A minimum on the mean number of steps taken in adaptive walks

J Theor Biol. 2003 Jan 21;220(2):241-7. doi: 10.1006/jtbi.2003.3161.


I consider the adaptation of a DNA sequence when mutant fitnesses are drawn randomly from a probability distribution. I focus on "gradient" adaptation in which the population jumps to the best mutant sequence available at each substitution. Given a random starting point, I derive the distribution of the number of substitutions that occur during adaptive walks to a locally optimal sequence. I show that the mean walk length is a constant:L = e-1, where e approximately 2.72. I argue that this result represents a limit on what is possible under any form of adaptation. No adaptive algorithm on any fitness landscape can arrive at a local optimum in fewer than a mean of L = e-1 steps when starting from a random sequence. Put differently, evolution must try out at least e wild-type sequences during an average bout of adaptation.

Publication types

  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, P.H.S.

MeSH terms

  • Adaptation, Biological / genetics*
  • Algorithms
  • Animals
  • Evolution, Molecular*
  • Models, Genetic*
  • Mutation
  • Selection, Genetic