Application of OU processes to modelling temporal dynamics of the human microbiome, and calculating optimal sampling schemes

Toby Kenney,Hong Gu,Junqiu Gao

doi:10.1186/s12859-020-03747-4

Abstract

BackgroundThe 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.ResultsFor 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.ConclusionsThere 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.

Highlights

The vast majority of microbiome research so far has focused on the structure of the microbiome at a single time-point
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
We focus on the dynamics of each individual genus without explicitely modelling the interactions between different genera

Summary

Introduction

The vast majority of microbiome research so far has focused on the structure of the microbiome at a single time-point. Pascal et al [6] found that under some β -diversity measures, there was more variation between multiple gut microbiome samples from individuals with Crohn’s disease than healthy controls, and there was less variation in samples from individuals with ulcerative colitis. This suggests that the dynamics of the microbiome may be affected by these diseases. They were able to improve classification accuracy They argued that this might be caused by IBD patients having more variable microbiomes. It could be explained by the fact that sampling more replicates would in general improve prediction

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