Error thresholds for quasispecies on single peak Gaussian-distributed fitness landscapes

Based on the Eigen and Crow-Kimura models with a single peak fitness landscape, we propose that the fitness values of all molecules be Gaussian distributed random variables to incorporate the fluctuation effects of the fitness landscapes (noise of environments). And we investigate the quasispecies distribution and error threshold using ensemble average method within this theoretical framework. Numerical results show 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 a sizable fluctuation, quite different from the previous deterministic models, our statistical results reveal that the transition from quasi-species to error catastrophe is no longer so sharp, indicating the error threshold is located within a certain range and shifts toward a larger value.