Bacteria and culture conditions
The bacteria used in this study were all derived from a single population, designated Ara-1, that is part of the long-term evolution experiment [1–3]. Details concerning the founding strain of E. coli B, culture conditions, and so on are given elsewhere . In brief, this population was propagated serially by 1:100 daily transfers for 20,000 generations (= 3,000 days) in Davis minimal (DM) salts medium supplemented with glucose at 25 μg/mL and incubated at 37°C. In this study, we use population samples from 1,000-generation intervals, which were stored at -80°C with glycerol as a cryo-protectant. Each sample contains millions of cells and includes essentially all of the genetic diversity present in the population at the time of storage.
The Ara-1 population and its ancestor are unable to grow on the sugar L-arabinose. However, an Ara+ variant of the ancestor has been generated, and it has previously served as the common competitor for samples from the evolving Ara-1 population. Numerous experiments have shown that this Ara+ marker is selectively neutral under the culture conditions used in the long-term evolution experiment. However, this marker allows evolved and ancestral competitors to be distinguished and enumerated by plating on tetrazolium-arabinose (TA) indicator agar .
For this study, we needed Ara+ clones derived from the Ara-1 population at generations 5,000, 10,000, 15,000 and 20,000 in addition to the ancestral Ara+ clone. We used an Ara+ mutant clone that was isolated previously from a clone sampled at generation 10,000 from Ara-1 . For generations 5,000, 15,000 and 20,000 we randomly chose single clones from each of the corresponding samples taken from Ara-1. Each clone was grown to high density, concentrated by centrifugation, and plated on minimal-arabinose agar medium  to find spontaneous Ara+ mutants. Three Ara+ mutants were isolated from each clone, and each mutant was assayed in preliminary competitions against the population sample from which it came. We retained for this study the single Ara+ mutant whose estimated fitness relative to its source sample was closest to unity (and, in all cases, not significantly different from 1). To summarize, this study uses 21 population samples of Ara- cells taken at 0, 1,000, 2,000,..., 20,000 generations from the evolving Ara-1 population, and 5 neutrally marked Ara+ mutant clones derived from generations 0, 5,000, 10,000, 15,000 and 20,000 of the same population.
Measuring relative fitness
We performed a total of 315 competitions to measure the fitness of each population sample relative to each marked clone, with three fold-replication. The competitions followed the same protocol described in detail elsewhere . To summarize briefly, the competitions were performed under the exact same culture conditions as in the long-term evolution experiment. To ensure that any two competitors were comparably acclimated to the competition environment, they were simultaneously removed from the freezer, grown separately in a nutrient-rich broth for one day, and then acclimated for another day to the competition environment. The competitors were then mixed at a 1:1 volumetric ratio, diluted 1:100 into fresh DM and incubated at 37°C for one day. Appropriate dilutions were plated on TA agar at the start of the competition and again after 24 h, to estimate the initial and final numbers of each competitor. In a few cases, plate counts were less than 50 total or less than 15 for one competitor. In these cases, we repeated the competition experiments to obtain more accurate estimates of relative fitness based on higher counts. The relative fitness of two competitors was calculated simply as the ratio of their realized population growth rates during competition . Let N (0) and N (1) denote initial and final population densities, respectively, and let subscripts i and j indicate the two competitors. Then relative fitness is calculated as:
W (j:i) = ln [N
Relative fitness is dimensionless because the same time units are used in calculating both competitors' realized population growth rates.
Standard statistical analyses were used throughout, with one exception. The jackknife method [, pp 795–799] was used to calculate the confidence interval around the mean value in Figure 5B. In particular, the mean cumulative gain observed over four 5,000-generation intervals was calculated as the product of four successive means, each based on six measured values (three from a later sample competed against an earlier clone, and three from a later clone competed against an earlier sample). Owing to the non-linear dependence of a multiplicative product of means on the measured values, one cannot calculate a confidence interval using standard methods. The jackknife method yields a confidence interval that accurately reflects variation in the 24 underlying measurements. The jackknife method was not needed to compute the confidence intervals around the means in Figure 5A and 5C, because both of these means are simple arithmetic averages and hence do not involve any non-linearities.