Orr H Allen
Department of Biology, University of Rochester, Rochester, NY 14627, U.S.A.
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.
我考虑当突变适应度从概率分布中随机抽取时DNA序列的适应性。我专注于“梯度”适应性，即种群在每次替换时跃迁至可用的最佳突变序列。给定一个随机起点，我推导出在向局部最优序列的适应性进化过程中发生的替换次数的分布。我表明平均进化长度是一个常数：L = e⁻¹，其中e约为2.72。我认为这一结果代表了任何形式的适应性可能达到的极限。当从随机序列开始时，在任何适应度景观上的任何适应性算法都无法在少于平均L = e⁻¹步的情况下达到局部最优。换句话说，在平均一轮适应性过程中，进化必须至少尝试e个野生型序列。
