进化的随机模型
A stochastic model of evolution
摘要：
我们提出了一个随机演化模型。物种的出生和死亡以恒定的概率发生。每个新物种都与从[0，1]上的均匀分布中采样的适应度相关联。每次有死亡事件，那么被杀死的类型是具有最小适应度的类型。我们证明了当出生概率大于死亡概率时，系统会发生剧烈的相变。适应度大于某一临界值的种群集合趋于均匀分布。另一方面，所有物种的适应度小于临界消失后，有限（随机）的时间。
英文摘要：
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event then the type that is killed is the one with the smallest fitness. We show that there is a sharp phase transition when the birth probability is larger than the death probability. The set of species with fitness higher than a certain critical value approach an uniform distribution. On the other hand all the species with fitness less than the critical disappear after a finite (random) time.
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