between size and fitness. Thus, the replicate populations may diverge not only in size and fitness, but also in the functional relationship between size and fitness. In that case, there need not be any systematic relationship between size and fitness in cross-sectional regressions, even if the longitudinal regressions are strong.
Figure 8D shows the results of the 12 longitudinal (1 for each population) and 8 cross-sectional (1 for each time point) regressions. The mean of the longitudinal slopes is 1.063 fl-1. (That is, relative fitness, which is a dimensionless quantity, increases by 1.063 per fl increase in cell volume.) This mean is significantly greater than 0 (t = 11.72; 11 df; P < 0.001). In contrast, the mean of the cross-sectional slopes is only 0.187 fl-1, which is not significantly different from 0 (t = 1.61; 7 df; P = 0.150) but is significantly less than the mean of the longitudinal slopes (t = 6.01; 18 df; P < 0.001). Therefore, these analyses do not support the hypothesis that the functional relationship between size and fitness is causal and rigidly fixed (Figure 8B) but suggest instead that the replicate populations have diverged in this relationship (Figure 8C). These results therefore also challenge the controversial assumption of certain evolutionary analyses that genetic covariances between traits are constant over long periods (Lande, 1975, 1979; Kohn and Atchley, 1988; Turelli, 1988).
Chance and Necessity. The 12 bacterial populations had similar trajectories for both cell size and fitness (Figures 2 and 6). It is perhaps surprising that the populations evolved in such a parallel fashion, given that their evolution depended on mutations that arose independently in each population. Of course, a critical factor promoting parallel evolution was the simple fact that populations evolved in identical environments. A second factor promoting parallelism may have been large population sizes, which would give rise to identical mutations in the replicate populations. Each population underwent 7.5 × 1011 cell replications (5 × 107 cell replications per ml per day × 10 ml × 1500 days). The estimated rate of mutation in E. coli (Drake, 1991) is 2.5 × 10-3 mutation per genome replication (5 × 10-10 mutation per bp replication × 5 × 106 bp per genome). Thus, each population experienced 2 × 109 mutations. With 5 × 106 bp per genome and three alternative point mutations at each bp (ignoring more complex mutations), this translates to >100 occurrences, on average, for every point mutation in the whole genome! (Of course, drift eliminates many mutations shortly after they occur, but even so this figure suggests redundancy.)