title: A minimum on the mean number of steps taken in adaptive walks.
abstract: 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.
authors.affiliation: Department of Biology, University of Rochester, Rochester, NY 14627, U.S.A. aorr@mail.rochester.edu
authors.forename: H Allen
authors.initials: HA
authors.lastname: Orr
mesh_terms: D000220:Adaptation, Biological / Q000235:genetics*; D000465:Algorithms; D000818:Animals; D019143:Evolution, Molecular; D008957:Models, Genetic; D009154:Mutation; D012641:Selection, Genetic