● Darwin believed that mutations have their causes, but they do not arise because they would be good for the organisms in which they occur; they are “random,” not “guided.” ● Darwin also held that adaptive evolution is a gradual process, meaning that it involves the accumulation of small phenotypic changes rather than large ones. ● An experiment by the Lederbergs is analyzed that is widely taken to refute the idea that mutations are guided. ● A thought experiment is provided to clarify what the theses of random and guided mutation mean. ● It is argued that the fact that microbial populations increase their mutation rates when they are starved does not show that mutations are guided. ● R.A. Fisher’s geometric argument for gradualism is analyzed. Motoo Kimura’s formula for the fixation probability of an allele shows why Fisher’s argument fails; Allen Orr’s follow-up does better. ● Fisher and Orr are talking about the likelihood of gradualism, not its probability.