A Minimum on the Mean Number of Steps Taken in Adaptive Walks
✍ Scribed by H.ALLEN ORR
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 138 KB
- Volume
- 220
- Category
- Article
- ISSN
- 0022-5193
No coin nor oath required. For personal study only.
✦ Synopsis
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.