Natural selection fails to optimize mutation rates for long-term adaptation on rugged fitness landscapes

Abstract

The rate of mutation is central to evolution. Mutations are required for adaptation, yet most mutations with phenotypic effects are deleterious. As a consequence, the mutation rate that maximizes adaptation will be some intermediate value. Here, we used digital organisms to investigate the ability of natural selection to adjust and optimize mutation rates. We assessed the optimal mutation rate by empirically determining what mutation rate produced the highest rate of adaptation. Then, we allowed mutation rates to evolve, and we evaluated the proximity to the optimum. Although we chose conditions favorable for mutation rate optimization, the evolved rates were invariably far below the optimum across a wide range of experimental parameter settings. We hypothesized that the reason that mutation rates evolved to be suboptimal was the ruggedness of fitness landscapes. To test this hypothesis, we created a simplified landscape without any fitness valleys and found that, in such conditions, populations evolved near-optimal mutation rates. In contrast, when fitness valleys were added to this simple landscape, the ability of evolving populations to find the optimal mutation rate was lost. We conclude that rugged fitness landscapes can prevent the evolution of mutation rates that are optimal for long-term adaptation. This finding has important implications for applied evolutionary research in both biological and computational realms.

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 U_opt≈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 U_opt.

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 U_opt = 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 U_opt 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.