  Species evolution is essentially a random process of interaction between
biological populations and their environments. As a result, some physical
parameters in evolution models are subject to statistical fluctuations. In this
paper, two important parameters in the Eigen model, the fitness and mutation
rate, are treated as Gaussian distributed random variables simultaneously to
examine the property of the error threshold. Numerical simulation results show
that the error threshold in the fully random model appears as a crossover
region instead of a phase transition point, and as the fluctuation strength
increases the crossover region becomes smoother and smoother. Furthermore, it
is shown that the randomization of the mutation rate plays a dominant role in
changing the error threshold in the fully random model, which is consistent
with the existing experimental data. The implication of the threshold change
due to the randomization for antiviral strategies is discussed.
