| Summary: | Under constant selection, each trait has a fixed fitness, and small mutation rates allow populations to efficiently exploit the optimal trait. Therefore, it is reasonable to expect that mutation rates will evolve downwards. However, we find that this need not be the case, examining several models of mutation. While upwards evolution of the mutation rate has been found with frequency- or time-dependent fitness, we demonstrate its possibility in a much simpler context. This work uses adaptive dynamics to study the evolution of the mutation rate, and the replicator–mutator equation to model trait evolution. Our approach differs from previous studies by considering a wide variety of methods to represent mutation. We use a finite string approach inspired by genetics as well as a model of local mutation on a discretization of the unit intervals, handling mutation beyond the endpoints in three ways. The main contribution of this work is a demonstration that the evolution of the mutation rate can be significantly more complicated than what is usually expected in relatively simple models.
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