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

Polyethylene glycol (PEG) is an osmotic laxative that induces concentration-dependent shifts in gut microbial composition. In mouse PEG-challenge experiments, Muribaculaceae decline during exposure, whereas Bacteroidaceae remain stable or increase in relative representation. We analyzed these family-level trajectories using an effective two-family competition-immigration model on the sequencing-derived relative-abundance scale. The model is a switching-regime generalized Lotka-Volterra system with logistic self-limitation, constant immigration, and separate PEG and post-PEG parameter sets fitted to longitudinal 16S rRNA data for 5%, 10%, and 15% PEG. The model reproduced PEG-period Muribaculaceae depletion, post-PEG recovery, Bacteroidaceae resilience, and incomplete return toward the pre-treatment state at 15% PEG. Near-optimal ensembles and sensitivity analyses indicated that the 15% PEG trajectory gave the most stable full-model interaction-summary signal, whereas the 10% PEG trajectory was more objective-sensitive. However, a nested raw-interaction-invariant comparator, retaining phase-specific growth and carrying-capacity parameters while sharing inter-family interaction coefficients across phases, reproduced the trajectories comparably and was favored by AICc/BIC, with the weakest model-comparison separation at 15% PEG. Thus, the robust conclusion is PEG/post-PEG dynamical regime separation and strong Muribaculaceae vulnerability during PEG; the data do not require phase-specific raw interaction switching. Fitted parameters should be interpreted as model-conditional observation-scale summaries rather than direct physiological competition estimates.