随机化的Eigen模型研究

Eigen model of randomness in species evolution

为了使Eigen模型能够更真实地描述物种的演化过程,将确定性Eigen模型改造成随机模型.以Eigen模型为理论框架,把基因序列中每一个位点的突变率看作一个高斯随机变量,从而导出随机性Eigen模型.对于此随机性Eigen模型,当突变率的涨落强度较小时,准物种的误差阈位置几乎没有改变,仍是个相变点;而当突变率的涨落强度变大时,误差阈由一个相变点变为一个转变区域.在真实的物种演化过程中,误差阈应是一个转变区域,而且在解决实际问题时应考虑该转变区域的上限.

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.