Characterizing the Temporally Dynamic Nature of Relative Growth Rates: A Kinetic Analysis on Nitrogen-, Phosphorus-, and Potassium-Limited Growth

Developing precision models to describe agricultural growth is a necessary step to promote sustainable agriculture and increase resource circulation. In this study, the researchers hydroponically cultivated Bibb lettuce ( Lactuca sativa ) across a variety of nitrogen, phosphorus, and potassium (NPK)-limited treatments and developed robust data-driven kinetic models observing nutrient uptake, biomass growth, and tissue composition based on all three primary macronutrients. The resulting Dynamic μ model is the first to integrate plant maturity’s impact on growth rate, significantly improving model accuracy across limiting nutrients, treatments, and developmental stages. This reduced error supports this simple expansion as a practical and necessary inclusion for agricultural kinetic modeling. Furthermore, analysis of nutrient uptake refines the ideal hydroponic nutrient balance for Bibb lettuce to 132, 35, and 174 mg L −1 (N, P, and K, respectively), while qualitative cell yield analysis identifies minimum nutrient thresholds at approximately 26.2–41.7 mg-N L −1 , 3.7–5.6 mg-P L −1 , and 17.4–31.5 mg-K L −1 to produce compositionally healthy lettuce. These findings evaluate reclaimed wastewater’s ability to offset the fertilizer burden for lettuce by 23–45%, 14–57%, and 3–23% for N, P, and K and guide the required minimum amount of wastewater pre-processing or nutrient supplements needed to completely fulfill hydroponic nutrient demands.