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Dynamics of the Eigen and the Crow-Kimura models for molecular evolution

David B. Saakian1,2, Olga Rozanova3, and Andrei Akmetzhanov4,*

  • 1Yerevan Physics Institute, Alikhanian Brothers Street 2, Yerevan 375036, Armenia
  • 2Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan
  • 3Mathematics and Mechanics Faculty, Moscow State University, Main building, Moscow 119992 Russia
  • 4Institute for Problems in Mechanics, Russian Academy of Sciences, Vernadsky Avenue 101-1, Moscow 115926, Russia

  • *saakian@yerphi.am
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Phys. Rev. E 78, 041908 – Published 8 October, 2008

DOI: https://doi.org/10.1103/PhysRevE.78.041908

Abstract

We introduce an alternative way to study molecular evolution within well-established Hamilton-Jacobi formalism, showing that for a broad class of fitness landscapes it is possible to derive dynamics analytically within the 1∕N accuracy, where N is the genome length. For a smooth and monotonic fitness function this approach gives two dynamical phases: smooth dynamics and discontinuous dynamics. The latter phase arises naturally with no explicite singular fitness function, counterintuitively. The Hamilton-Jacobi method yields straightforward analytical results for the models that utilize fitness as a function of Hamming distance from a reference genome sequence. We also show the way in which this method gives dynamical phase structure for multipeak fitness.

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Outline

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Phys. Rev. E 78, 041908– Published 8 October, 2008
  • Received 27 June 2007

© 2008 American Physical Society

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