A sustainable fishery management study: The yellowfin tuna fishery in the western and central Pacific Ocean

The yellowfin tuna population has been experiencing a significant decrease since far-sea fishery entered the West Central Pacific Ocean (WCPO) region in the 1950s. The development of the fish stock and the influence of fishing must be studied carefully. I start this study with the yellowfin tuna stock assessment. I combine the logistic growth function from the Schaefer model and the framework of an age-structure model to analyze the stock assessment. The total stock is separated into two subgroups by age (immature and mature). In the second part of this study, a two-cohort dynamic model is constructed to investigate the relationship between these two age groups. The Vector Auto-Regression (VAR) method is applied to this model using WCPO data from 1950 to 2004. The result suggests that the immature fish stock is extremely important to sustain a steady-state total fish population in the long term. The model is then expanded to include the influence of fishing in the third part of the study. A 3*3 differential equation system is built through application of the optimal control theory to examine the relationship between the total catch and the fish stock when the fish are exploited by a present-value-maximizing fishery. The numerical analysis shows that the total catch and the catch ratio between immature and mature fish are both important variables for a sustainable steady-state between the fish stock and the fishery.