Coding Optimization for an Ecological non-linear Age-structured Fish Population Model with a Shepherd Recruitment Function

Abstract

The study of the optimally density-regulated recruitment plays a crucial role in the overall management and determining of fishing efforts of marine fish populations. This paper will develop a Matlab code can determine what an optimal recruitment density regulation strategy would be for the un-fished population and what it changes to when fishing efforts are applied. This code can determine threshold values used to avoid fisheries from collapsing. The code will be applied to the Gulf of California Pacific sardine (Sardinops caeruleus) population. An age structured design with a Shepherd density regulating stock-recruitment function is used in this study. In this work, the parameter which is varied is captured in the Shepherd recruitment function and is associated with behavioral interventions such as selecting different drift routes and clumping on resources that will increase egg-larvae survival to the recruitment stage. A detailed background study of other models is explored, then a derivation of the Shepherd recruitment model is developed from the traditional discrete model. A special MATLAB code is then developed to illustrate the pair-wise invasive plots for the model structures. The code is for theoretical analysis of fish population models.