A Dynamic Bioeconomic Model for Aquaponic Farms

In a rapidly growing world, conventional agriculture is under pressure from climate change and is struggling to meet the growing food demand while protecting the environment. Adopting new technologies like Controlled Environment Agriculture (CEA), where farming is done in controlled environments shielded from external climate fluctuations, can ensure climate resilience. This paper develops a dynamic bioeconomic model of aquaponic production in which fish biomass is both a harvestable stock and a source of nutrients for plant production. The model links fish growth, waste generation, plant nutrient availability, fertilizer substitution, repeated plant harvests, and terminal fish harvest timing in a unified private-profit framework. The central mechanism is intertemporal: fish biomass evolves over a long production cycle, while leafy vegetables can be harvested repeatedly over shorter cycles. As fish biomass increases, fish-generated waste raises plant-available nutrients and can reduce the need for purchased fertilizer. A calibrated tilapia-kale application illustrates the model. In the baseline simulation, the profit-maximizing tilapia harvest occurs after approximately 262 days, while kale is harvested on a 27-day cycle. Repeated kale harvests generate revenue before the terminal fish harvest and therefore affect farm cash flow as well as fertilizer demand. Sensitivity analysis shows that fish profit is most responsive to biological growth conditions, especially temperature, and to revenue-side parameters such as fish price and harvestable-output share. Kale profit is driven primarily by crop price, harvestable yield, and production scale. The results show that the value of aquaponic integration depends not only on nutrient recycling, but also on the timing of biological growth, nutrient availability, and harvest decisions.