The Fractal Approach to Describe Growth of Farmed Marine Species: Using Double and Triple Logistic Models

Abstract

Modeling individual growth in marine species for aquaculture encounters many difficulties when the species pauses its growth but resumes its later after the disrupting phenomenon (environmental or physiological) has been overcome. Seasonal or oscillatory growth has been addressed by modifying existing models, such as von Bertalanffy and Gompertz, to include an oscillatory component in this study. The novelty of this study lies in the fractal approach used to analyze growth using multiple logistic functions. Three commercially farmed marine species were studied, including shellfish, crustacea, and finfish. The oscillatory version of the von Bertalanffy model as well as double and triple logistic functions were used for analysis. The best model was selected using the information theory, Specifically the Akaike criterion (AIC) and the Bayesian criterion (BIC). Normal and log-normal distributions of error were assumed. The triple logistic model with log-normal distribution in the error structure was found to be the best model to describe the growth pattern of the three commercially farmed species as it obtained the lowest AIC. Overall, this study concludes that the fractal approach is the most effective way to describe growth in farmed species, including shellfish, crustacean, and finfish.