The optimum mutation rate to adapt a new fitness peak

We examined the optimum mutation rate the fitness peak randomly disappears and reappears at a distance in the sequence space. We assumed that fitness landscape has a single peak and the peak position in the sequence space changes randomly with the rate of environment fluctuation P. The optimum mutation rate per genome depends on the rate P of environmental fluctuation , the relative fitness a0 of the peak sequence, and the Hamming distance n between the current peak and the new peak.Our analytical approximation shows that the mutation rate equals zero if there is no environmental fluctuation, and that the rate monotonically increases with the rate of environmental fluctuation.Comparing with analytical approximation and the simulation, the approximation agrees well with the simulation results as long as the rate of environmental fluctuation is small.European Conference on Mathematical and Theoretical Biolog