Phase diagram of the Eigen model under changing environments with a sharp-peak fitness function

We study the evolution dynamics of biological organisms under changing environments by using the Eigen model for quasi-species with the sharp-peak fitness function. While in the static case with the sharp-peak fitness function f(ξ)=(A - A _o) δ _ξn + A _o, (A > A _o), the critical value q ^static _c=(A _o/A) ^1/N appears as a lower bound on the copying fidelity, below which no effective selection can occur, in the dynamic case where the position of the sharp peak oscillates between ξ=N and ξ=0 with period T., the critical value on the copying fidelity is found to be q ^dynamic _c=(2A _o/(A + A ₀)) ^1/N and the phase diagram for the copying fidelity q and the fitness parameter A _o/A phase space is modified according to the environmental change. We also calculate the stationary values for the maximum and the minimum population probabilities of the master sequences with ξ=N and ξ=0.