Eigen model of randomness in species evolution

Abstract

We modify the deterministic Eigen model of species evolution into a randomized model in order to render the Eigen model more realistic for the description of species evolution. In the framework of the Eigen model, we regard the locus mutation rate of a genetic sequence as a Gaussian distributed random variable. Thus the Eigen model turns into a random model. In this randomized model, we can see that when the fluctuation strength of the mutation rate is small, the error threshold of the quasispecies changes slightly and still serves as a phase transition point. However, when the fluctuation strength becomes large, the error threshold shifts from a phase transition point into a crossover region. Since the error threshold in the real species evolution is a crossover region, we should consider the upper limit of the crossover region when dealing with practical problems.