Establishing long-term nitrogen response of global cereals to assess sustainable fertilizer rates

The study addresses how cereal yields respond to nitrogen (N) fertilizer over the long term and how this can guide sustainable fertilizer rates that balance food production with environmental protection. The context is that anthropogenic reactive nitrogen inputs now exceed planetary boundaries, with agriculture being the dominant source of ammonia, nitrate, and nitrous oxide pollution, imposing high environmental and health costs. The nitrogen response curve underpins agronomic efficiency (AE), nitrogen surplus, and nitrogen use efficiency (NUE), informing farmer decisions and policy. However, short-term experiments (STEs) often fail to capture steady-state soil N dynamics, risking soil N depletion or pollution when extrapolated. Long-term experiments (LTEs) are needed to quantify responses where soil N pools, inputs, losses, and yields approach steady state, yet LTEs are scarce in many regions. The paper proposes and tests a generic long-term nitrogen response function for major cereals (wheat, maize, barley), and integrates it into an economic framework to derive farming and societal optimal N rates and a safe operating space across regions and income levels.

The paper builds on literature highlighting the doubling of reactive N from human activities and transgression of planetary N boundaries, and the dominance of agricultural N pollutants affecting ecosystems, health, and climate. Prior work emphasizes the role of nitrogen response curves in determining AE and NUE, and the need for LTEs to capture steady-state soil N processes, which can take decades to establish. Classical agronomic principles such as the law of diminishing returns, Liebscher’s law (efficiency of a limiting factor increases as other factors improve), and Mitscherlich’s formulation are referenced to interpret response behavior. Previous LTE syntheses in Europe and elsewhere demonstrate the impacts of fertilizer regimes on soil C and N balances, but a globally applicable, scaled LT N response across cereals has been lacking. Economic studies show that societally optimal N rates are often lower than private profit optima due to unpriced externalities, motivating integration of biophysical response with damage cost valuation.

• Data and sites: Compiled 25 long-term field experiments (LTEs) for wheat, maize, and barley across Europe, North America, and Asia, spanning diverse soils, climates, and management, with N rates from 0 to 300 kg N ha−1 and yields from ~2.8 to 12.8 t ha−1. The Broadbalk LTE (UK; 1985–2018 subset) was used to conceptualize LT versus ST responses and to develop the scaling procedure. Trials with implausibly high soil N supply (SN > 100 kg N ha−1) were excluded.
• Conceptual contrast of ST vs LT: Compared first-year (ST) N response from UK commercial trials to LT response from Broadbalk to illustrate that ST responses shift over time towards the LT curve as soil N accumulates or depletes depending on historic vs current N rates.
• Scaling procedure: For each site-year:
  1. Normalize yield by that year’s maximum attainable yield (Ymax) to obtain relative yield Yr = Y/Ymax.
  2. Convert fertilizer N rate to total available N (Nav) by adding estimated non-fertilizer soil N supply (SN), including deposition (DEP), biological N fixation (BNF), and net mineralization. SN was estimated as the x-intercept of a second-order polynomial fit to the unscaled yield vs fertilizer N data for that year.
  3. Pool scaled observations and fit a second-order polynomial with zero intercept: Yr = a·Nav + b·Nav^2.
• Model fitting and validation: • Broadbalk wheat in rotation: Yr = −1.354×10−5·Nav^2 + 7.291×10−3·Nav (R2 = 0.954). Mean SN ≈ 30 kg N ha−1 (range 4–64); no time trend; consistent with DEP ~20 and BNF ~10 kg N ha−1. • Broadbalk continuous wheat yielded a near-identical quadratic (R2 = 0.903). • Nebraska maize LTE: similar quadratic (R2 = 0.934), with ~11% higher Yr at a given Nav than wheat. • Global pooled cereals (25 LTEs: wheat, maize, barley): Yr = −1.870×10−5·Nav^2 + 8.768×10−3·Nav (R2 = 0.818); max SN = 88 kg N ha−1. • Leave-one-site-out back-calculation of unscaled yields showed high agreement (correlation 0.945; RMSE 0.52 t ha−1). • National-scale comparison: Modeled yield responses matched European national data for rain-fed cereals reasonably well (R2 up to 0.796). In SSA, comparisons with Global Yield Gap Atlas-based N requirements showed a moderate fit (R2 = 0.671).
• Agronomic efficiency (AE) model: From the 25 LTEs, AE at each N rate was modeled as a linear function of Y0, Ymax, Nrate, and interactions: AE = 4.62 − 8.37·Y0 + 9.84·Ymax − 0.0365·Nrate + 0.0172·Y0·Nrate − 0.0223·Ymax·Nrate (R2 = 0.924; N = 94).
• Economic analysis: Defined net benefit B = Y·Pc − (Nrate·PN) − Cfixed − CNpollut. Derived economic optimal N rate for farming (EONR) by setting marginal revenue equal to marginal fertilizer cost using the LT response. Derived societal optimal N rate (SONR) by also accounting for marginal external damage cost of N surplus (approximated via surplus = Nav − N removal; N% in grain modeled from Broadbalk data). Damage costs scaled with GDP using UC = 0.3412·GDP^1.0362. Explored Pc at farm-gate and at a higher ‘food plate’ value (ratio 3). Mapped safe operating space as ranges where net benefits for farming and society are robust.
• Sensitivity and uncertainty: Assessed sensitivity of EONR/SONR to curve shape, prices, Ymax, and GDP; quantified uncertainties (e.g., SONR uncertainty ~6–8%, yield ~1–2%).

• A generic long-term (LT) scaled nitrogen response for global cereals (wheat, maize, barley) was established: Yr = −1.870×10−5·Nav^2 + 8.768×10−3·Nav (R2 = 0.818), closely matching Broadbalk wheat: Yr = −1.354×10−5·Nav^2 + 7.291×10−3·Nav (R2 = 0.954).
• The nitrogen input required to reach Ymax (Nmax) is largely independent of Ymax (Mitscherlich-like property). For equation (1) Nmax ≈ 234 kg N ha−1; across 25 LTEs mean Nmax ≈ 217 kg N ha−1 (s.d. 41; range 143–307) and uncorrelated with Ymax (R2 = 0.055).
• Soil N supply (SN) values consistent with deposition and modest BNF: Broadbalk mean SN ≈ 30 kg N ha−1; pooled LTEs max SN = 88 kg N ha−1.
• Long-term agronomic efficiency (AE) increases with Ymax and declines with higher Nrate; AE was accurately predicted by AE = 4.62 − 8.37·Y0 + 9.84·Ymax − 0.0365·Nrate + 0.0172·Y0·Nrate − 0.0223·Ymax·Nrate (R2 = 0.924).
• Validation: Leave-one-out back-calculation of unscaled yields achieved correlation 0.945 with RMSE 0.52 t ha−1, indicating strong generality of the LT curve across environments.
• Short-term (ST) responses differ markedly from LT; relying on ST curves risks soil N depletion (when lowering N) or pollution (when increasing N) because soils are not at steady state.
• Economic outcomes: Including external costs substantially lowers optimal N rates. For UK/Netherlands wheat case, moving from ST to LT curves reduced EONR from 219 to 157 kg N ha−1, and adding external costs further to 90 kg N ha−1 (~40% reduction vs LT farm optimum). Globally, at Ymax = 6 t ha−1: farm optimum ≈ 207–209 kg N ha−1; societal optimum ranges from ~88 kg N ha−1 (GDP US$50k) to ~197 kg N ha−1 (GDP US$2k).
• Safe operating space: LT sustainable N inputs generally 150–200 kg N ha−1; the robust range narrows with higher Ymax and lower GDP; higher GDP widens the gap between farm and societal optima due to greater willingness to pay to avoid pollution.
• Environmental thresholds (Broadbalk): Nitrogen surpluses and nitrate leaching risk begin around Nav ≈ 180 kg N ha−1 (≈ 150 kg fertilizer N ha−1 in Broadbalk conditions). Mean NUE rose to ~80% at Nav ~150 kg N ha−1, then declined to ~60% at higher Nav.
• Regional implications: In high-income settings (e.g., Netherlands, France), current N rates near 150–200 kg N ha−1 overlap with safe space but exceed SONR by ~15–30 kg N ha−1. In lower-income regions (e.g., Romania, India, Kenya), current rates are below EONR/SONR, indicating potential benefits from higher N to raise yields and replenish soils.
• Lowland rice exception: Preliminary evidence suggests much weaker N response due to higher non-symbiotic BNF, ammonia volatilization from urea, and denitrification under flooded conditions; generic cereal curve may not apply.
• Global production implication: Applying the LT curve reduces estimated global maize yield by ~120 Mt (20%) for the same fertilizer use compared to ST-based estimates, implying ~6 Mt N (40%) more fertilizer would be needed to reach a given target yield sustainably; current production likely draws on unsustainable soil N depletion.

The findings demonstrate a robust, scalable long-term relationship between relative cereal yield and total available nitrogen that holds across major cereals and diverse environments. A key implication is that the absolute N required to achieve a given fraction of Ymax is largely independent of Ymax, consistent with classical response theory, and that AE/NUE improve as Ymax increases, reflecting better synchronization of N supply and crop demand. Using LT response functions avoids the biases inherent to ST trials where soil N pools are not at steady state. Incorporating external costs in optimization shifts recommendations toward lower N in high-GDP regions, aligning farmer practices with societal welfare. The safe operating space concept provides policy-relevant ranges of N rates that sustain high yields and minimize pollution, highlighting that in high-input, high-income systems modest N reductions can yield substantial societal benefits, whereas in low-input systems increasing N can improve yields and soil fertility with limited external costs. The exception of lowland rice underscores the need for crop- and system-specific LT curves. Overall, the results support transitioning fertilizer policies and advisory systems to LT-based response functions and to pricing or regulating N externalities to achieve sustainable intensification and equitable global distribution of cereal production.

This study establishes a generic long-term nitrogen response function for global cereals (wheat, maize, barley) and an accompanying agronomic efficiency model, derived from 25 LTEs across three continents. The LT curve reveals that the N required to attain a given fraction of Ymax is largely constant across yield potentials, and that AE/NUE improve with higher Ymax. Integrating this biophysical response with GDP-scaled external damage costs yields societal-optimal N rates that are often well below farm-profit optima in high-income regions, while indicating the need for higher N in many low-income regions to raise yields and rebuild soil N. The safe operating space framework identifies robust ranges of N rates balancing yields, farm profits, and environmental costs. Policymaking based on LT responses and explicit externalities can reduce pollution, reallocate fertilizer use globally, and guide sustainable cereal production. Future work should: (1) expand LTE datasets, especially in Africa, Latin America, and for lowland rice; (2) improve regional estimates of SN and Ymax; (3) include manure and diverse fertilizer products with quantified long-term equivalence; (4) incorporate LT response functions and external cost accounting into economic equilibrium models; and (5) evaluate complementary measures (precision N timing/placement, enhanced-efficiency fertilizers, dietary shifts, and food waste reduction) to meet food and environmental goals.

• Geographic and system coverage: LTEs are scarce in Africa and Latin America; pooled results may underrepresent these regions. Lowland rice shows divergent N response.
• Management scope: Trials largely exclude manure; long-term fertilizer equivalence and volatilization dynamics may differ with organic inputs and urea dominance in some regions.
• Steady-state assumption: Although LTEs aim for near steady state, sites with high SN were excluded; remaining sites may vary in proximity to equilibrium.
• Economic simplifications: Welfare analysis uses a ceteris paribus approach without market feedbacks; assumes GDP-based scaling of damage costs; valuation of externalities is uncertain, especially in low-income countries.
• Parameter uncertainties: EONR/SONR sensitive to response curve shape and Ymax estimates; national data in developing regions may be limited or unreliable.
• Limited crop quality metrics: Grain N% model derived from Broadbalk may not generalize perfectly to all environments and cereals.