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                <term xml:lang="en">Crop model</term>
                <term xml:lang="en">Robustness</term>
                <term xml:lang="en">N losses</term>
                <term xml:lang="en">Weather uncertainty</term>
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              <p>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.</p>
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