Phase transition in random adaptive walks on correlated fitness landscapes.

@article{Park2015PhaseTI,
  title={Phase transition in random adaptive walks on correlated fitness landscapes.},
  author={Su-Chan Park and Ivan G. Szendro and Johannes Neidhart and Joachim H A Krug},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2015},
  volume={91 4},
  pages={
          042707
        }
}
We study biological evolution on a random fitness landscape where correlations are introduced through a linear fitness gradient of strength c. When selection is strong and mutations rare the dynamics is a directed uphill walk that terminates at a local fitness maximum. We analytically calculate the dependence of the walk length on the genome size L. When the distribution of the random fitness component has an exponential tail, we find a phase transition of the walk length D between a phase at… 

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Note that the random fitness components remain unchanged during the adaptive walk

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