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• Nitrogen use efficiency [NUE] is best understood in terms of its constituent parts. • Interpreting N utilization efficiency depends on both N nutrition index and biomass. • A critical N utilization efficiency curve can be defined based on previous theory. • Increasing N uptake efficiency [NUpE] will reduce N losses to the environment. • Maximizing NUE does not necessarily improve agronomic or environmental outcomes. Maximizing nitrogen (N) use efficiency [NUE] is commonly identified as a key strategy to improve both agronomic and environmental outcomes; however, interpretation of NUE requires explicit consideration of crop N status. In this study, we derived a set of novel theoretical relationships between the nitrogen nutrition index [NNI] and NUE used to better interpret values for nitrogen uptake efficiency [NUpE] and nitrogen utilization efficiency [NUtE]. A small-plot trial for potato [ Solanum tuberosum (L.) 'Russet Burbank'] was conducted in 2016 and 2017 in Central Minnesota, USA, on a Hubbard loamy sand with six N rate, source, and timing treatments and two irrigation rate treatments. Impacts of treatments on NNI, NUpE, NUtE, NUE, biomass, harvest index, and potential N losses were interpreted within the context of a theoretical quantitative relationship between NUE and NNI. We found that for a constant NNI value, NUtE values increased non-linearly as biomass increased; at an NNI value of 1.0, this relationship defines the critical N utilization efficiency curve. As N rate increased from 40 to 270 kg N ha−1, NUtE significantly decreased from 109.8–69.7 g g−1 N, corresponding with a significant increase in both biomass (from 12.0–17.8 Mg ha−1) and in NNI (from 0.520 to 0.973), respectively. Additionally, we found that potential N losses (e.g., leaching) decreased as NUpE increased, or as total N inputs decreased. Potential N loss was lower in 2016 than 2017 (135 and 187 kg N ha−1, respectively) due to both greater NUpE and lower total N input from all sources in 2016 (0.602 g N g-1 N and 339 kg N ha-1, respectively) than in 2017 (0.526 g N g-1 N and 395 kg N ha-1, respectively). Interpreting NUE to evaluate agronomic and environmental outcomes requires separate consideration of its constituent factors (e.g., NUpE, NUtE, and HI) and explicit consideration of both NNI and biomass. [ABSTRACT FROM AUTHOR]

Multiple critical N dilution curves [CNDCs] have been previously developed for potato; however, attempts to directly compare differences in CNDCs across genotype [G], environment [E], and management [M] interactions have been confounded by non-uniform statistical methods, biased experimental data, and lack of proper quantification of uncertainty in the critical N concentration [%N c ]. This study implements a partially-pooled Bayesian hierarchical method to develop CNDCs for previously published and newly reported experimental data, systematically evaluates the difference in %N c [∆%N c ] across G × E × M effects, and directly compare CNDCs from the Bayesian framework to CNDCs from conventional statistical methods. The partially-pooled Bayesian hierarchical method implemented in this study has the advantage of being less susceptible to inferential bias at the level of individual G × E × M interactions compared to alternative statistical methods that result from insufficient quantity and quality of experimental datasets (e.g., unbalanced distribution of N limiting and non-N limiting observations). This method also allows for a direct statistical comparison of differences in %N c across levels of the G × E × M interactions. Where found to be significant, ∆%N c was hypothesized to be related to variation in the timing of tuber initiation (e.g., maturity class) and the relative rate of tuber bulking (e.g., planting density) across G x E × M interactions. In addition to using the median value for %N c (i.e., CNDC), the lower and upper boundary values for the credible region (i.e., CNDC lo and CNDC up) derived using the Bayesian framework should be used in calculation of N nutrition index (and other calculations) to account for uncertainty in %N c. Overall, this study provides additional evidence that%N c is dependent upon G × E × M interactions; therefore, evaluation of crop N status or N use efficiency must account for variation in %N c across G × E × M interactions. • Critical N dilution curves [CNDCs] for potato are subject to G x E x M effects. • Bayesian methods can quantify uncertainty in critical N concentration [%N c ]. • Partial pooling Bayesian method enables direct comparison of G x E x M effects. • Variation in %N c for potato due to tuber initiation timing and tuber bulking rate. • N use efficiency and N nutrition index depend on %N c variability and uncertainty. [ABSTRACT FROM AUTHOR]