Optimizing plant nutrient uptake: cost function sensitivity analysis of the FUN model

Abstract This study explores the cost functions of the Fixation & Uptake of Nutrients (FUN) model, which aims to optimize the amount of carbon used when plants acquire their necessary nutrients from the soil to maximize nitrogen (N) and phosphorus (P) uptake while minimizing the carbon cost. Specifically, we aimed to quantify the sensitivity of FUN outputs to the parameters belonging to the cost of nitrogen and phosphorus uptake functions by arbuscular mycorrhizal and ectomycorrhizal fungi. We present three dimensions of sensitivity analysis: (1) adjusting all parameters at the same time; (2) keeping one parameter constant while varying the other; and, (3) assessing the individual impacts by reversing the direction of the held constant parameter. We validated outcome variations of modeled outputs against measured observations including parameters of plant-soil interactions such as soil temperature, carbon net primary production, evapotranspiration, root carbon, and nitrogen and phosphorus contents in leaves and soil. When analyzing the cost of resorption of leaf phosphorus, increasing the kR cost parameter, which represents the cost of resorption, decreased the coefficient of determination ( R 2 ) value, and the model’s predictions became lower than observed, with a larger residual spread; this introduced uncertainty in the predictions with a more negative bias and increased root mean square error. We ran an optimization function on the parameters but found that this did not significantly improve the model, indicating that the original parameterizations are robust against the available data. This study aligns with and builds upon previous research in the field, emphasizing the need to perform sensitivity analysis further to enhance predictive accuracy of plant nutrient uptake and corresponding impacts to carbon cycling.