Abstract
In this article, we model analytically the evolution of mutation rate in asexual organisms. Three selective forces are present. First, everything else being equal, individuals with higher mutation rate have a larger fitness, thanks to the energy and time saved by not replicating DNA accurately. Second, as a flip side, the genome of these individuals is replicated with errors that may negatively affect fitness. Third, and conversely, replication errors have a potential benefit if beneficial mutations are to be generated. Our model describes the fate of modifiers of mutation rate under the three forces and allows us to predict the long-term evolutionary trajectory of mutation rate. we obtain three major results. First, in asexuals, the needs for both adaptation and genome preservation are not evolutionary forces that can stabilize mutation rate at an intermediate optimum. When adaptation has a significant role, it primarily destabilizes Mutation rate and yields the emergence of strong-effect mutators. Second, in contrast to what is usually believed, the appearance of modifiers with large mutation rate is more likely when the fitness cost of each deleterious mutation is weak, because the cost of replication errors is then paid after a delay. Third, in small populations, and even if adaptations are needed, mutation rate is always blocked at the minimum attainable level, because the rate of adaptation is too slow to play a significant role. Only populations whose size is above a critical mass see their mutation rate affected by the need for adaptation.