Data from: Understanding past population dynamics: Bayesian coalescent-based modeling with covariates

Effective population size characterizes the genetic variability in a population and is a parameter of paramount importance in population genetics and evolutionary biology. Kingman's coalescent process enables inference of past population dynamics directly from molecular sequence data, and researchers have developed a number of flexible coalescent-based models for Bayesian nonparametric estimation of the effective population size as a function of time. Major goals of demographic reconstruction include identifying driving factors of effective population size, and understanding the association between the effective population size and such factors. Building upon Bayesian nonparametric coalescent-based approaches, we introduce a flexible framework that incorporates time-varying covariates that exploit Gaussian Markov random fields to achieve temporal smoothing of effective population size trajectories. To approximate the posterior distribution, we adapt efficient Markov chain Monte Carlo algorithms designed for highly structured Gaussian models. Incorporating covariates into the demographic inference framework enables the modeling of associations between the effective population size and covariates while accounting for uncertainty in population histories. Furthermore, it can lead to more precise estimates of population dynamics. We apply our model to four examples. We reconstruct the demographic history of raccoon rabies in North America and find a significant association with the spatiotemporal spread of the outbreak. Next, we examine the effective population size trajectory of the DENV-4 virus in Puerto Rico along with viral isolate count data and find similar cyclic patterns. We compare the population history of the HIV-1 CRF02_AG clade in Cameroon with HIV incidence and prevalence data and find that the effective population size is more reflective of incidence rate. Finally, we explore the hypothesis that the population dynamics of musk ox during the Late Quaternary period were related to climate change.有效种群大小（effective population size）可表征种群内的遗传变异水平，是种群遗传学与进化生物学领域中极为关键的参数。金曼溯祖过程（Kingman's coalescent process）能够直接基于分子序列数据推断历史种群动态，此前已有研究者开发出多种基于溯祖过程的灵活模型，用于以时间为自变量的有效种群大小贝叶斯非参数估计。种群历史重建的核心目标包括识别有效种群大小的驱动因素，以及厘清有效种群大小与这些影响因子间的内在关联。本研究基于贝叶斯非参数溯祖方法，提出一种融入时变协变量的灵活建模框架，该框架借助高斯马尔可夫随机场（Gaussian Markov random fields）实现有效种群大小动态轨迹的时间平滑。为近似后验分布，本研究适配了专为高结构化高斯模型设计的高效马尔可夫链蒙特卡洛（Markov chain Monte Carlo）算法。将协变量纳入种群历史推断框架，可在考量种群历史不确定性的同时，建模有效种群大小与协变量间的关联；此外，该策略还可获得更为精准的种群动态估计结果。我们将所提模型应用于四个实例：其一，重建北美地区浣熊狂犬病的种群历史，发现其与疫情的时空传播存在显著关联；其二，分析波多黎各地区登革病毒4型（DENV-4）的有效种群大小动态轨迹，并结合病毒分离株计数数据，发现二者呈现相似的周期性模式；其三，对比喀麦隆地区HIV-1 CRF02_AG亚型的种群历史与HIV感染发病率及流行率数据，发现有效种群大小更能反映感染发病率；最后，验证了晚更新世时期麝牛的种群动态与气候变化相关的假说。