Abstract
AbstractIn fisheries economics, multispecies or ecosystem models typically focus on interactions among fish species, often overlooking the flow of nutrients. However, biologists widely acknowledge that nutrients–Âİsuch as nitrogen, phosphorus, potassium, and calcium–Âİare vital for organisms and play crucial roles in ecosystem dynamics. This paper delves into a bioeconomic predator‐prey model incorporating nutrient enrichment through Holling Type II and Michaelis–Menten functional forms. Initially, we examine the system's dynamics before formulating an optimal time‐dependent harvest policy using the Pontryagin maximum principle. Our findings reveal that heightened nutrient enrichment can lead to the breakdown of a positive stable equilibrium, resulting in the extinction of both prey and predator. The stability of the ecosystem may also be influenced by the interplay of nutrient enrichment and predator harvest.
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