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BP: Fachverband Biologische Physik

BP 26: Posters: Statistical Physics of Biological Systems

BP 26.9: Poster

Tuesday, March 17, 2015, 14:00–16:00, Poster A

Phase transition in random adaptive walks on correlated fitness landscapes — Su-Chan Park¹, Ivan Szendro², •Johannes Neidhart², and Joachim Krug² — ¹The Catholic University of Korea, Bucheon, Korea — ²Institut für Theoretische Physik, Universität zu Köln, Deutschland

We study biological evolution on a random fitness landscape with linear fitness gradient. When selection is strong and mutations rare the dynamics is an uphill walk that terminates at a local fitness maximum. The mean walk length is a function of the genome size L. We show that if and only if the random contribution to the fitness is exponentially distributed, the mean walk length displays a phase transition as a function of the strength of the fitness gradient. For all other distributions only a single phase exists. The considered process is equivalent to a zero temperature Metropolis dynamics for the random energy model in an external magnetic field which leads to a connection to the aging dynamics of spin glasses. See also arXiv:1408.4856.