Fig. 3

Forecasting population-level dynamics based on attractor reconstruction. a Workflow of forecasting. For a target replicate community, the reference database of state space is reconstructed based on the time-series data of other replicate communities (i.e., reference replicate communities). Future abundance of each ASV in a target replicate community was then predicted using the state-space reference databases (see “Methods” section for details). b Nonlinearity parameters (θ). Proportions of microbial ASVs showing linear (θ = 0) and nonlinear (θ > 0) population dynamics are shown. c Example of population-level forecasting. Predicted and observed abundance through the time-series are shown for simplex projection, S-map with optimized nonlinearity parameter (optimized θ), and S-map assuming linearity (θ = 0). For each target replicate community, the remaining seven replicate communities were used as references. Results are shown for 1-day-ahead and 7-day-ahead forecasting of an ASV (X_0003) in replicate nos. 1–3 of Water/Medium-A treatment. See Additional file 8: Figure S8 for detailed results. d R² values between predicted and observed population size is shown for each microbial ASV in each replicate community