Comparison of statistical methods to fit critical nitrogen dilution curves

Abstract

The critical nitrogen dilution curve (CNDC) is one of the most important models underpinning diagnostic tools of crop nitrogen (N) status. The CNDC relates plant N content (%N) to plant biomass under optimal nutritional conditions, using a simple nonlinear function with two parameters. More precisely, the CNDC estimates the critical %N (%NC) - the amount of %N needed to achieve maximum biomass at a certain moment. Thus, the comparison of a measured %N to %NC diagnoses if a plant is N deficient and if application of N fertilizer is necessary. Because of the practical importance of the CNDC, its parameters should be estimated as accurately as possible from field data. Two contrasting frameworks have been proposed in the literature for parameter estimation of the CNDC. The most popular approach is a sequential framework that consists of fitting two statistical models sequentially. Recently, an alternative framework has been introduced to estimate the parameters in a single step, using a hierarchical Bayesian model (hierarchical framework). In this study, we compare both methods and evaluate their performances for a large range of experimental designs. We consider datasets with different numbers of observation times (4, 8, 16), N fertilizer rates (3, 4, 5), and levels of measurement accuracy (low, medium, high). Our results show that the hierarchical framework outperforms the sequential framework under most scenarios. The sequential framework often resulted in poor statistical properties of the parameter estimates (e.g., increased bias and poorly calibrated confidence intervals) and to overestimated %NC values. The estimates for the amount of N needed to sustain N sufficiency levels were between 30 and 100 kg N ha−1 greater under the sequential framework, compared to the hierarchical framework. Thus, adopting the hierarchical framework could contribute to decreasing the risk of overfertilization and increasing the sustainability of agricultural systems.