On the role of the degradation rates for the dominance of the fittest in Eigen's quasispecies model

The existence of an error threshold of the mutation rate in Eigen's quasispecies model has been computationally demonstrated exclusively in the case when the degradation rates of all model genotypes are equal. Here we explore the case with different degradation rates and demonstrate examples for which the type that has highest fitness in the absence of mutation can preserve its dominance independently of the value of the mutation rate. The examples are formulated based on analysis of the equilibria at the two extreme mutation rate values and suggest absence of an error threshold in a number of cases, most prominently when the degradation rate of the wild type is much smaller that the degradation rates of the mutants.