Figure 1.
Evolution of suboptimal mutation rates on a complex fitness landscape.
Fitness is shown as a function of the genomic mutation rate. The solid line shows mean fitness of the final population, itself averaged over 50 runs, for 15 different static mutation rates (U = 10−5, 10−4 and from 10−3 to 10 at 1/3 log10 intervals). The shaded area represents±1 s.e.m. The optimal mutation rate—the rate that maximized final fitness—was Uopt≈4.641 (vertical dashed line). The two colored points show the mean fitness and mutation rate of the final population, averaged over 50 runs, in experiments where mutation rates freely evolved with starting values of either 10 (red) or 10−3 (blue) (error bars represent±1 s.e.m). Evolved mutation rates and fitness values were both orders of magnitude lower than those observed in the experiment with Uopt.
Figure 2.
Evolutionary trajectories for fitness and mutation rate on a complex fitness landscape.
(A) Evolution of average log-fitness±1 s.e.m. for treatments with the mutation rate fixed at Uopt = 4.641 (black) and for treatments with variable mutation rates starting at either 10 (red) or 10−3 (blue). (B) Evolution of average log genomic mutation rate±1 s.e.m. for treatments with variable mutation rates starting at either 10 (red) or 10−3 (blue). The black line indicates the mutation rate that had produced the highest average fitness for that time point.
Figure 3.
Evolution of mutation rates on simple fitness landscapes with different ruggedness.
Here, fitness depended solely on the match between the environment and the number of a key instruction that organisms had in their genomes. In season A (left column) the key instruction was deleterious while it was beneficial in season B (center column). Rugged fitness landscapes with maladaptive valleys (rows 2–4) were introduced by setting the fitness of organisms with intermediate numbers of the key instruction to the minimum fitness level of one. The right-most column shows the results of evolution experiments under each of these selective regimes. Final fitness is shown as a function of genomic mutation rate for both static and dynamic mutation rates. The solid black line represents the average of the mean fitness across 10 runs for each of 100 different static mutation rates ranging from U = 0.01 to 1 in increments of 0.01. The two colored points represent the mean fitness and mutation rate, both averaged over 50 runs where the mutation rate freely evolved, with initial rates of U = 1 (red) or 10−5 (blue). Mutation rate and fitness values were time-averaged over the last 10 of 50 environmental changes. Owing to very similar final values, despite the very large initial differences, the individual colored points are indistinguishable in the first two rows, and error bars are not visible. The arrows indicate where mutation rates began and ended, on average, for the dynamic-rate experiments. Although the optimal mutation rate increases as a function of valley size (note the right-shift in the dashed line from top to bottom), the evolved mutation rates in fact decrease as a function of valley size (note the left-shift of the blue and red points from top to bottom).
Figure 4.
Evolutionarily stable mutation rate does not depend on the frequency with which the mutation rate changes (Π).
The evolution of mutation rates in the explicit fitness landscape with a valley size of three is shown for several values of Π, as indicated by the colored key. Each curve shows the average of 20 runs; the adjacent bands represent±1 s.e.m. The value of Uopt was determined in previous experiments (see text). The rate of approach toward the evolutionarily stable mutation rate depends on Π, but the equilibrium value itself does not.
Table 1.
Outcomes of competitions between lineages with optimal (Uopt = 0.24) versus suboptimal (Usubopt) mutation rates in the explicit fitness landscape with a valley size of 3.