Increase in maximum sustainable yield of a phytoplankton–zooplankton–fish community in a two-patch fishery system

In the case of a single-species model with fish logistic growth and Schaefer-type catch at two fishing patches, it is already known that the optimal catch at Maximum Sustainable Yield (MSY) connected by fast fish migration cannot exceed the sum of the MSY catches from the two isolated patches. In this study, we extend the analysis to a tri-trophic Phytoplankton–Zooplankton–Fish (PZF) model to investigate the influence of lower trophic levels and spatial heterogeneity on optimal harvesting strategies. By applying aggregation methods based on time-scale separation, we derive a global model that describes the dynamics of coupled ecological patches. Our results demonstrate that, in contrast to single-species models, the connected tri-trophic system can achieve a total maximum sustainable yield (MSY) that exceeds the sum of yields from isolated systems, provided asymmetric migration rates and spatial heterogeneity are present. Comparative analysis further indicates that the tri-trophic structure enhances biomass transfer to harvested fish populations by introducing phytoplankton as a basal level, which allows zooplankton to function as an energy buffer and decouples optimal harvesting from the Ideal Free Distribution (IFD). thereby significantly enhancing the yield benefits derived from spatial connectivity. We then examine the impact of establishing a Marine Protected Area (MPA). Our findings indicate that the creation of an MPA can further enhance fishery productivity at MSY, depending on regional heterogeneity and asymmetric migration rates. We identify an optimal MPA configuration that generates higher excess yields than scenarios where both patches are fished. The study emphasizes the importance of regional interactions and migration dynamics in fisheries management and suggests strategies to optimize MSY while protecting marine ecosystems.