标题： 生物进化中的秩统计量 显示英文标题

标题： Rank Statistics in Biological Evolution

摘要： 我们对生物进化过程进行统计分析。 具体来说，我们研究了随机复制-突变-死亡模型，其中某一物种的种群可能通过出生或死亡而增长或减少，此外，突变会导致新物种的产生。 我们按起源的时间顺序对各种物种进行排序。 第k个物种的平均种群N_k随排名呈代数衰减，N_k ~ M^{mu} k^{-μ}，其中M是平均总种群。 特征指数mu=(alpha-gamma)/(alpha+beta-gamma)依赖于复制率alpha、突变率beta和死亡率gamma。 此外，第k个物种所有后代的平均种群P_k具有普遍的代数行为，P_k ~ M/k。 显示英文摘要

摘要： We present a statistical analysis of biological evolution processes. Specifically, we study the stochastic replication-mutation-death model where the population of a species may grow or shrink by birth or death, respectively, and additionally, mutations lead to the creation of new species. We rank the various species by the chronological order by which they originate. The average population N_k of the kth species decays algebraically with rank, N_k ~ M^{mu} k^{-mu}, where M is the average total population. The characteristic exponent mu=(alpha-gamma)/(alpha+beta-gamma)$ depends on alpha, beta, and gamma, the replication, mutation, and death rates. Furthermore, the average population P_k of all descendants of the kth species has a universal algebraic behavior, P_k ~ M/k.