The vast majority of microbiome research so far has focused on the structure of the microbiome at a single time-point. There have been several studies that measure the microbiome from a particular environment over time. A few models have been developed by extending time series models to accomodate specific features in microbiome data to address questions of stability and interactions of the microbime time series. Most research has observed the stability and mean reversion for some microbiomes. However, little has been done to study the mean reversion rates of these stable microbes and how sampling frequencies are related to such conclusions. In this paper, we begin to rectify this situation. We analyse two widely studied microbial time series data sets on four healthy individuals. We choose to study healthy individuals because we are interested in the baseline temporal dynamics of the microbiome. For this analysis, we focus on the temporal dynamics of individual genera, absorbing all interactions in a stochastic term. We use a simple stochastic differential equation model to assess the following three questions. (1) Does the microbiome exhibit temporal continuity? (2) Does the microbiome have a stable state? (3) To better understand the temporal dynamics, how frequently should data be sampled in future studies? We find that a simple Ornstein–Uhlenbeck model which incorporates both temporal continuity and reversion to a stable state fits the data for almost every genus better than a Brownian motion model that contains only temporal continuity. The Ornstein–Uhlenbeck model also fits the data better than modelling separate time points as independent. Under the Ornstein–Uhlenbeck model, we calculate the variance of the estimated mean reversion rate (the speed with which each genus returns to its stable state). Based on this calculation, we are able to determine the optimal sample schemes for studying temporal dynamics. There is evidence of temporal continuity for most genera; there is clear evidence of a stable state; and the optimal sampling frequency for studying temporal dynamics is in the range of one sample every 0.8–3.2 days.

中文翻译：

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OU过程在人类微生物组时间动态建模和计算最佳采样方案中的应用

迄今为止，绝大多数微生物组研究都集中在单个时间点的微生物组结构上。随着时间的流逝，已经有一些研究测量来自特定环境的微生物组。通过扩展时间序列模型以适应微生物组数据中的特定特征，解决了微生物时间序列的稳定性和相互作用的问题，已经开发了一些模型。大多数研究已经观察到某些微生物组的稳定性和均值回复。但是，几乎没有做过研究这些稳定微生物的平均回复率以及采样频率如何与这些结论相关的工作。在本文中，我们开始纠正这种情况。我们分析了四个健康个体的两个广泛研究的微生物时间序列数据集。我们选择研究健康的个体，因为我们对微生物组的基线时间动态感兴趣。对于此分析，我们专注于单个属的时间动态，以随机的方式吸收所有相互作用。我们使用一个简单的随机微分方程模型来评估以下三个问题。（1）微生物组是否表现出时间连续性？（2）微生物组是否稳定？（3）为了更好地了解时间动态，在未来的研究中应该多久采样一次数据？我们发现，与仅包含时间连续性的布朗运动模型相比，结合时间连续性和恢复稳定状态的简单Ornstein-Uhlenbeck模型适合几乎所有属的数据。与将单独的时间点建模为独立的时间相比，Ornstein–Uhlenbeck模型还更适合数据。在Ornstein–Uhlenbeck模型下，我们计算估计的平均回复率（每个属返回其稳定状态的速度）的方差。基于此计算，我们能够确定用于研究时间动态的最佳采样方案。大多数属都有时间连续性的证据。有明确的证据表明状态稳定；研究时间动力学的最佳采样频率为每0.8-3.2天采样一次。我们能够确定用于研究时间动态的最佳采样方案。大多数属都有时间连续性的证据。有明确的证据表明状态稳定；研究时间动力学的最佳采样频率为每0.8-3.2天采样一次。我们能够确定用于研究时间动态的最佳采样方案。大多数属都有时间连续性的证据。有明确的证据表明状态稳定；研究时间动力学的最佳采样频率为每0.8-3.2天采样一次。