title: Dynamics of the Eigen and the Crow-Kimura models for molecular evolution.
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 1N 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.
authors.affiliation: Yerevan Physics Institute, Alikhanian Brothers Street 2, Yerevan 375036, Armenia and Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan. saakian@yerphi.am
authors.forename: David B
authors.initials: DB
authors.lastname: Saakian
authors.forename: Olga
authors.initials: O
authors.lastname: Rozanova
authors.forename: Andrei
authors.initials: A
authors.lastname: Akmetzhanov
mesh_terms: D003198:Computer Simulation; D019143:Evolution, Molecular; D016678:Genome; D008954:Models, Biological