A400_12c 664..667

664 NATURE | VOL 400 | 12 AUGUST 1999 | www.nature.com point mutations on the performance of digital organisms. In all cases, the ®tness (replication rate) of each mutant was calculated in the same environment in which its simple or complex parent evolved, and the mutant's ®tness is expressed relative to the parent. The ®rst tool makes every possible one-step point mutant for a particular parent. The default set includes 28 different instructions; given a parent of genome length 80, for example, there are 80 3 …28 2 1† ˆ 2;160 different one-step point mutants. The mean ®tness of these mutants permits exact calculation of a in the decay test. The second tool produces a random sample of progeny that differ from their parent by two or more point mutations. For each parent, we generated between 10 and 10 progeny with two mutations, three mutations and so on, up to ten mutations. The third tool produces and analyses pairs of point mutations alone and in combination; for each two-step mutant, we have both corresponding one-step mutants. Having the single mutants allows us to compare a double mutant's actual ®tness with the exact value expected under the hypothesis that the mutations interact in a multiplicative manner. We ran the pair test on 10 and 10 mutational pairs for each complex and simple organism, respectively. Statistical methods. We performed the Wilcoxon signed-ranks test on the difference scores for all comparisons between complex and simple organisms. This test re ̄ects the evolutionary relationship between pairs of organisms; it is also non-parametric and thus insensitive to deviations from a normal distribution. To estimate b in the decay tests, we minimized the sum of squared deviations around the log-transformed mean ®tness values. We excluded samples with fewer than 100 viable mutants, in which case log mean ®tness was poorly estimated. By increasing sample size to 10, we can obtain additional viable mutants; the exclusion of some values because of insuf®cient sampling appears to have no systematic effect on estimation of b.