Linking Osmotic Laxative Exposure to Gut Microbial Competition: A Treatment--Dependent Lotka--Volterra Analysis

Polyethylene glycol (PEG) is an osmotic laxative that produces concentration-graded shifts in gut community composition. In PEG challenge experiments in mice, members of the family \textit{Muribaculaceae} are depleted during exposure, whereas \textit{Bacteroidaceae} remain stable or increase in relative representation. To probe mechanisms underlying this contrast, we construct a treatment-dependent two-family competition--immigration model with \emph{effective} state variables defined directly on the sequencing-derived fraction (relative-abundance) scale. The model is a switching-regime generalized Lotka--Volterra system with logistic self-limitation, constant immigration, and separate parameter sets for the PEG and post--PEG phases. We fit the model to longitudinal 16S rRNA family-level trajectories using an unweighted \(L^2\) discrepancy between model-implied and observed \textit{Bacteroidaceae} and \textit{Muribaculaceae} time series. For each PEG concentration (5\%, 10\%, 15\%) we estimate parameters by global optimization under bounded phenomenological domains and examine ensembles of near-optimal fits to assess practical identifiability. The calibrated model reproduces treatment-phase depletion and post--PEG recovery of \textit{Muribaculaceae} together with the resilience of \textit{Bacteroidaceae}; at the highest concentration it captures an incomplete return toward the pre-treatment state within the observation window despite continued environmental re-seeding via the immigration term. Across concentrations, the most robust treatment-associated signal occurs in the inferred inhibition of \textit{Muribaculaceae} by \textit{Bacteroidaceae} during PEG exposure, whereas effective growth-rate estimates vary less in order-of-magnitude terms and are less well constrained when \textit{Muribaculaceae} is rare. Under this model class and the tested bounds, the analysis supports PEG-driven reshaping of \emph{effective} competitive interactions, rather than uniform growth suppression alone, as a parsimonious explanation for the observed concentration--response trajectories of these two families.