Abstract Branching processes in random environments arise in a variety of applications such as biology, finance, and other contemporary scientific areas. Motivated by these applications, this article investigates the problem of ancestral inference. Specifically, the article develops point and interval estimates for the mean number of ancestors initiating a branching process in i.i.d. random environments and establishes their asymptotic properties when the number of replications diverges to infinity. These results are then used to quantitate the number of DNA molecules in a genetic material using data from polymerase chain reaction experiments. Numerical experiments and data analyses are included to support the proposed methods. An R software package for implementing the methods of this manuscript is also included.

中文翻译：

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随机环境中分支过程的祖先推断及其在聚合酶链反应中的应用

摘要 随机环境中的分支过程出现在各种应用中，例如生物学、金融和其他当代科学领域。受这些应用的启发，本文研究了祖先推理的问题。具体而言，本文开发了在 iid 随机环境中启动分支过程的祖先的平均数量的点和区间估计，并在重复次数发散到无穷大时建立了它们的渐近特性。然后将这些结果用于使用聚合酶链反应实验的数据对遗传材料中的 DNA 分子数量进行定量。包括数值实验和数据分析以支持所提出的方法。还包括一个用于实现本手稿方法的 R 软件包。