  The stochastic Eigen model proposed by Feng et al. (Journal of theoretical
biology, 246 (2007) 28) showed that error threshold is no longer a phase
transition point but a crossover region whose width depends on the strength of
the random fluctuation in an environment. The underlying cause of this
phenomenon has not yet been well examined. In this article, we adopt a single
peak Gaussian distributed fitness landscape instead of a constant one to
investigate and analyze the change of the error threshold and the statistical
property of the quasi-species population. We find a roughly linear relation
between the width of the error threshold and the fitness fluctuation strength.
For a given quasi-species, the fluctuation of the relative concentration has a
minimum with a normal distribution of the relative concentration at the maximum
of the averaged relative concentration, it has however a largest value with a
bimodal distribution of the relative concentration near the error threshold.
The above results deepen our understanding of the quasispecies and error
threshold and are heuristic for exploring practicable antiviral strategies.
