Abstract We study a simple model of DNA evolution in a growing population of cells. Each cell contains a nucleotide sequence which randomly mutates at cell division. Cells divide according to a branching process. Following typical parameter values in bacteria and cancer cell populations, we take the mutation rate to zero and the final number of cells to infinity. We prove that almost every site (entry of the nucleotide sequence) is mutated in only a finite number of cells, and these numbers are independent across sites. However independence breaks down for the rare sites which are mutated in a positive fraction of the population. The model is free from the popular but disputed infinite sites assumption. Violations of the infinite sites assumption are widespread while their impact on mutation frequencies is negligible at the scale of population fractions. Some results are generalised to allow for cell death, selection, and site-specific mutation rates. For illustration we estimate mutation rates in a lung adenocarcinoma.

中文翻译：

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呈指数增长的细胞群的遗传组成

摘要 我们在不断增长的细胞群中研究了一个简单的 DNA 进化模型。每个细胞都包含一个核苷酸序列，该序列在细胞分裂时会随机突变。细胞根据分支过程分裂。遵循细菌和癌细胞群中的典型参数值，我们将突变率设为零，将最终细胞数设为无穷大。我们证明几乎每个位点（核苷酸序列的条目）仅在有限数量的细胞中发生突变，并且这些数量在位点之间是独立的。然而，独立性因在人口的正比例中发生突变的稀有位点而崩溃。该模型不受流行但有争议的无限站点假设的影响。违反无限位点假设的情况很普遍，而它们对突变频率的影响在人口比例上可以忽略不计。一些结果被概括为允许细胞死亡、选择和位点特异性突变率。为了说明，我们估计了肺腺癌的突变率。