There has been a lot of research about the role of the microbiome in various processes. The research has focused almost exclusively 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. However, even in these studies, little has been done to study the temporal dynamics of the microbiome. In this paper, we begin to rectify this situation. We analyse a widely studied microbial data set that contains a time series of the microbiome from four body sites on two healthy individuals. We choose a data set based on 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, ignoring the interactions. We use simple stochastic differential equation models 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 all genera 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 at least some 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.