Algebraic equilibrium solution of tissue nitrogen quota in algae and the discrepancy between calibrated parameters and physiological properties

Tissue nutrient concentrations are a key factor in determining primary production in a variety of algae, for example the marine macroalga Ulva. We present a novel algebraic solution to calculate the equilibrium tissue nitrogen concentration or “quota” Q. The solution is derived from a classical mechanistic description of “luxury uptake” in marine macroalgae using a computer algebra system. Forced by ammonium (NH4+) and nitrate plus nitrite (NOx−) concentrations, water temperature and irradiance, equilibrium Q can be calculated directly without the need for numerical integration, and the model performs well in reproducing observations of Q in frondose Ulva spp. A Sobol’ global sensitivity analysis reveals that the degree of uncertainty in physiological parameters has a similar magnitude of influence on model output as the typical environmental range of nutrient forcing data. The environmental forcing variables NH4+ and NOx− together account for 60% of variance in model output, while the two most influential physiological parameters together account for another 32% of variance. Repeated parameter calibrations with random first guesses and evolutionary adaptations lead to broad and even multimodal distributions for some parameters, as well as values at the extremes of their literature ranges. This shows that although model performance as quantified by statistical measures is high, individual calibrations are not sufficient to give reliable parameter estimates that can be interpreted as physiological system properties.