Identifiability of metabolic resilience from sparse longitudinal metabolomics

Sparse, irregular longitudinal metabolomic sampling fundamentally constrains which dynamical properties of gut metabolism can be robustly inferred from observational data. We develop an effective landscape inference framework to characterize these identifiability limits while quantifying aspects of metabolic resilience that remain recoverable under realistic sampling regimes. Using stochastic simulations with known ground truth, we first characterize the identifiability limits of multistability detection under sparse sampling, showing that bistable dynamics can appear monostable at sampling densities typical of existing human cohorts. Guided by these identifiability limits, we illustrate the framework using a small subset (N = 4) of longitudinal stool metabolomic trajectories meeting stringent quality-control criteria. Within this sparse-sampling regime, landscape curvature, a bootstrap-quantified measure of local recovery strength, remains identifiable and provides preliminary evidence of inter-individual variability in inferred recovery dynamics. An autoregressive extension prioritizes bile acids and fermentation intermediates as candidate modulators of butyrate return dynamics.