Crow-Kimura模型中位点突变率对误差阈的随机效应（英文）

Randomization Effect of The Site Mutation Rate on The Error Threshold in the Crow-Kimura Model

为了补充Eigen模型和Crow-Kimura模型的随机效应研究,Crow-Kimura模型中的位点突变率被处理成高斯分布随机变量,从而研究误差阈值的特征以及误差阈值的扩展与随机突变率涨落强度之间的关系.准物种浓度和群体序参数分析表明,在位点突变率涨落较大时,误差阈值不再是相变点,而是平滑的转变区域.定量分析表明,随机Crow-Kimura模型中转变区宽度与涨落强度之间的关系是非线性的.将Crow-Kimura模型与Eigen模型的随机特征进行比较发现,在两个模型中适应值随机化使得转变区域的宽度和随机变量涨落强度之间的关系是线性的,而位点突变率随机化中两者的关系是非线性的(指数).对于随机化的Crow-Kimura模型,适应值随机化与位点突变率随机化引起的误差阈扩展效应相当.对于随机Eigen模型,误差阈的扩展效应则主要是由位点突变率的随机化引起的.之后,本文概述了Eigen模型和Crow Kimura模型中适应值和位点突变率随机化对误差阈值随机效应的影响,并讨论了上述结果对抗病毒策略、癌症治疗和动植物育种的重要意义.

In order to complement the randomization of the Eigen model and the Crow-Kimura model,the site mutation rate in the Crow-Kimura model is treated as a Gaussian distributed random variable.The characteristics of the error threshold as well as the relationship between the extension of the error threshold and the fluctuation strength of the randomized mutation rate are investigated.It is shown that both the relative concentrations and the order parameter indicate the error threshold is no longer a phase transition point but a smooth crossover region in the presence of a sizable fluctuation of the site mutation rate.The quantitative analysis demonstrates that the relationship between the width of the crossover region and the fluctuation strength in the mutation randomized Crow-Kimura model is nonlinear.The obtained results are compared with those from the randomized Eigen model and it is found that for the two randomized models the relationship between the width and the fluctuation strength is linear for the randomized fitness and nonlinear(exponential)for the randomized site mutation rate.For the randomized Crow-Kimura model the width caused by the randomized fitness is comparable to that caused by the randomized site mutation rate.Nevertheless,for the randomized Eigen model the width is mainly caused by the randomized site mutation rate.A full picture about the randomization effects of the fitness and site mutation rate on the error threshold based of the Eigen model and the Crow-Kimura model is then outlined.The implications of the above results for anti-viral strategies,cancer therapy and breeding of animals and plants are discussed.