Optimizing Predator-Prey Relation of Atlantic Bonito and Anchovy, and their Sustainable Fishery in the Black Sea

Abstract There is no consistent harvesting strategy for the fisheries of the Atlantic bonito (Sarda sarda) and the Black Sea anchovy (Engraulis encrasicolus) on the southern part of the Black Sea. To address this problem, the predator-prey relation of the Atlantic bonito and the Black Sea anchovy is optimized and stabilized as both species are facing harvesting on the southern part of the Black Sea. A fishery model was built and a stability analysis was applied to the fishery model to obtain stable predator-prey dynamics. After that, it was coupled with Optimal Control Theory (OCT) to optimize the stable predator-prey dynamics of these species, and to obtain an optimal and sustainable landing. This study not only provides optimal and stable predator-prey dynamics for these species but also provides more landings and profits for the commercial fishery of these species as compared with the predicted current harvesting strategy obtained in this study. It also provides optimal and sustainable yields to be considered as fishing quotes for these fisheries. MSC Classification: 92B05 , 92B99 , 34H15 , 93D99