Interaction of Genotype, Environment, and Management on Organ-Specific Critical Nitrogen Dilution Curve in Wheat

The organ-specific critical nitrogen (Nc) dilution curves are widely thought to represent a new approach for crop nitrogen (N) nutrition diagnosis, N management, and crop modeling. The Nc dilution curve can be described by a power function (Nc = 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 Nc 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 Nc is in general consistent with NNI estimated with overall shoot Nc, indicating that a simple organ-specific Nc dilution curve may be used for wheat N diagnosis to assist N management. However, the significant differences in organ-specific Nc dilution curves across G × E × M conditions imply potential errors in Nc and crop N demand estimated using a general Nc dilution curve in crop models, highlighting a clear need for improvement in Nc 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.


Introduction
Wheat is widely acknowledged as a key cereal crop for global food security. However, due to increasing wheat demand and decreasing arable land, further increase in yield is necessary to ensure food security. Nitrogen (N) fertilizers are widely used to match the N demand for high-yielding wheat crops. However, excessive N fertilizer input in agricultural systems can negatively affect wheat growth [1] and pollute the environment, leading to low nitrogen use efficiency and waste of resources [2]. Therefore, crop N diagnosis, crop N requirement estimation, and improved N fertilizer management are crucial to improving wheat yield and N use efficiency [3].
Estimating crop N demand requires information about crop growth and the N nutritional status of crop, which is generally estimated based on the critical N concentration (N c ). N c is the minimum N concentration required to meet the maximum growth of crops [4]. Lemaire and Salette [5] proposed the concept of the N c dilution curve. The N nutrition index derived from the N c dilution curve has been considered as a reliable tool for quantifying plant N status, optimizing fertilization strategies, and estimating crop yield [6]. Over the years, more than 30 crops have been evaluated, including rice [7][8][9][10], wheat [11,12], maize [13,14], potato [15], and oilseed rape [16].
Most N c dilution curves developed up to now have been based on shoot biomass. However, leaf is the major photosynthetic organ that is highly responsive to N application [17,18], while stem biomass dominates shoot biomass at late growth stage. Plants maintain higher leaf N concentration throughout the vegetative period for optimal photosynthesis, with reduced N concentrations in shaded leaves in a closed canopy. Current evidence suggests that distribution patterns of assimilates in different organs are altered by N stress. Consequently, the shape of the N c dilution curve vary depending on the plant organs [19]. Zhao et al. [20] and Yao et al. [21,22] developed N c dilution curves based on leaf biomass of rice, winter wheat, and maize. The curves for wheat based on leaf biomass (A 1 = 3.06; A 2 = 0.15) were lower than those based on shoot biomass [11,12]. Interestingly, a study found that compared with irrigation conditions, rainfed wheat had lower leaf critical N in southeastern China [23]. N c dilution curves based on stem biomass generally yield lower initial values and steeper declines [23,24]. The variability of curve parameters indicates that it is affected by the interaction of genotype (G), environment (E), and management (M), which embody sources of the uncertainty in model parameter estimation [25,26]. Ata-Ul-Karim et al. [24] compared the nitrogen nutrition index (NNI) derived from N c dilution curves based on the shoot, organ biomass, and leaf area index (LAI) in rice, and found that NNI derived from shoot and leaf biomass was the most relevant. Sieling and Kage [27] indicated that the NNI derived from different organ and shoot biomass was inconsistent across oilseed rape, winter wheat, and maize under different N nutrition levels.
In recent years, the uncertainty of agricultural models and the uncertainty of fitted N c dilution curves have received extensive attention. For analysis of N c dilution curves, the often used classical sequential methods [11] have limitations and cannot estimate the error of the fitted curves. An alternative method to analyze the uncertainty and difference of N c dilution curve parameters for major field crops (rice, wheat, and maize) was proposed based on Bayesian theory [28], which can directly fit the curve from crop biomass and N concentration observations in one step. Using this method, the uncertainties of N c dilution curves of maize [29], wheat [25], tomato [30], and tall fescue [31] under different G × E × M conditions have been evaluated.
For crop models that rely on N c curves to determine crop N demand, the parameters may need to be updated because most existing crop models were established more than 20 years ago. They were developed using a small dataset and the N c curves were mostly developed based on shoot biomass. To our knowledge, no study has hitherto reported the uncertainty of the N c dilution curve based on wheat organs, nor is it clear whether the NNI derived from different N c dilution curves is consistent.
Here, we use data from 14 wheat N fertilizer experiments under different G × E × M conditions to develop and compare organ-specific N c dilution curves. We further analyze the uncertainty of the organ-based (leaf, stem biomass, and LAI) N c dilution curves, variations in their parameters, and the source of uncertainty under different experimental (G × E × M) conditions. Finally, we compare the differences in different organbased NNI.

Experiment design
Fourteen wheat N experiments were carried out in central and eastern China at 5 sites: Yizheng, Rugao, Xinxiang, Xuzhou, and Sihong (Table S1). Five widely planted wheat genotypes (Jimai 22, Xumai 30, Ningmai 13, Aikang 58, and Yangmai 16) were used to evaluate the N c dilution curves. All the experiments involved different N application rates from 0 kg N/ha to a high N rate of >300 kg N/ha. Except for experiment 5 (with 3 N rates), at least 5 N fertilizer application rates were used in all other experiments. N fertilizer was split into 2 applications, one before sowing and the other at the jointing stage. The field management followed the local recommendations, with sufficient phosphorus and potassium fertilizer application, irrigation if necessary to avoid water stress, and proper control of diseases, pests, and weeds. Table S1 shows the details of the experimental design, Table S2 shows the information of the experiment site, and Fig. S1 shows the meteorological conditions.

Plant sampling and N concentration
In each experiment, wheat plant was sampled at least 5 times before flowering to evaluate the N c dilution curve (Table S3). The leaf area was immediately measured for fresh leaves to calculate the LAI (device: LI-3000, Li-COR, Lincoln, USA). Plant samples were separated into organs (leaves and stems), and tissue metabolism was deactivated at 105 °C in an oven for 30 min. Then, they were dried to constant weight at 80 °C to calculate biomass. The dried samples were mechanically crushed and passed through a 2-mm sieve, and then the organ N concentration was determined by the Kjeldahl method [32].

Parameter estimation
Organ-specific N c dilution curves were evaluated by a hierarchical Bayesian model [28], which follows the response of biomass or LAI to N concentration (organ or shoot N concentration) as a linear-plus-plateau function [11,13]. According to the probability distribution estimated by the Bayesian method, the uncertainty of parameters of the linear-plus-plateau function at different observation dates (at the biomass or LAI level) can be analyzed. For the classical method, a N c dilution curve can be estimated only after variance analysis and curve fitting, and the uncertainty of the whole process cannot be determined. The advantage of the Bayesian method is that the parameters and uncertainty of the N c dilution curve are directly from the probability distribution. Therefore, the difference of curve parameters under different G × E × M conditions can be compared (Fig. 1).
In this study, the range of prior information is adjusted without strong restrictions so that a stable posterior distribution can be obtained. The prior ranges of organ-specific curve parameters A 1 and A 2 were 0 to 12 and 0 to 5, respectively. The other settings were consistent with Makowski et al. [28]. The fitted curves that were not convergent in Markov chain Monte Carlo (MCMC) were deleted.
where N c is the critical N concentration of organs and shoot, and W is the biomass of organs and shoot and LAI. A 1 and A 2 are the N c dilution curve parameters. The R package "rjags" was used to fit the posterior distribution of curve parameters with the MCMC algorithm [33]. The MCMC algorithm first iterated about 100,000 times to achieve convergence, and the algorithm continued to be run 30,000 times to analyze multiple quantities of interest (median and 95% credible interval). The N c dilution curves based on stem, leaf, and shoot biomass and LAI were derived from stem biomass and stem N concentration, leaf biomass and leaf N concentration, shoot biomass and shoot N concentration, and LAI and shoot N concentration, respectively.

Significance analysis
The generalized linear model was used for analysis of variance with SPSS16.0 software. Differences between the posterior curve parameters (A 1 and A 2 ) were compared by Tukey significant difference test at the 0.05 probability level.

Correlation
The R package "Hmisc" was used to calculate the correlation matrix to determine the source of parameter differences [34]. The relationship between N c dilution curve parameters (A 1 and A 2 ) under different G × E × M conditions and corresponding G, E and M information was comprehensively analyzed. The G × E × M information included the maximum shoot biomass (DMmax), maximum shoot N concentration (Nmax) during the vegetative growth period, vegetative growth period duration (VPD), accumulated growth degree days (AGDD), daily average GDD, and rainfall during the vegetative growth period and planting density (Fig. 1).
where N is the duration of the vegetative growth period in days, T base is the lowest temperature for wheat to start physiological activities, and T min and T max are the lowest and highest temperature of the day, respectively; the T base is 0 °C in this study [35,36].

Nitrogen nutrition index
The NNI for each observation point was calculated as follows [11]: where NNI is the ratio between measured N concentration (N t ) and critical N concentration (N c ) of different organ or shoot biomass for each sampling date.
The RMSE (root-mean-square error) and n-RMSE (normalized root-mean-square error) were calculated as follows: where n is the data size, O i and P i are the NNI derived by the hybrid N c dilution curve and the specific N c dilution curve, and S is the average value for the data.

Coefficient of variation
where CV is the coefficient of variation, SD is the standard deviation, and MN is the mean value.

Variations in organ-specific N c dilution curve parameters
The posterior parameter distribution of the N c dilution curves for the organs, shoot biomass, and LAI are shown in Figs. S2 to S5, and Tables S4 to S7 describe the quantiles of the posterior distribution of parameters, with non-convergent curve parameters deleted. Only a few curves exhibited the same curve parameters, and there were significant differences in fitted curves derived using the 4 different types of data, across genotypes and planting environment (Fig. 2). Notably, cultivation under the same planting sites and years and management yielded differences across genotypes. Significant differences were observed in parameters for a given genotype under different environment × management conditions, indicating that environment × management has significant effects on parameters A 1 and A 2 . For parameter A 1 , 6 curves based on leaf biomass have the same A 1 value (P > 0.05, Fig. 2A). Curves based on stem, shoot biomass, and LAI yielded significantly different values (P < 0.05). For parameter A 2 , two curves based on leaf and shoot biomass have the same value (P > 0.05, Fig. 5E and H). For stem biomass and LAI, no curve yielded the same value (P < 0.05), which indicates that the curve based on leaf biomass may be subject to less variation under different G × E × M conditions. The values of the curve parameters A 1 and A 2 mean the starting position and the dilution rate of the curve, respectively. The CVs between the effects of the G × E × M interaction of parameter A 2 were higher than parameter A 1 . In particular, the CV of parameter A 1 based on leaf biomass was much smaller than that of parameter A 2 . For parameter A 1 , it has the least variation with leaf biomass, but the greatest variation with shoot biomass. For parameter A 2 , it has the least variation with LAI, but the greatest variation with leaf biomass. More experimental observations also made the variation in the posterior distribution of the parameters smaller.

The drivers in organ-specific N c dilution curve parameters
The curve parameter A 1 based on leaf, stem, shoot biomass, and LAI was significantly correlated with parameter A 2 (P < 0.05, Fig. 3). The initial maximum shoot N concentration (Nmax), which is the characteristic of the wheat genotype, has no significant correlation with the curve parameters for different organs (P > 0.1). Similarly, the maximum shoot biomass (DMmax) during the vegetative period was only negatively correlated with the curve parameter A 1 and A 2 for the stem biomass (P < 0.1, Fig.  3B), which indicated that the fitted curve parameters might be less affected by genotype differences. Interestingly, VPD was significantly negatively correlated with curve parameters (A 1 and A 2 ) for shoot and leaf biomass basis (Fig. 3A and D), but it was not significantly correlated with curve parameters (A 1 and A 2 ) for stem biomass and with LAI basis (P > 0.1, Fig. 3B and C). For the environmental characteristics involved in the analysis, there was no significant correlation between rainfall and the above curve parameters (P > 0.1). AGDD was only significantly correlated with the parameter A 1 for shoot biomass basis and A 2 for LAI basis (P < 0.05, Fig. 3C and D). The average daily GDD was significantly correlated with parameters A 1 and A 2 for LAI (P < 0.1, Fig. 3C). Notably, AGDD significantly correlated with VPD (P < 0.001). Only sowing density was included in the analysis as management information, and curve parameter A 1 for stem biomass was significantly negatively correlated with sowing density (P < 0.05, Fig. 3B). However, it was significantly positively correlated with curve parameters A 1 and A 2 for LAI (P < 0.05, Fig. 3C). Overall, genotype affects curves based on LAI and stem and shoot biomass, but not leaf biomass. Environment affects all curves except for leaf biomass. Density affects all curves, except for leaf biomass. The leaf N c concentration level under different experimental conditions exhibited significant differences (Fig. 4A). However, the N c concentration of the stem was lower than the leaf and decreased faster with increased stem biomass. The differences in the N c concentration of stem under different experimental conditions were less than the leaf (Fig. 4B). The N c curve of the shoot biomass was higher than the stem biomass.

Variation in organ-specific N c dilution curves and uncertainty in parameters
There was a small difference in the N c curves of the shoot biomass under different experimental conditions (Fig. 4D). In addition, the N c curve for the LAI basis was higher than the shoot biomass ( Fig. 4C and D). There also was a substantial  The hybrid organ-specific N c dilution curves were fitted across all experimental data points (Fig. 4, black lines). The difference between the NNI derived from organ-specific curves under specific conditions and the NNI derived from corresponding hybrid curves was relatively small (Fig. 5). For NNI derived from leaf and stem biomass, and LAI, the n-RMSE values were 9.48%, 18.49%, and 13.53%, respectively (Fig. 5). This indicated that the errors were statistically acceptable if the organ N status was estimated using the universal curve. The N c dilution curves based on organs, shoot biomass, and LAI were compared with the published N c dilution curve (Fig. 6); the curve parameter A 1 for leaf biomass basis was in between the comparison curves [22,23,37,38]; the curve parameter A 1 for stem biomass [23,38], LAI, and shoot biomass basis [11,12] was lower than the comparison curve [38]. The curve parameter A 2 for organs, shoot biomass, and LAI basis was lower than all comparison curves.
The uncertainty of the N c curve (the 95% credible interval width) based on organs, shoot biomass, and LAI is shown in Fig. 7. The uncertainty decreased rapidly when the biomass or LAI was low and then remained stable or rose slightly. However, some curves showed a narrow credible interval. Furthermore, it is well-established that more observation points can reduce the uncertainty of the N c curve. In this study, the experiment 2012-XX-AK58 (n = 91) included 13 N fertilizer treatments, including 5 N application rates, 3 topdressing ratios, and 7 sampling dates. Under higher biomass and LAI (leaf biomass > 2 t ha −1 , stem biomass > 3 t ha −1 , LAI > 2.5, and shoot biomass > 5 t ha −1 ), the uncertainty was least in shoot biomass, followed by stem biomass, LAI, and leaf biomass.

NNI derived from organ-specific N c dilution curves
The NNI for leaf, stem, shoot biomass, and LAI basis was subsequently calculated (Fig. S6). The NNI for each organ basis at different stages was increased with an increased N fertilizer rate. The NNI for leaf biomass basis maintained a higher NNI value (mean = 0.84) during the vegetative growth period across several N treatments, and the CV was smaller (CV = 22.83%). Compared with leaf, the CV of NNI of stem biomass basis was larger (40.45%) and maintained a lower value (mean = 0.74). Notably, the N c dilution curves for LAI and shoot biomass were derived from shoot N concentration. However, the NNI value of the LAI was higher (mean = 0.72) than the shoot biomass (mean = 0.69), and the CV was larger (CV = 43.28%).
The relationship between the NNI for leaf, stem biomass, and LAI and the NNI for shoot biomass in each experiment is shown in Fig. 8. When the shoot-based NNI exceeded 0.84, the increase in leaf NNI decreased; when the shoot NNI exceeded 1.02, the leaf NNI was lower than the 1:1 line. In contrast, when the shoot NNI exceeded 0.79, the stem NNI was relatively higher. Moreover, when the shoot NNI exceeded 1.35, the stem NNI showed a more significant increase rate. LAI NNI was similar to stem NNI, but the LAI NNI was higher than the 1:1 line when the shoot NNI exceeded 1.20. When the shoot NNI exceeded 0.89, the increased rate of LAI NNI increased. In addition, the correlation between stem NNI and shoot NNI was low (R 2 = 0.7867). These findings indicated that the N status of different organs was different from the shoot.
Overall, leaf biomass NNI yielded the smallest difference with shoot NNI (RMSE = 0.1094; n-RMSE = 11.39%), followed by LAI NNI (RMSE = 0.1096; n-RMSE = 12.36%), while stem NNI yielded the largest difference (RMSE = 0.1384; n-RMSE = 14.63%). However, there was little difference between different organs and shoot N status (n-RMSE < 15%). For each specific experimental condition (Fig. 9), the difference between leaf biomass NNI and LAI NNI and plant NNI was in RMSE < 0.2 and n-RMSE < 20%. In some experiments, the difference between stem NNI and shoot NNI was more than 20% (n-RMSE). Notably, the difference between shoot NNI and weighted mean NNI for leaf and stem basis was very small.

Drivers altering the organ-specific N c dilution curve parameters
Most N c dilution curves fitted for organ biomass and LAI bases are different, reflecting the effect of G × E × M interaction. This implies that changes of wheat genotypes, planting environment, and management can affect the curve parameters, leading to potential errors in crop N nutrition status diagnosis and N demand estimations [28,39,40]. The uncertainty of the fitted parameter A 1 was significantly less than that of parameter A 2 , indicating that the curve parameter A 1 for organ basis was less affected by G × E × M. The organ-specific N c dilution curves showed that the N concentration in the leaf for all experiments was higher than in the stem (Fig. 4), mainly due to the different demands of plant organs on metabolic and structural N [41]. The wheat leaf N concentration decreased slightly (almost linearly) during the whole vegetative growth stage due to the effective utilization of physiological N in the leaves to ensure optimal photosynthetic activity [18,24]. The accurate estimation of the N c dilution curve can reflect the real difference under different conditions [6] and allow to find the source of the difference [25,28,29]. For the N c dilution curves for leaf biomass, parameters A 1 and A 2 were negatively correlated with the VPD. The proportion of the lower leaves increased and were shaded by the upper leaves. Accordingly, the difference of light environment and leaf age may lead to this dilution phenomenon [19,[42][43][44][45]. Notably, the datasets ignored the changes of N concentration under initial low biomass (shoot biomass <1 t ha −1 ), which is a more standardized method according to Justes et al. [11]. Therefore, all curve parameters developed based on organ biomass and LAI had no significant correlation with plant N concentration during the early growth stage. For the N c dilution curves for stem biomass basis, parameters A 1 and A 2 were negatively correlated with the maximum biomass in the vegetative growth period. The N concentration dilution was much stronger in stem and shoot during the early dilution process [23]. It is widely acknowledged that stem biomass accounts for a major component of shoot biomass. The negative correlation between parameter A 1 and planting density indicated that high density affected N uptake by the stem during the early growth stage. In addition, planting density was positively correlated with curve parameters A 1 and A 2 for LAI, and wheat canopy coverage was changed by planting density, wheat plants could quickly enter the dilution process under high density, and plant biomass increased faster [14,46]. Parameter A 2 reflects a specific mode of plant N concentration dilution with the increase of biomass. Our results indicated that the change degree of curve parameter A 1 was lower than parameter A 2 [7,11,14,19]. Because all experiments were irrigated when necessary, the significant effect of rainfall on parameters A 1 and A 2 of the organ-specific curve was not determined. The effect of the G × E × M interaction was slightly greater than parameter A 1 , and its planting environment easily determined the response of biomass or LAI to N uptake during wheat growth.

Universal organ-specific N c dilution curves
The classic method of developing N c dilution curves is obtained through analysis of variance and a series of curve fitting [11,47]. Therefore, the error of the whole process cannot be considered. The datasets under different G × E × M conditions are particularly important for the uncertainty analysis. This study used Bayesian theory and the MCMC method to test the wheat N fertilizer experimental dataset under 14 different G × E × M conditions, and an N c dilution curve based on the wheat leaf, stem, and shoot biomass, and LAI was proposed [28]. The published curves were not consistent with the curve constructed based on the Bayesian theoretical framework in this study [11,12,21,23,37,38,48], which showed the difference in wheat N dilution under different wheat genotypes, planting environments, and managements, and also reflected that the traditional methods might overestimate the N c concentration [31], given that part of the experimental data used in this study came from a previous study [38]. Indeed, the difference in wheat genotypes leads to differences in N uptake capacity, and this difference may also be related to wheat's initial N uptake capacity during the seedling stage and the soil N supply [41].
Similar to the N c dilution curve for shoot biomass basis [25,28,29], the uncertainty of the N c dilution curve for leaf and stem biomass and LAI basis is related to the biomass or LAI level. The response curve of biomass or LAI to N% was steep at low biomass levels. The uncertainty of N c became less as the response curve asymptotically approached horizontal with higher biomass or LAI. Therefore, the early less accurate N c value was unreliable for decision-making. Besides, the uncertainty level of the fitting curve was related to the experimental dataset. Indeed, the curve parameters can be accurately estimated by an effective dataset, and the real difference of the curve parameters can be obtained [25]. Accordingly, effective experimental design, such as more and reasonable N application treatments, will reduce the uncertainty of each observation date (by reducing data point scattering). Meanwhile, increasing the number of observations (by increasing sampling frequencies) will reduce the uncertainty in the time series [49].
Too many N c dilution curves under specific conditions are undoubtedly not conducive to practical application. Therefore, it is necessary to simplify the model while ensuring the performance of N status estimation. This study proposed the potential for establishing universal organ-specific N c dilution curves. The results indicated that the universal curves have good nitrogen diagnostic ability under different conditions, which is consistent with Yao et al. [25] and Fu et al. [50]. The applicability of the universal curve is expected to be tested in the future.

NNI derived from organ-specific N c dilution curves and application
The correlations between organs and plant N status make it possible to use organ N status to estimate shoot N status. Previous studies have shown that the NNI based on rice leaf biomass was closer to the shoot biomass basis [24], and the NNI based on wheat leaf biomass was better for N diagnosis [38]. In particular, the N status for leaf biomass and LAI basis was synchronous and stable with the shoot biomass (Fig. 9). The weighted average NNI for leaf and stem biomass basis was closer to the NNI for shoot biomass basis, indicating that leaf and stem were not balanced in the N distribution of the whole plant, which provided a reference for simulating the N distribution among different organs of wheat crops [37]. It was worth noting that leaves started to consume N extravagantly when the shoot N status was not very high (NNI > 0.84; Fig. 8), while stems started to serve as N storage organs when the shoot N status was very high (NNI > 1.35). Indeed, wheat plants first use enhanced N supply to increase their leaf N concentration to optimize photosynthesis, and the stem is then used as a temporary storage organ [27]. For the same observation sample, there were differences in N status among leaf, stem, and shoots. Therefore, the plant and organ N status should be reevaluated in practical application. The difference in organ N status can improve our understanding of organ function response to N nutrition.
At present, many crop growth models use organ N c dilution curves to estimate organ N distribution. The N c curve for APSIM (Agricultural Production Systems sIMulator) [37], STICS (Simulateur Multidisciplinaire pour les Cultures Standards) [51], and RiceGrow [52] models has been developed using a small dataset or special planting conditions, which have yielded great uncertainty. Especially for crop growth modeling, this difference in N dilution effects at the organ level seems to be a useful and logical method for describing their different roles as storage pools and assimilation organs. Oryza2000 used organ N c curves in relation to development time based on a small dataset, which is empirical and has high uncertainty in nitrogen modeling. This study develops new organ N c curves using a multi-source dataset, which could be useful for the application of wheat models. The uncertainty of the N c dilution curve in the crop model and the theory of N distribution warrant further study.

Conclusion
This study investigated the uncertainty and drivers of organspecific critical nitrogen dilution curves under different conditions. By using hierarchical Bayesian theory, parameters A 1 and A 2 of the organ-specific N c dilution curves for wheat were derived and evaluated under 14 different G × E × M N fertilizer experiments. The uncertainty of the N c dilution curve was related to biomass and LAI level. Although the variation of parameter A 1 was less than that of A 2 , the values of both parameters can change significantly in response to G × E × M. The drivers include maximum biomass, duration, and AGDD during the vegetative growth period and planting density. NNI calculated using organ-specific N c is generally 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.