The production-function structure of marine primary-production models: Marginal products, elasticities, and light–nutrient trade-offs

Marine primary-production equations can be analysed as physical input–output functions using production-theory measures, without assuming phytoplankton optimization. From canonical bio-optical and mixed-layer terms we derive marginal products, elasticities, isoquant slopes, a self-shading correction, and a light–nutrient compensation threshold. The threshold is the nutrient gain per metre of deepening required to offset the light-related loss in average production; temperature and micronutrients enter the general differential as separate controls. A matched Bermuda Atlantic Time-series Study (BATS) profile panel illustrates the calculations. Profile-date fixed effects imply a net apparent depth coefficient of − 0.0263 m − 1 ; 2037 adjacent-depth intervals give an observed log-production gradient of − 0.0264 m − 1 . On 239 nitrate＋nitrite-matched intervals, Δ ϕ N / Δ z = + 0.00419 m − 1 ; its local Monod conversion at N = N k = 0.5 μ mol kg -1 is Δ log ϕ N / Δ z ≈ + 0.0084 m − 1 . These are profile diagnostics, not a physiological calibration or a dynamic threshold test.