Error Thresholds in Single-Peak Gaussian Distributed Fitness Landscapes

Based on the Eigen and Crow-Kimura models with a single-peak fitnesslandscape, we propose the fitness values of all sequence types to beGaussian distributed random variables to incorporate the effects ofthe fluctuations of the fitness landscapes (noise of environments)and investigate the concentration distribution and error thresholdof quasispecies by performing an ensemble average within thistheoretical framework. We find that a small fluctuation of the fitness landscape causes only a slight change in the concentration distribution and error threshold, which implies that the error threshold is stable against small perturbations. However, for asizable fluctuation, quite different from the previous deterministicmodels, our statistical results show that the transition fromquasi-species to error catastrophe is not so sharp, indicating that theerror threshold is located within a certain range and has a shifttoward a larger value. Our results are qualitatively in agreementwith the experimental data and provide a new implication forantiviral strategies.