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Under constant selection, each trait has a fixed fitness, and small mutationrates allow populations to efficiently exploit the optimal trait. Therefore itis reasonable to expect mutation rates will evolve downwards. However, we findthis need not be the case, examining several models of mutation. While upwardsevolution of mutation rate has been found with frequency or time dependentfitness, we demonstrate its possibility in a much simpler context. This workuses adaptive dynamics to study the evolution of mutation rate, and thereplicator-mutator equation to model trait evolution. Our approach differs fromprevious studies by considering a wide variety of methods to representmutation. We use a finite string approach inspired by genetics, as well as amodel of local mutation on a discretization of the unit intervals, handlingmutation beyond the endpoints in three ways. The main contribution of this workis a demonstration that the evolution of mutation rate can be significantlymore complicated than what is usually expected in relatively simple models.

The Point of No Return: Evolution of Excess Mutation Rate is Possible Even for Simple Mutation Models