Quantifying critical N dilution curves across G × E × M effects for potato using a partially-pooled Bayesian hierarchical method

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.