Investigation Of The Random Error Model In Species Evolution

As is well known, evolution is the essence of biology. If there were no evolution, there would be no life. In the evolution of species, the mutation causes the evolution. Therefore, we should carefully deal with the mutation rate appearing in the species evolution theories in order to better understand evolution of species.In various extant models of species evolution, the evolution is described as a deterministic process. Randomized models for the evolution are rare, especially for those where the mutation rate is treated as a random variable.The present study is mainly based on the Eigen model which is a species evolution model at the molecular level. Currently, the locus mutation rate in the Eigen model is a given value, however, the evolution at the molecular level is affected by many factors: genetic factors and external environment factors of genes. As a result, the mutation rate could change with space and time irregularly and should be a random variable. So in this study, we first consider mutation rate as a Gaussian distributed random variable, which converts the deterministic model to random model, so that we can make the Eigen model more realistically. Second, the mutation rate model further extension of randomization, through quantitative change fitness, observe its effect on the randomized model of mutation rate Third, we put the fitness and the mutation rate of gauss random at the same time, and make this random model compares with the randomized model of mutation rate and the randomized model of fitness. Through the comparison of the randomized model with deterministic model, we found that, in the randomized model, when the fluctuation strength of the rate becomes large, the error threshold transforms from a phase transition point into a crossover region. When we make the fitness quantitative changing, we found that in the randomized model of mutation rate, error threshold becomes wider when the ratio of main sequence and mutation sequence′fitness increase, but there is no link to the numerical of each sequence′fitness. Finally, we also found that the relationship between the randomized model of the two rate at the same time and the randomized model of mutation rate and the randomized model of fitness is that their error threshold′width conforms to the approximate linear superposition. This conclusion can make us understand the mutation breeding, virus and evolution of cancer cells better.