Mechanistic Modeling of Porphyridium sp. Growth under Photoperiod Variation Using a Droop–Steele Dynamical System

Longer illumination can increase Porphyridium sp. biomass but requires more energy. We studied growth under 6 h, 12 h, and 24 h photoperiods using a Droop–Steele dynamical model for external nutrient N, internal quota Q, and cell density X. Photoperiod modifies nutrient uptake through a daily-effective Steele factor. We established forward invariance of the biologically feasible region and ultimate boundedness, derived washout and positive-biomass equilibria, and characterized local stability. Parameters were estimated jointly from 81 container-day observations across nine independent cultures using Bayesian inference. Four Markov chain Monte Carlo chains met the reported convergence criteria (maximum ). Posterior draws were mapped onto analytical persistence and stability conditions and propagated to biomass predictions. All tested photoperiods yielded a feasible, locally stable positive equilibrium within the fitted model. Predicted biomass increased with illumination but showed diminishing gains per additional lighting hour. The fitted effective-light Steele response was nearly linear over the tested range; the modeled flattening was consistent with nutrient depletion and quota limitation without requiring photoinhibition. Droop–Steele had the lowest AICc among the models compared, although Logistic had marginally lower raw log-RMSE. Energy-use and cost data are needed before identifying a cost-optimal photoperiod.