# Critical nitrogen dilution curves for winter oilseed rape (Brassica napus L.) along the whole crop cycle: A Bayesian analysis

Raphael Paut, Muriel Valentin-Morison, Baptiste Rayon, Marie-Hélène Jeuffroy, Céline Richard-Molard

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Raphael Paut, Muriel Valentin-Morison, Baptiste Rayon, Marie-Hélène Jeuffroy, Céline Richard-Molard. Critical nitrogen dilution curves for winter oilseed rape (Brassica napus L.) along the whole crop cycle: A Bayesian analysis. European Journal of Agronomy, 2025, 168, pp.127642. 10.1016/j.eja.2025.127642. hal-05085184

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# Critical nitrogen dilution curves for winter oilseed rape (Brassica napus L.) along the whole crop cycle: A Bayesian analysis

Raphael Paut<sup>a,*</sup> <sup>Δ</sup>, Muriel Valentin-Morison<sup>a</sup>, Baptiste Rayon<sup>b</sup>, Marie-Hélène Jeuffroy<sup>a,Δ</sup>, Céline Richard-Molard<sup>c,Δ</sup>

## ARTICLE INFO

### Keywords:

- Critical N dilution curve

- Nitrogen nutrition index

- N management

- Plant-based N diagnosis

- Brassica napus L.

- WOSR

## ABSTRACT

Nitrogen (N) is the most limiting nutrient for crop growth. Determining the dynamics of N uptake by crops is essential to optimize N management and improve the sustainability of crop production, especially for winter oilseed rape (Brassica napus L.), a highly N-dependent crop. The concept of critical nitrogen concentration is an effective way to diagnose plant nitrogen status, defining the minimum concentration of nitrogen in the aerial parts needed to maximize shoot biomass at a given time in the crop growth. For winter oilseed rape the existing nitrogen dilution curve was developed in the 1990s, but the curve was established only until the beginning of flowering, the reproductive part not being covered. The main objective of this study is to determine new critical N dilution curves for winter oilseed rape over the whole crop cycle. To achieve this, we used data from 36 field trials, conducted between 2003 and 2020 under various N application rates and cultivars, and a new Bayesian statistical framework. For the vegetative phase, the critical curve (Ncvege=4.556 W-0.241) determined in this study was close to the curves found in previous studies. In addition, new critical N dilution curves were determined for the first time in winter oilseed rape, for the reproductive phase (Ncrepro =4.764 W-0.424) and for the entire growth period (Ncunique=7.364 W-0.582). Interestingly the parameters differed markedly from those recently obtained in spring canola. These new dilution curves should provide useful tools for determining the N nutritional status of winter oilseed rape over a longer period, and thus improve nitrogen nutrition diagnosis and enable optimal nitrogen management.

## 1. Introduction

In agricultural systems, nitrogen (N) is the main limiting nutrient element for crop production, but is also directly responsible for many environmental issues. A significant fraction of nitrogen used in field crops comes from synthetic fertilizers, whose production and transport are fossil-fuel intensive (Tilman et al., 2002). Moreover, N use generates risks of N2O emissions, NH3 volatilization and nitrate leaching (EU Commission, 2013; Ma et al., 2010; Pellerin et al., 2017). Despite research efforts and fertilization management tools that have been widely deployed, it remains challenging to minimize nitrogen losses while maximizing grain yield quantity and quality.

Winter oilseed rape (WOSR) (Brassica napus L.), has high nitrogen requirements and the N content of seeds and plant tissues is higher than in most small-grain cereals and other oilseed crops (Ma and Herath,

2016; Svečnjak and Rengel, 2006). However, despite the high nitrogen uptake capacity of WOSR during autumn (mean of 40–80 kg N/ha, but sometimes 200 kg N/ha) (Barraclough, 1989; Dejoux et al., 2003), nitrogen leaching is often a significant problem in rotations including rapeseed (Beillouin et al., 2021; Sieling and Kage, 2006). Indeed, due to its early development, winter oilseed rape often uses only a small proportion of the nitrogen mineralized in late spring, particularly under weather conditions where temperatures rise slowly in spring (Sieling et al., 1998; Sieling and Kage, 2010). In addition, a large amount of quickly mineralized WOSR residues (petals and leaves) return to the soil after flowering, increasing the risk of N losses generated by the mineralization of rapeseed residues during cultivation (Dejoux et al., 2000; Di and Cameron, 2002). Nitrogen fertilization management must take into account three related sources of uncertainty: N requirement (regulated by crop growth rate), soil N availability, and N uptake capacity (also

<footnote><sup>a</sup> Université Paris-Saclay, AgroParisTech, INRAE, UMR Agronomie, Palaiseau 91123, France</footnote>

<footnote><sup>b</sup> Terres Inovia, Thiverval-Grignon 78850, France</footnote>

<footnote><sup>c</sup> Université Paris-Saclay, AgroParisTech, INRAE, UMR EcoSys, Palaiseau 91123, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: raphael.paut@inrae.fr (R. Paut).</footnote>
feedback regulated by crop growth rate). Therefore, it is rather difficult to correctly decide the proper requirement of nitrogen and a dynamic tool is needed. Monitoring the dynamics of N uptake for winter oilseed rape is therefore essential to optimize N management and limit N losses in the ecosystem.

The minimum shoot N concentration required to produce the maximum biomass at a given time has been conceptualized as the critical N concentration of the aerial biomass (Nc). The critical N concentration follows a negative exponential relationship as the shoot biomass increases, that can be attributed to a decrease in the leaf/stem ratio and remobilization of N from shaded to lit parts of the canopy to maximize photosynthetic capacity (Lemaire et al., 2019, 1992). From the critical N concentration, the N status of a crop for a given shoot biomass can be estimated by using the nitrogen nutrition index (NNI). NNI is calculated as the actual shoot nitrogen concentration (Na) divided by Nc. This unit-less indicator is a key indicator for identifying N deficiencies that can later impact yield (Lemaire and Meynard, 1997), and for monitoring nitrogen fertilization (Ravier et al., 2017a).

N dilution curves were first established for graminaceous grasslands (Lemaire and Salette, 1984), and have since been applied to many field crops, such as wheat (Greenwood et al., 1990; Justes et al., 1994; Yao et al., 2021; Yin et al., 2018; Ziadi et al., 2010), potato (Giletto et al., 2020), maize (Yue et al., 2014), rice (Wang et al., 2016) and other crops. For winter oilseed rape, a nitrogen dilution curve was developed in France more than 20 years ago by Colnenne et al. (1998) from the method proposed by Justes et al. (1994). The re-evaluation of this curve, considering new Bayesian framework (Makowski et al., 2020), current winter oilseed rape cultivars, and longer growth period is lacking. Recently, Jégo et al. (2022) defined a critical N dilution curve for spring canola using data obtained in Canada. The curve obtained for canola, cultivated in spring, was statistically different from Colnenne's curve obtained for winter oilseed rape (Brassica napus L.), suggesting that the crop type, i.e., spring versus winter, may generate different curves, as demonstrated for wheat (Jégo et al., 2022). The differences could also arise from contrasted pedoclimatic situations, as recent studies have shown that genotype × environment × management practices interactions do influence the critical nitrogen dilution curve parameters (Ciampitti et al., 2021).

While most critical N dilution curves focus on the vegetative period, as N dynamics are theorized to shift during the reproductive phase due to changes in allometry ratios (e.g., leaf fall and lignified tissues, Lemaire et al., 1997), Jégo et al. (2022) recently provided an example of a critical N dilution curve for spring canola during the reproductive phase. Their results highlighted distinct differences in N dynamics between the two phases, underlining the importance of extending the analysis of critical N dilution to include the reproductive phase, when biomass accumulation and N requirements remain significant. For winter oilseed rape, no data on NNI during the reproductive period is currently available. Nevertheless, nitrogen absorption does not stop suddenly in WOSR, suggesting a demand for nitrogen after the flowering period, and a possible delay in the need for nitrogen fertilization, compared with current practices favoring early N (Bouchet et al., 2016). Consequently, a tool for optimizing N diagnosis and N nutrition in WOSR after flowering would be of great interest. Moreover, this pre-and-flowering period are key moments for the establishment of the number of grains, suggesting that NNI could help in forecasting the yield performance.

In this study, our overall objective was to determine new critical N dilution curve for winter oilseed rape, using a Bayesian approach, and to compare them with previously established curves. More precisely, our study aims to (i) redefine the critical N dilution curve during the vegetative period for current winter oilseed rape cultivars using a Bayesian method that provides parameters with uncertainty, and compare it with those determined initially by Colnenne et al. (1998) for winter oilseed rape in France, and recently by Jégo et al. (2022) for canola in Canada; (ii) evaluate the variation of the critical N dilution curve according to the plant phenological stage and define a curve for the reproductive

phase in winter oilseed rape, (iii) investigate possible applications for crop N status diagnoses and N fertilization management applications. This study can provide a faster and more robust method to estimate crop N status and optimize N fertilizer management for current winter oilseed rape production.

## 2. Material and methods

### 2.1. Experimental design

Data were collected from 36 sites where trials were carried out from 2003 to 2020 growing seasons in different regions of France (Fig. 1). This represents a total of total of 90 site × year trials with varying rates of N fertilization and cultivars under field conditions. The sites cover a large range of soil and climatic conditions. For each year-location combination, data used were shoot dry mass (t ha-1), shoot nitrogen content (%N), fertilizer N rate level (kg N ha-1) and sampling times. A detailed description of experimental information is given in Table 1. The experimental designs were arranged in a randomized complete block design with three to four repetitions. For the statistical analysis, the average of these repetitions was used. The sowing dates were in summer-autumn, between August 14th and October 3rd, and the harvest dates were in summer, between June 26th and July 17th. Sowing densities varied from 25 to 73 plants m⁻² and total N rates ranged from 0 to 300 kg N ha-1. N was the only experimental factor that varied intentionally in the trials. Inputs of other nutrients (P, K and S) did not vary between treatments. Crop management practices, including irrigation, weeding, and pesticide application, were conducted following local recommendations to minimize biotic and abiotic stresses. While minor effects of other factors cannot be entirely excluded, N was considered the primary limiting factor, in alignment with the experimental design. An average of 4.1 nitrogen doses were tested (from 2 to 13 different N rates modalities per trial) and there was a total of 191 sampling dates (Table 2).

### 2.2. Plant sampling and measurement

Plants were harvested, fresh and dry shoot biomass and nitrogen content were determined. The sampling consisted of harvesting an area of about 1 m² in each of the experimental blocks. The shoot dry matter was weighed after oven drying for 48 h at 70 °C. Samples were then ground to a fine powder and analyzed for total N content according to the Dumas combustion method (Buckee, 1994) using an automated CN analyzer.

### 2.3. Establishment of critical Nitrogen dilution curves

The critical nitrogen dilution curve is a allometric mathematical function that describes the relationship between optimal nitrogen concentration and shoot biomass (Lemaire et al., 2008). This relationship is expressed as:

$$N_c = aW^{-b} \qquad (1)$$

where Nc (%) is the critical nitrogen concentration expressed as a percentage of shoot dry matter (W in t ha-1), a is the N concentration when W is 1 t ha-1 and b is the dilution coefficient representing the rate of the power decline.

To establish critical N dilution curves for winter oilseed rape, the Bayesian hierarchical model described by Makowski et al. (2020) was implemented. This model assumes that the relationship between shoot biomass and N content follows a linear-plateau function, a widely used approach in many studies. The model operates in three levels. At the first level, for a specific observation date, which corresponds to a particular growth stage in a given year, the shoot biomass response to N content is modeled using the linear-plateau function. Biomass and N content
<figure><img src="image_3.png" /><figcaption>Fig. 1. Location of the winter oilseed rape (Brassica napus L.) nitrogen fertilization trials used in this study. Numbers correspond to trial ID.</figcaption></figure>

measurements are collected across different nitrogen fertilizer levels. The second level captures the variability in the parameters of the linear-plateau function across observation dates and is used to compute the Nc dilution curve. The third level incorporates prior knowledge of parameter values. To limit the influence of the choice of the priors on the results, we used the weakly informative priors (a graphical representation of the model and the individual curves is provided in supplementary material S1). The statistical model can be presented as:

$$ Nc_{ij} \sim N(\mu_{ij}, \sigma^2), \\ \mu_{ij} = aW_{ij}^{-b} \qquad (2) $$

where i is the date of observation and j is the N treatments

Compared to the classical sequential framework initially described by Justes et al. (1994) for wheat and used by Colnenne et al. (1998) for winter oilseed rape, this hierarchical Bayesian model estimates the parameters in a single step, eliminating the need to fit two statistical models sequentially. A recent study by Lacasa et al. (2023) compared the two methods and showed that the hierarchical framework led to a more precise estimation of dilution curve parameters and to less over-estimation of Nc values (also see Fernández et al., 2021).

The statistical model was fitted with a Markov chain Monte Carlo algorithm (MCMC) implemented with the R package rjags (Plummer,

2022). The algorithm was first run with three chains of 50,000 iterations each. After checking for convergence, the algorithm was run again during 100,000 additional iterations which were then used to compute the median and 95 % credibility intervals for the parameters of the Nc dilution curve. This procedure was applied to the vegetative and reproductive growth period, as well as to the whole crop cycle.

To assess differences both between the critical N dilution curves estimated in this study and those reported in the literature —as well as among the curves within our study— we approximated the posterior distributions for the parameters using available statistics (mean, median, 5th and 95th quantiles). Assuming a normal posterior distribution, we estimated the standard deviation as $(q_{0.975} - q_{0.025})/2 \times 1.96$. Based on these parameters, we generated 10,000 simulated draws from each normal distribution. The difference between the study parameter and the literature parameter was then computed for each simulation, and the 95 % credible interval for this difference was determined from the 2.5th and 97.5th percentiles. A difference was considered significant if the interval did not include zero. The parameters of the critical dilution curve equations, along with their 95 % credibility intervals, are presented in Table 3.

The data were separated into two distinct sets in order to define three N dilution curves: one for the vegetative period, one for the reproductive period and one for the whole crop cycle. For the vegetative growth period, we selected samples from the stem elongation stage (BBCH 30)
<table><caption>**Table 1**
Description of study sites and management practices.</caption><thead><tr><th>Trial ID</th><th>Site</th><th>Coordinates (lat, long)</th><th>Year</th><th>Soil type</th><th>Cultivar</th><th>Sowing rate (NP/m2)</th><th>Sowing date</th><th>Harvest date</th><th>Total N rates (kg N ha-1)</th></tr></thead><tbody><tr><td>1</td><td>Aiseray</td><td>47° 10' N, 5° 10' E</td><td>2015–2016</td><td>Clay</td><td>DK Exstorm</td><td>40</td><td>27/08/2015</td><td>19/07/2016</td><td>0, 50, 100, 100 a, 150, 200</td></tr><tr><td>2</td><td>Beziers</td><td>43° 20' N, 3° 17' E</td><td>2008–2009</td><td>Sandy clay</td><td>Alias</td><td>50</td><td>09/09/2008</td><td>30/06/2009</td><td>0, 130</td></tr><tr><td>3</td><td>Bretenière</td><td>47° 13' N, 5° 31' E</td><td>2014–2015</td><td>Silty clay loam</td><td>DK Exstorm</td><td>38</td><td>03/10/2014</td><td>15/07/2015</td><td>0, 40, 100, 140</td></tr><tr><td>4</td><td></td><td></td><td>2017–2018</td><td></td><td>DK Exstorm</td><td>-</td><td>-</td><td>-</td><td>0, 50, 100, 150, 200</td></tr><tr><td>5</td><td>Chambon</td><td>46° 5' N, 0° 52' W</td><td>2007–2008</td><td>Clay</td><td>Ovation</td><td>46</td><td>30/08/2007</td><td>09/07/2008</td><td>0, 180</td></tr><tr><td>6</td><td></td><td></td><td>2018–2019</td><td></td><td>DK Exstorm</td><td>-</td><td>-</td><td>-</td><td>0, 40, 80, 120, 170, 170, 170</td></tr><tr><td>7</td><td></td><td></td><td>2019–2020</td><td></td><td>LG Architect</td><td>-</td><td>-</td><td>-</td><td>0, 50, 100, 150, 200, 250, 250, 250, 250, 250, 250, 300</td></tr><tr><td>8</td><td>Domèvre-en-Haye</td><td>48° 48' N, 5° 56' E</td><td>2016–2017</td><td>Silty clay loam</td><td>DK Exstorm</td><td>42</td><td>22/08/2016</td><td>18/07/2016</td><td>0, 50, 100, 150, 200</td></tr><tr><td>9</td><td>Estrées-Mons</td><td>49° 52' N, 3° 1' E</td><td>2018–2019</td><td>Silt</td><td>DK Exstorm</td><td>36</td><td>28/08/2018</td><td>26/07/2019</td><td>0, 50, 100, 150, 200, 250, 250</td></tr><tr><td>10</td><td></td><td></td><td>2019–2020</td><td></td><td>LG Architect</td><td>33</td><td>27/08/2019</td><td>22/07/2020</td><td>0, 50, 100, 150, 200, 250, 250, 250, 250, 250, 250, 300</td></tr><tr><td>11</td><td>Grignon</td><td>48° 50' N, 1° 56' E</td><td>2003–2004</td><td>Silt loam</td><td>Capitol, Pollen, Saturnin</td><td>70</td><td>27/08/2003</td><td>06/07/2004</td><td>0, 100, 200</td></tr><tr><td>12</td><td></td><td></td><td>2004–2005</td><td></td><td>Capitol, Pollen, Saturnin</td><td>70</td><td>01/09/2004</td><td>11/07/2005</td><td>0, 100, 200</td></tr><tr><td>13</td><td></td><td></td><td>2013–2014</td><td></td><td>Aviso, Montego, Pollen, Express</td><td>33</td><td>03/09/2013</td><td>17/07/2014</td><td>0, 135</td></tr><tr><td>14</td><td>Issoudun</td><td>46° 57' N, 2° 0' E</td><td>2015–2016</td><td>Silty clay</td><td>DK Exstorm</td><td>43</td><td>20/08/2015</td><td>19/07/2016</td><td>0, 50, 100, 150, 200</td></tr><tr><td>15</td><td>Jazeneuil</td><td>46° 27' N, 0° 2' E</td><td>2007–2008</td><td>Silt</td><td>Safran</td><td>30</td><td>30/08/2007</td><td>15/07/2008</td><td>0, 180</td></tr><tr><td>16</td><td></td><td></td><td>2008–2009</td><td>Silt</td><td>Safran</td><td>50</td><td>26/08/2008</td><td>07/07/2008</td><td>0, 210</td></tr><tr><td>17</td><td>La Champenoise</td><td>46° 55' N, 1° 48' E</td><td>2017–2018</td><td>Silty clay</td><td>DK Exstorm</td><td>50</td><td>25/08/2017</td><td>04/07/2018</td><td>0, 50, 100, 150, 200</td></tr><tr><td>18</td><td>Lagardelle</td><td>43° 22' N, 1° 22' E</td><td>2007–2008</td><td>Clay</td><td>Corail</td><td>30</td><td>28/08/2007</td><td>07/07/2008</td><td>0, 171</td></tr><tr><td>19</td><td>Vic sur Nahon</td><td>47° 4' N, 1° 32' E</td><td>2019–2020</td><td>Silty clay loam</td><td>LG Architect</td><td>55</td><td>28/08/2019</td><td>01/07/2020</td><td>50, 100, 150, 200, 250, 250, 250, 250, 250, 250, 300</td></tr><tr><td>20</td><td>Le Rheu</td><td>48° 6' N, 1° 46' W</td><td>2014–2015</td><td>Silty clay</td><td>Aviso, Montego, Amber, Astrid, Bolko, Express, Mohican, Pollen</td><td>40</td><td>09/09/2014</td><td>02/07/2015</td><td>0, 70</td></tr><tr><td>21</td><td></td><td></td><td>2015–2016</td><td></td><td>Aviso, Montego, Amber, Astrid, Bolko, Express, Mohican, Pollen</td><td>46</td><td>09/09/2015</td><td>02/07/2016</td><td>0, 70</td></tr><tr><td>22</td><td>Lunery</td><td>46° 55' N, 2° 14' E</td><td>2008–2009</td><td>Silty clay loam</td><td>Beluga</td><td>50</td><td>10/09/2008</td><td>09/07/2009</td><td>0, 120</td></tr><tr><td>23</td><td></td><td></td><td>2016–2017</td><td>Silty clay loam</td><td>Beluga</td><td>50</td><td>-</td><td>-</td><td>0, 50, 100, 150, 200</td></tr><tr><td>24</td><td>Marquein</td><td>43° 17' N, 1° 42' E</td><td>2007–2008</td><td>Silty clay loam</td><td>Flash</td><td>30</td><td>10/09/2007</td><td>30/06/2008</td><td>0, 171</td></tr><tr><td>25</td><td>Martincourt</td><td>48° 50' N, 5° 56' E</td><td>2007–2008</td><td>Clay</td><td>Grizzly</td><td>30</td><td>14/08/2007</td><td>16/07/2008</td><td>0, 160</td></tr><tr><td>26</td><td>Monbalen</td><td>44° 17' N, 0° 44' E</td><td>2008–2009</td><td>-</td><td>Corail</td><td>50</td><td>26/08/2008</td><td>10/07/2009</td><td>0, 159</td></tr><tr><td>27</td><td>Pigny</td><td>47° 8' N, 2° 27' E</td><td>2018–2019</td><td>Silty clay loam</td><td>Architect</td><td>35</td><td>20/08/2018</td><td>11/07/2019</td><td>0, 50, 100, 150, 200, 250, 250</td></tr><tr><td>28</td><td>Rosières-en-Haye</td><td>48° 47' N, 6° 1' E</td><td>2019–2020</td><td>Silty clay</td><td>Lg Architect</td><td>40</td><td>22/08/2019</td><td>-</td><td>0, 50, 100, 150, 200, 250, 250, 250, 250, 250, 250, 250, 300</td></tr><tr><td>29</td><td>Saint-Exupéry</td><td>45° 43' N, 5° 6' E</td><td>2008–2009</td><td>Sandy clay loam</td><td>Excel</td><td>73</td><td>28/08/2008</td><td>26/06/2009</td><td>0, 190</td></tr><tr><td>30</td><td>Tarabel</td><td>43° 31' N, 1° 40' E</td><td>2015–2016</td><td>Sandy clay loam</td><td>DK Exstorm</td><td>32</td><td>07/09/2015</td><td>20/07/2016</td><td>0, 40, 80, 120, 170</td></tr><tr><td>31</td><td>Vielmur-sur-Agout</td><td>43° 37' N, 2° 4' E</td><td>2016–2017</td><td>Sandy clay loam</td><td>DK Exstorm</td><td>39</td><td>20/09/2016</td><td>27/06/2017</td><td>0, 40, 80, 120, 170</td></tr><tr><td>32</td><td></td><td></td><td>2017–2018</td><td></td><td>DK Exstorm</td><td>39</td><td>04/09/2017</td><td>-</td><td>0, 40, 80, 120, 170</td></tr><tr><td>33</td><td>Villedieu</td><td>46° 50' N, 1° 30' E</td><td>2007–2008</td><td>Silty clay loam</td><td>Cooper</td><td>30</td><td>30/08/2007</td><td>15/07/2008</td><td>0, 171</td></tr><tr><td>34</td><td></td><td></td><td>2007–2008</td><td>Silty clay loam</td><td>Cooper</td><td>30</td><td>30/08/2007</td><td>15/07/2008</td><td>0, 189</td></tr></tbody></table>

(continued on next page)
<table><caption>**Table 1 (continued)**</caption><thead><tr><th>Trial ID</th><th>Site</th><th>Coordinates (lat, long)</th><th>Year</th><th>Soil type</th><th>Cultivar</th><th>Sowing rate (NP/m2)</th><th>Sowing date</th><th>Harvest date</th><th>Total N rates (kg N ha-1)</th></tr></thead><tbody><tr><td>35</td><td></td><td></td><td>2008–2009</td><td>Silty clay loam</td><td>Catalina</td><td>50</td><td>28/08/2008</td><td>10/07/2009</td><td>0, 120</td></tr><tr><td>36</td><td>Virson</td><td>46° 8' N, 0° 53' W</td><td>2008–2009</td><td>Clay</td><td>NK Aviator</td><td>25</td><td>08/09/2008</td><td>03/07/2009</td><td>0, 210</td></tr></tbody></table>

a Consecutive identical nitrogen doses indicate dose splits at different dates

<caption>**Table 2**</caption>

Number of dates of measurement, average number of N levels per date, total number of data for each growth period.

<table><caption>**Table 3**</caption><thead><tr><th>Growth period</th><th>Number of sampling dates</th><th>Average number of N levels per date</th><th>Number of unique dose × sampling date</th></tr></thead><tbody><tr><td>Vegetative period</td><td>107</td><td>3.80</td><td>407</td></tr><tr><td>Reproductive period</td><td>82</td><td>4.67</td><td>383</td></tr></tbody></table>

Parameter values of the critical N dilution curves of oilseed rape (Brassica napus L.) with the approach described by Makowski et al. (2020) and comparison with parameters values available in the literature.

<table><thead><tr><th rowspan="2"></th><th colspan="2">Vegetative growth period</th><th colspan="2">Reproductive growth period</th><th colspan="2">Entire growth period</th></tr><tr><th>a</th><th>b</th><th>a</th><th>b</th><th>a</th><th>b</th></tr></thead><tbody><tr><td>Parameters of the new critical N dilution curves</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0.05 quantile</td><td>4.206</td><td>0.186</td><td>3.710</td><td>0.321</td><td>6.644</td><td>0.530</td></tr><tr><td>Median</td><td>4.556</td><td>0.241</td><td>4.764</td><td>0.424</td><td>7.364</td><td>0.582</td></tr><tr><td>Mean</td><td>4.565</td><td>0.241</td><td>4.843</td><td>0.427</td><td>7.388</td><td>0.583</td></tr><tr><td>0.95 quantile</td><td>4.982</td><td>0.302</td><td>6.445</td><td>0.549</td><td>8.275</td><td>0.640</td></tr><tr><td>Parameters of the published Nc dilution curve of Colnenne et al. (1998) for winter oilseed rape (Brassica napus L.)</td><td>4.48</td><td>0.26</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Parameters of the published Nc dilution curve of Jégo et al. (2022) canola (Brassica campestris L. and Brassica rapa L.)</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0.05 quantile</td><td>4.181</td><td>0.233</td><td>2.070</td><td>0.032</td><td>-</td><td>-</td></tr><tr><td>Median</td><td>4.255</td><td>0.255</td><td>2.159</td><td>0.057</td><td>-</td><td>-</td></tr><tr><td>Mean</td><td>4.261</td><td>0.257</td><td>2.227</td><td>0.071</td><td>-</td><td>-</td></tr><tr><td>0.95 quantile</td><td>4.334</td><td>0.278</td><td>2.309</td><td>0.095</td><td>-</td><td>-</td></tr></tbody></table>

a No confidence intervals were defined in this study

to the end of flowering stage (BBCH 69, Lancashire et al., 1991). For the reproductive period, samples from the pod formation (BBCH 70) to pod development stages (BBCH 79) were selected. BBCH 79 corresponds to the end of pod development, where pods have reached final size, but seed filling has not yet peaked. At this stage, seeds are not yet major sinks for N, the primary N compartments remain the vegetative tissues.

The total number of data was 407 for the vegetative growth period and 383 for the reproductive growth period (Table 2). An analysis was carried out to assess the model sensitivity to the number of doses at each date, especially for cases where the number of doses was limited, no difference was observed (supplementary material S2).

## 2.4. Relations between NNI and yield

From Eq. (1), the nitrogen nutrition index is calculated at each growth stage according to Justes et al. (1994) as follows:

$$NNI = \frac{Na}{Nc} \qquad (3)$$

where Na is the observed N concentration, and Nc is the critical N concentration for the observed shoot dry mass. Based on Eq. (3), when NNI = 1, N nutrition is considered optimal, while NNI > 1 and NNI < 1 indicate excess and deficient N nutrition, respectively.

Relative yield (RY) was calculated as the ratio between the yield of a treatment and the maximum yield for the same cultivar × site × year. To analyze the relationship between the NNI and relative yield, we employed a linear-plateau model using the linearPlateau function from the soiltestcorr R package (Correndo et al., 2023). The statistical model can be expressed as:

$$RY \sim N(\mu, \sigma^2), \\ \mu = \begin{cases} \beta + \alpha \text{ NNI, if } NNI < \gamma \\ \beta + \alpha\gamma, \text{ otherwise} \end{cases} \qquad (4)$$

where α is the slope of the linear portion, β is the intercept, γ is the threshold NNI value at which the plateau begins, and θ represents the plateau level of relative yield.

The linearPlateau function estimates these parameters by minimizing the sum of squared residuals. This approach allows us to quantify the response of relative yield to NNI, identifying the point beyond which additional increases in NNI do not result in further yield gains.

## 3. Results

### 3.1. Nc dilution curves for the vegetative and reproductive growth periods

The critical N dilution curves defined with the Bayesian approach are presented and compared to existing curves in Fig. 2. More detailed figures of the parameters of these curves are presented in Fig. 3 and Table 3. For the vegetative growth period, crop shoot biomass (W) ranged from 1.01 to 13.06 t ha-1 (Fig. 2a) while shoot N concentration ranged from 0.78 % to 6.08 %. No statistical difference with existing curve parameters was found for the Nc curve parameters (Colnenne et al., 1998; Jégo et al., 2022) in the vegetative period (Fig. 3a).

For the reproductive period, crop shoot biomass ranged from 3.28 to 21.7 t ha-1 and shoot N concentration from 0.79 % to 3.06 %. We defined a critical Nc dilution curve for winter oilseed rape during the reproductive period (Fig. 2b), which was distinct from the existing curves in the literature, but also from the vegetative Nc curve we obtained (Fig. 2c). This divergence was primarily driven by the b parameter, which had a posterior median of 0.424 and 0.241 for the vegetative curve. The non-overlapping 95 % credible intervals for these parameters confirm the significant difference between the two curves (Fig. 3).

Finally, a unique Nc dilution curve was defined for the whole growth period, including vegetative and reproductive periods. As a result, the new Nc dilution curves defined with the Bayesian approach are $Nc_{vege} = 4.556 W^{-0.241}$ for the vegetative period and $Nc_{repro} = 4.764 W^{-0.424}$ for the reproductive period and Nc = 7.364W$^{-0.582}$ for the entire growth period.
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Critical nitrogen (Nc) dilution curves and observation data used to define them for (a) the vegetative growth period, (b) the reproductive period and (c) the whole growth period of winter oilseed rape according to the Bayesian approach proposed by Makowski et al. (2020). Solid black curve represents the critical N dilution curve while dashed curves represent its 95 % credibility intervals. Solid red curves represent the Nc dilution curves from Jégo et al. (2022) for canola while the solid green curve represents the Nc dilution curve from Colnenne et al. (1998) for winter oilseed rape.</figcaption></figure>

## 3.2. Relationship between NNI and seed yield

Fig. 4 shows the fitted linear-plateau model for NNI calculated at different growth periods, depicting the relationship between NNI and the relative yield. The linear part of the curves shows the positive response of yield to increasing NNI up to a breakpoint. This breakpoint represents the optimal NNI value beyond which no significant yield gain is observed, indicating the plateau phase. The plateau value signifies the maximum achievable yield given the current conditions and management practices. Depending on the vegetative stage and whether one or two dilution curves are employed, the RY plateau ranges from 0.92 to 0.95, the NNI at the breakpoint lies between 0.78 and 1.31, and the model's coefficient of determination (R²) fluctuates between about 0.52 and 0.84. Overall, these parameters remain very similar, although predictions tend to be more accurate with two dilution curves at earlier stages, while a single curve provides better predictions at later stages.

## 4. Discussion

### 4.1. Methodological challenges in determining critical nitrogen dilution curves

In this paper, we introduce updated critical nitrogen curves for winter oilseed rape, derived from field experiments conducted across various years, using different current cultivars, under diverse pedoclimatic conditions. Accurate estimation of critical dilution curves necessitates a substantial number of sampling sites, dates, and diverse nitrogen rates, a challenging requirement to fulfill. The use of extensive databases often introduces variations in biomass and nitrogen concentration attributable to varying nitrogen fertilization rates, but also to heterogeneity in soil and climate conditions (Table 2). The statistical framework used in this study, proposed by Makowski et al. (2020), provided a robust approach for calculating parameters associated with the critical nitrogen dilution curve. This approach showed at least identical or better performance than the classical 'sequential' approach
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Estimated values (medians) and 95 % credibility intervals for the parameters a and b of the Nc dilution curves. The values are compared with data available in the literature for canola in vegetative and reproductive period (Jégo et al., 2022), and for winter oilseed rape in vegetative period (Colnenne et al., 1998) (no data available for reproductive period).</figcaption></figure>

(Fernández et al., 2021; Jégo et al., 2022; Lacasa et al., 2023). In contrast to the classical approach (Colnenne et al., 1998; Justes et al., 1994), our approach involves estimating critical nitrogen concentrations through linear-plateau functions and eliminates the need for prior classification of N-limited and non N-limited data or identifying critical nitrogen concentration values. It also offers higher consistency (lower bias), along with better-calibrated credible intervals (Lacasa et al., 2023; Makowski et al., 2020).

## 4.2. *New and updated critical N curves: implications for crop N status assessment*

For the vegetative period, the Nc dilution curve parameters were consistent with the ones initially reported by Colnenne et al. (1998) for winter oilseed rape in France and Jégo et al. (2022) for spring canola in a North-American context. Our results showed that the intercept of the curve (the “a” parameter) was slightly, but not significantly, higher than the parameter a of existing studies (4.556 versus 4.480 and 4.255 respectively for Colnenne et al. 1998 and Jégo et al. 2022). The dilution

coefficient (“b” parameter) was slightly but not significantly, lower, than those of the same published studies (0.241 versus 0.260 and 0.255 respectively for Colnenne et al. 1998 and Jégo et al. 2022). Since our trials had a large range of cultivars and soil conditions, these results reflect a relative stability of the parameter across genotype × environment × management practices during the vegetative period.

In contrast, the curve we were able to identify for the first time in winter oilseed rape for the reproductive period differed significantly from the one obtained in spring version, i.e., in canola (Jégo et al., 2022). Both “a” and “b” parameters were significantly higher than the canola parameter (4.764 and 0.424 respectively in our study, versus 2.159 and 0.057 in Jégo et al. (2022). The observed difference between canola and winter oilseed rape in the reproductive Nc dilution curve could be attributed to several factors, including sowing density, which was three to five times higher for canola than for winter rapeseed (45 plants/m² on average in our study, compared to about 150 plants/m² for canola). This increased density can lead to less branched plants and reduced incident light on the leaves, resulting in a lower leaf-to-stem biomass ratio in canola compared to winter oilseed rape. We can
<figure><img src="image_6.png" /><figcaption>Fig. 4. Relationship between the relative yield and NNI for different phenological stages and different Nc dilution curves. Regression equations, relative yield plateau values, NNI plateau values and the coefficient of determination of linear-plateau regressions (R2) are displayed.</figcaption></figure>

hypothesize that nitrogen dilution was lower in spring canola because there were fewer nitrogen-rich leaves and more nitrogen-poor stems for the same biomasses. However, these hypotheses need to be tested in future research, to elucidate the relative contributions of these factors to the differences observed between canola and winter oilseed rape. It is also important to note that the estimation of a critical curve during the reproductive phase comes with a higher level of uncertainty, suggesting that further data and future experiments are required to establish a more robust critical dilution curve. Furthermore, a unique Nc dilution curve was also determined for the entire growth period, with “a” and “b” parameters of 7.364 and 0.582 respectively.

Oilseed rape has an indefinite growth pattern, which affects how nitrogen fertilization can be managed; the amount of available nitrogen determines the number of stems and pods. Although a significant portion of acquired nitrogen –approximately two-thirds– is absorbed and stored in the shoot during the vegetative growth, in the reproductive stage, pods keep contributing to photosynthesis, supporting various metabolic processes, including the absorption and assimilation of nitrogen (Gombert et al., 2010; Guo et al., 2021; Malagoli et al., 2005). The N absorbed after flowering and during the seed filling period which accounts for roughly one-third of the total nitrogen uptake, enriches the plant's available N pool, maintaining overall plant function, and it may be remobilized later in the seeds (Bouchet et al., 2016; He et al., 2021). In canola, a similar pattern is observed, the N uptake is much greater during vegetative growth than between flowering and harvest. After flowering, depending on studies, N absorption either stopped or decreased or continued (Bouchet et al., 2016; Chamorro et al., 2002; Malagoli et al., 2005; Rossato et al., 2001). Further studies with a more extensive dataset on the different organs of winter rapeseed could provide a better insight into these processes (He et al., 2021; Sieling and Kage, 2021).

### 4.3. Perspectives for practical applications of Nc dilution curves and NNI

The use of NNI derived from Nc dilution curves is a common widely used indicator for crop N diagnosis, for determining the crop N status and optimizing nitrogen management (Lemaire et al., 2008). In this study, we define two specific Nc dilution curves to diagnose the nitrogen status of winter oilseed rape according to the growth stage and a unique unifying curve. Our results could be useful to better estimate the nitrogen needs of oilseed rape, and to monitor the nitrogen nutrition throughout the crop cycle, including after flowering. These new Nc dilution curves are interesting for two main reasons: (i) they provide a diagnostic tool to evaluate nitrogen deficiencies during early reproductive stages, which could inform fertilization decisions in response to climatic variability; (ii) they allow for computing the NNI shortly after flowering to support the forecasting of potential yield at the field scale approximately two months before harvest.

The choice between using a single curve or two curves nevertheless needs further investigation. In the present dataset, we carried out an analysis of the differences in classification (N-deficient vs. non-N-deficient) depending on whether the single curve or the two separate curves are used. The result shows that points classified differently represent 33 situations, i.e. 4.06 % of the dataset (see supplementary material S3). The transition between vegetative and reproductive phases could be driven by different biological factors—such as shifts in phenology at flowering, reaching a critical biomass threshold that leads to an increasing proportion of structural tissues diluting the plant N concentration, or changes in the leaf-to-stem ratio throughout development. While a single curve remains a simpler approach, these underlying mechanisms might justify the use of two distinct curves. We tested the data to detect potential biomass threshold breaks, but this analysis did not yield a clear conclusion (see supplementary material S4). Exploring these phenological aspects in future research would provide further insight into whether and when a switch between two separate dilution curves is warranted.
Our findings open up opportunities to develop dynamic approaches to nitrogen fertilization in oilseed rape. Currently, most approaches are based on a predictive N-balance taking into account soil mineral nitrogen concentration (Wehrmann and Scharpf, 1979) or the amount of nitrogen absorbed in the canopy before spring (Hebinger, 2009; Lagarde and Champolivier, 2006; Makowski et al., 2005). Based on a static diagnosis, nitrogen fertilization plans are often predetermined according to the crop's growth stage (Rathke et al., 2006). Fertilization methods recently developed for wheat (Paut et al., 2024; Ravier et al., 2018, 2017b) enable real-time monitoring of the crop's nitrogen nutrition status to manage topdressing N fertilization, which reduces nitrogen losses without compromising yield. The new dilution curves proposed here could lead to the development of dynamic N management methods in oilseed rape during a longer period in spring. Nevertheless, these dynamic methods require an accurate estimation of the NNI throughout the season, either by chlorophyll meters, active crop sensors or vegetation indices (Liu et al., 2020; Ravier et al., 2017b; Xia et al., 2016). Late in-season fertilization also implies the technical feasibility to fertilize during the season, according to weather conditions and crop biomass development.

Finally, critical N dilution curves are often integrated into the most common crop models to estimate N requirements (e.g. Azodyn (Gervois et al., 2015; Jeuffroy et al., 2006); STICS (Brisson et al., 2003); APSIM (Robertson and Lilley, 2016)). Our new Nc curves could be used as input for such crop models which would enable to simulate nitrogen fertilization strategies closely aligned with crop N requirements. However, we acknowledge that accurately integrating these curves into crop models requires further experimental validation, particularly for defining maximum and minimum Nc dilution curves, as the nitrogen dynamics in these models are often oversimplified. Beyond adjusting fertilization strategies, integrating these new Nc curves can enhance some aspects of crop models. For example, while our curve for the vegetative phase aligns with previous work, the reproductive phase remains an area where significant improvements could be achieved. Greater precision in modeling this phase can lead to more accurate forecasts of grain quality and final yields, optimize harvest dates, and reduce post-harvest losses. Nevertheless, further research is necessary to ensure these curves are robust particularly during the reproductive phase. In addition, these improvements could promote more sustainable N resource management by minimizing losses through leaching and volatilization, and reducing the environmental footprint of agricultural practices. Consequently, integrating these Nc curves could not only improve yield predictions but also strengthen the resilience of cropping systems to climate variability and environmental constraints.

## 5. Conclusion

The use of a large dataset including data under contrasting soil and climatic conditions allowed us to determine new critical dilution curves and to extend the range of validity of previously established curves for winter oilseed rape. This confirms the interest of using a larger data set and over a wider vegetative period, incorporating more genotype × environment × management practices interactions have an effect on the parameters of the critical nitrogen dilution curves. This work constitutes a contribution to a better understanding of the effect of nitrogen nutrition on the growth of winter oilseed rape in a European production context. Defining new dilution curves paves the way for potential applications in crop models and the development of more efficient tools for nitrogen management, thereby enhancing nitrogen use efficiency. Additionally, these advancements can promote more sustainable nitrogen resource management by reducing N losses and lowering the environmental impact of fertilization practices. As a result, these Nc curves can improve yield predictions and increase the resilience of cropping systems to climate variability and environmental challenges.

## CRediT authorship contribution statement

**Jeuffroy Marie-Hélène:** Writing – review & editing, Supervision, Methodology. **Richard-Molard Céline:** Writing – review & editing, Supervision, Methodology, Data curation, Conceptualization. **Rayon Baptiste:** Writing – original draft, Formal analysis, Data curation. **Paut Raphaël:** Writing – original draft, Methodology, Data curation, Conceptualization. **Valentin-Morison Muriel:** Writing – review & editing, Methodology, Funding acquisition.

## Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgements

The authors would like to thank L. Champolivier (Terres Inovia), J. M. Allirand (INRAE), A. Butier (INRAE), A. Laperche (INRAE) and C. Bissuel (Institut Agro) for conducting trials and providing part of the data used in this article. The work was founded by the French Program "Investments for the Future" (Rapsodyn project, Grant 11-BTBR-0004).

## Appendix A. Supporting information

Supplementary data associated with this article can be found in the online version at doi:10.1016/j.eja.2025.127642.

## Data availability

Data will be made available on request.

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