Tavaré Simon
Irving Institute for Cancer Dynamics, Columbia University, 1190 Amsterdam Avenue, New York, NY 10027, USA.
Philos Trans R Soc Lond B Biol Sci. 2025 Feb 13;380(1919):20230300. doi: 10.1098/rstb.2023.0300. Epub 2025 Feb 20.
This review focuses on linear birth-and-death processes (LBDPs), describing the basic properties of the population-size process and the underlying ancestral trees that record how the evolving species (or individuals or cells) are related. The first section describes the Yule, or linear birth, process setting. Analogous results for the birth-and-death process (BDP) are given. The stochastic structure of the reconstructed tree obtained by pruning branches that do not survive to the present time is detailed. In §2, the BDP with immigration is described. Immigration is a mechanism to introduce new types into a population evolving through time. For the Yule process, marked Poisson process arguments are used to illustrate properties of the sample variance of the number of families observed in two consecutive time intervals. In the final section, we describe a recent method for approximate Bayesian computation using random forests, and illustrate it with an example of inference from DNA sequence data about the split rate and mutation rate in a birth-and-death model for the evolution of a cell population.This article is part of the theme issue '"A mathematical theory of evolution": phylogenetic models dating back 100 years'.
本综述聚焦于线性生死过程（LBDPs），描述了种群规模过程的基本特性以及记录进化物种（或个体或细胞）如何关联的潜在祖先树。第一节描述了尤尔过程或线性出生过程的设定，并给出了生死过程（BDP）的类似结果。详细阐述了通过修剪未存活至今的分支而得到的重建树的随机结构。在第2节中，描述了具有迁入的BDP。迁入是一种将新类型引入随时间演化的种群的机制。对于尤尔过程，使用标记泊松过程的论据来说明在两个连续时间间隔内观察到的家族数量的样本方差的性质。在最后一节中，我们描述了一种使用随机森林进行近似贝叶斯计算的最新方法，并以从DNA序列数据推断细胞群体进化的生死模型中的分裂率和突变率为例进行说明。本文是主题特刊“‘进化的数学理论’：可追溯到100年前的系统发育模型”的一部分。
