合流过程是一个强大的统计框架，它允许我们从分子序列数据中重建祖先关系，推断过去人口动态。在许多生物医学应用中，如感染性疾病、细胞发育和肿瘤发生研究中，几个不同的人群共享演化历史，因此变得相互依存。推断这种依存关系是一个非常重要的，但也是一个具有挑战性的问题。随着测序技术的进步，我们可以利用高分辨率的生物数据来解决这个问题。在这里，我们介绍adaPop，一种概率模型，用于估计相互依存人群的过去人口动态并量化它们之间的依存程度。我们方法的一个重要特征是能够跟踪人群之间的时间变化关系，同时通过马尔可夫随机场先验在最小假设下来建模。我们提供了非参数估计器、扩展了基础模型的多个数据源集成方法，以及快速可扩展的推断算法。我们使用模拟数据测试了我们的方法，并在深入研究SARS-CoV-2的不同变体的演化历史方面展示了我们模型的实用性。版权所有：©2023 Cappello等人。本文是一个开放获取文章，根据知识共享署名许可证分发，在任何媒介和形式下都允许无限制的使用、分发和复制，前提是保留原作者和来源的出处。

The coalescent is a powerful statistical framework that allows us to infer past population dynamics leveraging the ancestral relationships reconstructed from sampled molecular sequence data. In many biomedical applications, such as in the study of infectious diseases, cell development, and tumorgenesis, several distinct populations share evolutionary history and therefore become dependent. The inference of such dependence is a highly important, yet a challenging problem. With advances in sequencing technologies, we are well positioned to exploit the wealth of high-resolution biological data for tackling this problem. Here, we present adaPop, a probabilistic model to estimate past population dynamics of dependent populations and to quantify their degree of dependence. An essential feature of our approach is the ability to track the time-varying association between the populations while making minimal assumptions on their functional shapes via Markov random field priors. We provide nonparametric estimators, extensions of our base model that integrate multiple data sources, and fast scalable inference algorithms. We test our method using simulated data under various dependent population histories and demonstrate the utility of our model in shedding light on evolutionary histories of different variants of SARS-CoV-2.Copyright: © 2023 Cappello et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.