitness landscape, we show that the evolutionary trajectories traced out by a population initially localized at a randomly chosen point in sequence space can be described in close analogy to record dynamics, with two complications. First, the increasing number of genotypes that become available with increasing distance from the starting point implies that fitness records are more frequent than for the standard case of independent, identically distributed random variables. Second, fitness records can be bypassed, which strongly reduces the number of genotypes that take part in an evolutionary trajectory. For exponential and Gaussian fitness distributions, this number scales with sequence length N as N, and it is of order unity for distributions with a power law tail. This is in strong contrast to the number of records, which is of order N for any fitness distribution.

Suggested Citation

  • Krug, Joachim & Jain, Kavita, 2005. "Breaking records in the evolutionary race," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 358(1), pages 1-9.
    • Handle: RePEc:eee:phsmap:v:358:y:2005:i:1:p:1-9
    DOI: 10.1016/j.physa.2005.06.002
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    Citations

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    Cited by:

    1. Paolo Sibani & Stefan Boettcher & Henrik Jeldtoft Jensen, 2021. "Record dynamics of evolving metastable systems: theory and applications," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(1), pages 1-23, January.
    2. Wergen, Gregor, 2014. "Modeling record-breaking stock prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 396(C), pages 114-133.
    3. Claude Godreche & Satya N. Majumdar & Gregory Schehr, 2015. "Record statistics for random walk bridges," Papers 1505.06053, arXiv.org, revised Jan 2016.
    4. Claude Godreche & Satya N. Majumdar & Gregory Schehr, 2017. "Record statistics of a strongly correlated time series: random walks and L\'evy flights," Papers 1702.00586, arXiv.org.
    5. Gregory Schehr & Satya N. Majumdar, 2013. "Exact record and order statistics of random walks via first-passage ideas," Papers 1305.0639, arXiv.org.

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