Umibato: estimation of time-varying microbial interaction using continuous-time regression hidden Markov model

Abstract

MotivationAccumulating evidence has highlighted the importance of microbial interaction networks. Methods have been developed for estimating microbial interaction networks, of which the generalized Lotka-Volterra equation (gLVE)-based method can estimate a directed interaction network. The previous gLVE-based method for estimating microbial interaction networks did not consider time-varying interactions.ResultsIn this study, we developed unsupervised learning based microbial interaction inference method using Bayesian estimation (Umibato), a method for estimating time-varying microbial interactions. The Umibato algorithm comprises Gaussian process regression (GPR) and a new Bayesian probabilistic model, the continuous-time regression hidden Markov model (CTRHMM). Growth rates are estimated by GPR, and interaction networks are estimated by CTRHMM. CTRHMM can estimate time-varying interaction networks using interaction states, which are defined as hidden variables. Umibato outperformed the existing methods on synthetic datasets. In addition, it yielded reasonable estimations in experiments on a mouse gut microbiota dataset, thus providing novel insights into the relationship between consumed diets and the gut microbiota.AvailabilityThe C++ and python source codes of the Umibato software are available at http://github.com/shion-h/UmibatoContactshion_hosoda@asagi.waseda.jp, mhamada@waseda.jp

Ecological modelling approaches for predicting emergent properties in microbial communities

“…In addition, equilibrium conditions and their stability can be identified analytically. Lotka-Volterra has therefore been widely used for connecting species interactions to community dynamics in various complex communities including the gut microbiome [ 24 , 28 , 30 , 42 , 58 , 59 , 63 , 64 , 67 ] and cheese fermentation communities [ 68 ].…”

“…Similarly, the confidence intervals for inferred interaction coefficients can be estimated using stochastic fitting [ 66 ]. Environmental heterogeneity has been modelled as fluctuations in mortality rates [ 82 ], and by using time-varying interactions [ 64 ]. Another means to incorporate stochasticity is through adding a noise term to the equations [ 79 , 83 ], or by randomly drawing interaction coefficients and/or intrinsic growth rates from predefined distributions [ 30 , 56 , 66 , 84 ].…”

Conceptual strategies for characterizing interactions in microbial communities

“…One popular approach, particularly when absolute abundance data are available, is the generalized Lotka-Volterra (gLV) method. Algorithms based on this approach primarily use sparse regression techniques to quantify interaction parameters of the classic Lotka-Volterra differential equations of population dynamics ( Fisher and Mehta, 2014 ; Mounier et al., 2008 ; Stein et al., 2013 ; Marino et al., 2014 ; Bucci et al., 2016 ; Hosoda et al., 2021 ). As an example, a gLV based model combined with Tikhonov regularization enabled the quantification of species-species interactions in the intestinal microbiome to numerically predict ecological dynamics under time-dependent external perturbation and additionally characterize community stability ( Stein et al., 2013 ).…”