Analyzing uncertainty in critical nitrogen dilution curves

Nitrogen critical curves are frequently used to diagnose the N status of crops and grasslands. They play an important role in plant modelling and are frequently used in fertilizer management tools. During the last 20 years, a number of studies have been conducted for comparing critical curves obtained in various conditions (e.g., different cultivars) and understanding the origin of their differences. However, uncertainty in the determination of these curves is generally poorly analyzed in these studies, which increase the risk of false conclusions, in particular on the existence of differences between species, cultivars and cropping systems. Here, we present a Bayesian statistical model for estimating parameters of critical nitrogen dilution curve from experimental data. Contrary to standard methods commonly used for fitting critical nitrogen dilution curves, the proposed approach allows one to fit these curves in only one step, i.e., directly from the original biomass and nitrogen content measurements. Specifically, this method does not require the classification of nitrogen-limited data against non-nitrogen-limited data and does not necessitate the preliminary identification of critical nitrogen concentrations. Another advantage of the proposed method is that it can be easily implemented using freely-available software. We illustrate its practical interest using experimental data collected for winter wheat in France, and for maize and rice in China. We show that this method is useful for analyzing uncertainty in the fitted critical nitrogen curves and for comparing several curves obtained for different crop species and cultivars. The proposed method is based on the specification of prior probability distributions defining plausible ranges of values for the critical curve parameters, and we show here that it is preferable to use prior distributions that are not very informative if we want to limit their influence on the final result.