A comparative study of five classical nonlinear models for kinetic growth modelling of Dunaliella sp.

Abstract

Mathematical modelling of microalgal growth is a fundamental tool for describing biomass dynamics and supporting the analysis and optimisation of cultivation processes. In this study, the batch growth of the halotolerant microalga Dunaliella sp. was investigated using five classical nonlinear growth models: exponential, logistic, Gompertz, Richards, and Baranyi. The experimental growth profile exhibited a clear sigmoidal pattern characterised by an adaptation phase, rapid biomass accumulation, and a transition to stationary conditions. Model parameters were estimated using nonlinear least-squares regression based on the Levenberg–Marquardt algorithm. Model evaluation combined descriptive and information-theoretic criteria, including root mean square error (RMSE), bias factor (BF), residual diagnostics, Akaike’s information criterion corrected for small sample size (AICc), ΔAICc, and Akaike weights.

The results indicated that flexible sigmoidal formulations provided a more realistic representation of the observed growth dynamics. Specifically, the logistic model received the strongest statistical support based on AICc while maintaining parameter parsimony. The Richards model remained statistically plausible but did not provide a sufficiently better fit to the experimental data to justify its additional complexity. These findings demonstrate the value of rigorous information-theoretic model selection. They also provide a robust framework for predictive modelling of Dunaliella sp. growth, supporting improved process design, operational decision-making, and scale-up strategies in microalgal biotechnology.