The Studys On The Randomization Of Mutation Rate In Eigen Model

The Eigen model is a dynamic model for describing the evolution of microscopic molecular species.It describes the biological evolution process of selection and mutation by mathematical form.It is of great theoretical significance for the study of the origin and evolution of species and the study of biodiversity.In 1989,Eigen Proposed predictions of quasi-species and error thresholds,which provided a theoretical basis for studying the evolution of viruses and new antiviral strategies.Species evolution can be seen as a stochastic process of interaction between biological groups and their surroundings,while random mutations provide a rich basis for the natural selection of species and are an important factor in the random process of species evolution.There are few studies on the random effects of mutations in species evolution.It is important to analyze the effect of mutation rate and the random effect on the basis of Eigen model.In this paper,the exact solution of quasi-species equation is solved by analytic method.Numerical simulation of quasi-species and error threshold is given by means of ensemble method.Some of the physical parameters in the species evolution model are affected by the fluctuation of the external environment,and the physical parameters in the model are processed as Gaussian distribution random variables,and the following main results are obtained:1?The two important parameters in the Eigen model.the fitness and mutation rate,are treated as Gaussian distributed random variables simultaneously.When the two are coupled by randomization,the width of the crossover region is linearly related to the fluctuation of the fitness.the width of the crossover region is exponentially related to the fluctuation of the mutation rate.2?The two important parameters in the Eigen model.the fitness and mutation rate,are treated as Gaussian distributed random variables simultaneously.In the case of the random coupling,the relationship between the width of the crossover region and the fluctuating strength of the variable is consistent with the previous one.At the same time,the variable and the width of the crossover region show different trends under different fluctuation strengths.3?When both fitness and mutation rate are randomized,the randomization of mutation rate dominates,which requires further analysis of the matrix elements in the mutation probability matrix,and then studies the extension mechanism of the error threshold.