Nitrogen (N) fertilizer is commonly applied to wheat crops (Triticum aestivum L.) during the vegetative growth to meet crop requirements. Current decision rules for N application result in N losses to the environment, and thus to low N use efficiency, due to excess of N fertilizer and/or poor synchrony between soil supply and crop N demand. Despite existing tools and methods to manage N fertilization, combining maximum grain yield, high grain protein content, and minimum N losses to the environment remains challenging. There is thus a need to provide decision rules to apply N fertilizer at the time of optimal weather conditions and high crop N demand, without exceeding N crop requirements, thereby increasing N use efficiency and limiting N losses. Here we developed, for the first time, a modeling approach based on the Azodyn model and using the mathematical framework of the viability theory to build decision rules where 1) N is applied only if weather conditions are optimal and if there is a risk that a period of N deficiency becomes detrimental to grain yield and protein content, and 2) the N rate is the minimum sufficient to prevent from detrimental N deficiencies whilst minimizing N losses to the environment. We computed metric of robustness to build decision rules for timing and rates of N fertilizer in the view to manage crop N nutrition according to such targets. We showed that, comparing those decision rules with current recommendations, by simulations over 20 years, the average total N rate could be decreased by 50 kg N ha⁻¹ and N losses by 42 kg N ha^-1 whilst maintaining similar yield, and reaching grain protein content above 11.5% more often (17 years out of 20, compared to 10 years out of 20 with current recommendations). In respect of those theoretical results, the next step should be to experimentally assess performances in real situations and to assess to which extend the method could help farmers to change their practices.

氮肥通常用于小麦作物（Triticum aestivum L。）在营养生长期间，以满足作物的需求。由于氮肥的过量使用和/或土壤供应与作物氮需求的同步性差，当前氮素施用的决策规则导致氮素对环境的损失，从而导致氮素利用效率低下。尽管已有管理氮肥的工具和方法，将最大的谷物产量，高的谷物蛋白含量和最小的氮素流失相结合仍然具有挑战性。因此，需要提供决策规则，以在最佳天气条件和高作物氮需求时施用氮肥，而又不超过氮作物的需求，从而提高氮的利用效率并限制氮的损失。在这里，我们第一次开发了 一种基于Azodyn模型并使用生存力理论的数学框架建立决策规则的建模方法，其中1）仅当天气条件最佳且存在一段时间的N亏缺对谷物产量有害的风险时才应用N和蛋白质含量，以及2）氮素含量的最低水平足以防止有害的氮素缺乏，同时最大程度地减少对环境的氮素损失。我们计算了稳健性度量标准，以建立氮肥施用时间和施用量的决策规则，以期根据此类目标来管理作物的氮素营养。我们表明，将这些决策规则与当前的建议进行比较，通过20年的模拟，平均总氮含量可以降低50 kg N ha 2）氮素含量的最小值足以防止有害的氮素缺陷，同时最大程度地减少对环境的氮素损失。我们计算了稳健性度量标准，以建立氮肥施用时间和施用量的决策规则，以期根据此类目标来管理作物的氮素营养。我们表明，将这些决策规则与当前的建议进行比较，通过20年的模拟，平均总氮含量可以降低50 kg N ha 2）氮素含量的最小值足以防止有害的氮素缺陷，同时最大程度地减少对环境的氮素损失。我们计算了稳健性度量标准，以建立氮肥施用时间和施用量的决策规则，以期根据此类目标来管理作物的氮素营养。我们表明，将这些决策规则与当前的建议进行比较，通过20年的模拟，平均总氮含量可以降低50 kg N ha^-1和N的损失为42 kg N ha ^-1，同时保持相似的产量，并经常使谷物蛋白含量达到11.5％以上（20年中的17年，而当前建议的20年中的10年）。关于这些理论结果，下一步应该是通过实验评估实际情况下的表现，并评估该方法可以帮助农民改变其做法的范围。