Fig. 4

Application of MDSINE to an experimental dataset evaluating stability of a probiotic cocktail in gnotobiotic mice. Germ-free mice were inoculated with 13 Clostridia strains from the VE-202 cocktail, a mixture of bacteria previously shown to be Treg inducers [24]. Over the 9-week experiment, mice were alternated between a standard high-fiber diet and a low-fiber dietary perturbation. We collected 56 fecal samples per mouse and these were interrogated using strain-specific qPCR primers to estimate strain concentrations. a Example of inferred growth and interaction parameters and their variability. The top grid displays mean parameter estimates and the bottom grid displays standard deviations of parameter estimates. Strains are ordered by their mean estimated growth rates on the standard diet. Pert. perturbation effect, St. strain. b Example forecasts of microbial concentration trajectories. Forecasts were obtained using a hold-one-subject-out procedure. Briefly, MDSINE was run on all data from all but one of the mice (the held-out subject) and model parameters were inferred. Using the inferred model parameters (including for the perturbation) and the measured concentrations of the microbiota at an initial time point for the held-out mouse, the trajectories of the microbiota for the held-out mouse were then forecast for all the remaining time points; the procedure was repeated for each mouse. Solid lines denote predicted trajectories and circles denote data. c Keystoneness analyses for high-fiber (top) and low-fiber (bottom) diets. Rows represent all possible stable states in which each strain has been removed in turn and the others are present (if that configuration is stable). The grid displays predicted steady-state concentrations of strains (log₁₀ ng strain DNA/μg total fecal DNA), with white entries indicating absent strains. Ky keystoneness, a measure assessing the marginal predicted quantitative effect of removing each strain from the full community, with larger values indicating greater effects on the overall ecosystem