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Originally published as Genetics Published Articles Ahead of Print on December 18, 2006.

Genetics, Vol. 175, 1275-1288, March 2007, Copyright © 2007
doi:10.1534/genetics.106.067165

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Deterministic and Stochastic Regimes of Asexual Evolution on Rugged Fitness Landscapes

Kavita Jain*,1 and Joachim Krug{dagger}

* Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel and {dagger} Institut für Theoretische Physik, Universität zu Köln, 50937 Köln, Germany

1 Corresponding author: Department of Physics of Complex Systems, Weizmann Institute of Science, P.O. Box 26, Rehovot 76100, Israel.
E-mail: kavita.jain{at}weizmann.ac.il

We study the adaptation dynamics of an initially maladapted asexual population with genotypes represented by binary sequences of length L. The population evolves in a maximally rugged fitness landscape with a large number of local optima. We find that whether the evolutionary trajectory is deterministic or stochastic depends on the effective mutational distance deff up to which the population can spread in genotype space. For deff = L, the deterministic quasi-species theory operates while for deff < 1, the evolution is completely stochastic. Between these two limiting cases, the dynamics are described by a local quasi-species theory below a crossover time Tx while above Tx the population gets trapped at a local fitness peak and manages to find a better peak via either stochastic tunneling or double mutations. In the stochastic regime deff < 1, we identify two subregimes associated with clonal interference and uphill adaptive walks, respectively. We argue that our findings are relevant to the interpretation of evolution experiments with microbial populations.




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