Modeling Probiotic-associated Growth Dynamics in Juvenile Red Drum

Probiotic supplementation is increasingly used in aquaculture to improve fish performance. However, growth responses vary over time and therefore, effects of probiotic supplementation may not be fully resolved using endpoint- or timepoint-based standard statistical comparisons. We examined growth responses of juvenile red drum (Sciaenops ocellatus; 4-15 g) exposed to the multistrain probiotic PrimaLac®, administered directly to tank water rather than to feed. Fish were assigned to one of three treatments: untreated controls, a 28-day probiotic exposure in which supplementation occurred during the first 28 days of a 56-day experiment and was then discontinued, and a 56-day probiotic exposure in which supplementation continued throughout the full experimental period. Conventional analysis of variance (ANOVA) and Bayesian ANOVA comparisons of observed wet mass and total length found that probiotic supplementation improved growth relative to controls, but did not distinguish growth responses between the two probiotic exposure treatments. In contrast, a mechanistic hierarchical Bayesian growth model using a latent size trajectory and daily geometric growth-rate parameter $\lambda$, revealed phase-dependent differences in inferred growth dynamics that were not fully captured by observed size comparisons alone. The model indicated higher growth rates during the early portion of the experiment and suggested that growth in the 28-day treatment was reduced after supplementation ceased. Yet the 56-day treatment showed a more persistent response under continued probiotic exposure. By quantifying uncertainty in latent growth trajectories and phase-specific growth rates, the Bayesian growth model provided a process-oriented framework for interpreting time-dependent growth responses in aquaculture experiments. These results demonstrate the value of mechanistic hierarchical Bayesian modeling for resolving probiotic-associated growth dynamics, while also highlighting the need for companion microbiological analyses to link growth responses with specific host- or environment-associated microbial mechanisms.