Fig. 1
From: Dynamic linear models guide design and analysis of microbiota studies within artificial human guts
A generative model for microbial dynamics obscured by technical variation. a Microbial dynamics result from biological variation. The time series (θ1, , …, θt, …, θT) defines the dynamics of a microbial community and results from biological variations (w1, , …, wt, …, wT) which are assumed to be independent and identically distributed (i.i.d.) logistic-normal with mean zero and covariance W. b Technical variation obscures microbial dynamics. Technical variation (v1, , …, vt, …, vT) from sample processing introduces noise into measurements of microbial dynamics and are assumed to be i.i.d. logistic-normal with mean zero and covariance V. c Replicate sampling enables quantification of technical variation. Hypothetical collected samples are denoted by green squares. Differences between longitudinal samples reflect both biological and technical sources of variation. In contrast, differences between technical replicates (samples from the same time point) should reflect only technical sources of variation and can be used to estimate V (“Methods” section). d Overview of longitudinal model. The microbial dynamics and the confounding technical variation (a, b) are modeled in an isometric log-ratio (ILR) space such that the logistic-normal distribution transforms to a multivariate normal distribution for mathematical convenience (“Methods” section). The observed count data is assumed to be distributed multinomial from the compositions (η1, , …, ηt, …, ηT) (“Methods” section)