A two-year field experiment was conducted to measure the effects of densification methods on photosynthesis and yield of densely planted wheat. Inter-plant and inter-row distances were used to define rate-fixed pattern (RR) and row-fixed pattern (RS) density treatments. Meanwhile, four nitrogen (N) rates (0, 144, 192, and 240 kg N ha⁻¹, termed N0, N144, N192, and N240) were applied with three densities (225, 292.5, and 360 × 10⁴ plants ha⁻¹, termed D225, D292.5, and D360). The wheat canopy was clipped into three equal vertical layers (top, middle, and bottom layers), and their chlorophyll density (ChD) and photosynthetically active radiation interception (FIPAR) were measured. Results showed that the response of ChD and FIPAR to N rate, density, and pattern varied with different layers. N rate, density, and pattern had significant interaction effects on ChD. The maximum values of whole-canopy ChD in the two seasons appeared in N240 combined with D292.5 and D360 under RR, respectively. Across two growing seasons, FIPAR values of RR were higher than those of RS by 29.37% for the top layer and 5.68% for the middle layer, while lower than those of RS by 20.62% for the bottom layer on average. With a low N supply (N0), grain yield was not significantly affected by density for both patterns. At N240, increasing density significantly increased yield under RR, but D360 of RS significantly decreased yield by 3.72% and 9.00% versus D225 in two seasons, respectively. With an appropriate and sufficient N application, RR increased the yield of densely planted wheat more than RS. Additionally, the maximum yield in two seasons appeared in the combination of D360 with N144 or N192 rather than of D225 with N240 under both patterns, suggesting that dense planting combined with an appropriate N-reduction application is feasible to increase photosynthesis capacity and yield.

The organ-specific critical nitrogen (N_c) dilution curves are widely thought to represent a new approach for crop nitrogen (N) nutrition diagnosis, N management, and crop modeling. The N_c dilution curve can be described by a power function (N_c = A₁·W^−A2), while parameters A₁ and A₂ control the starting point and slope. This study aimed to investigate the uncertainty and drivers of organ-specific curves under different conditions. By using hierarchical Bayesian theory, parameters A₁ and A₂ of the organ-specific N_c dilution curves for wheat were derived and evaluated under 14 different genotype × environment × management (G × E × M) N fertilizer experiments. Our results show that parameters A₁ and A₂ are highly correlated. Although the variation of parameter A₁ was less than that of A₂, the values of both parameters can change significantly in response to G × E × M. Nitrogen nutrition index (NNI) calculated using organ-specific N_c is in general consistent with NNI estimated with overall shoot N_c, indicating that a simple organ-specific N_c dilution curve may be used for wheat N diagnosis to assist N management. However, the significant differences in organ-specific N_c dilution curves across G × E × M conditions imply potential errors in N_c and crop N demand estimated using a general N_c dilution curve in crop models, highlighting a clear need for improvement in N_c calculations in such models. Our results provide new insights into how to improve modeling of crop nitrogen–biomass relations and N management practices under G × E × M.

Establishing the universal critical nitrogen (N_C) dilution curve can assist in crop N diagnosis at the regional scale. This study conducted 10-year N fertilizer experiments in Yangtze River Reaches to establish universal N_C dilution curves for Japonica rice based on simple data-mixing (SDM), random forest algorithm (RFA), and Bayesian hierarchical model (BHM), respectively. Results showed that parameters a and b were affected by the genetic and environmental conditions. Based on RFA, highly related factors of a (plant height, specific leaf area at tillering end, and maximum dry matter weight during vegetative growth period) and b (accumulated growing degree days at tillering end, stem–leaf ratio at tillering end, and maximum leaf area index during vegetative growth period) were successfully applied to establish the universal curve. In addition, representative values (most probable number [MPN]) were selected from posterior distributions obtained by the BHM approach to explore universal parameters a and b. The universal curves established by SDM, RFA, and BHM-MPN were verified to have a strong N diagnostic capacity (N nutrition index validation R² ≥ 0.81). In summary, compared with the SDM approach, RFA and BHM-MPN can greatly simplify the modeling process (e.g., defining N-limiting or non-N-limiting groups) while maintaining a good accuracy, which are more conducive to the application and promotion at the regional scale.