Environmental and societal costs of maize production decrease by addressing the uncertainty in nitrogen rate recommendations

Domain: neuroscience
Published: 2026-02-05
Editorial outcome: minor_revision

Abstract
Excessive crop nitrogen (N) fertilization has negative environmental and social consequences. Using maize grain yield response to nitrogen field trials, we consider the uncertainty surrounding N rate recommendations to demonstrate that fertilizer N rates can be reduced by 12─16% in the US Corn Belt, with negligible risk of maize yield losses. This reduction in N fertilizer applications decrease N2O–N emissions by 10% and N leaching by 13%, leading to a social benefit of 230─$530M, due to enhanced air and water quality. Additional N reductions could benefit ecosystems and human health. However, the high risk of yield loss associated with additional N reductions makes this practice unacceptable for farmers. This emphasizes the need for incentive programs that consider the responsibilities and limitations of all actors along the food supply chain.

Introduction
Maize (Zea mays L.) is inefficient at utilizing nitrogen (N), meaning N fertilizer applied to croplands typically drives water pollution and increases nitrous oxide emissions while failing to fully optimize the targeted crop productivity1. Addressing this challenge is therefore a pressing priority for securing more sustainable agricultural and environmental systems. A thorough assessment of N application rate uncertainty dynamics, in particular, could provide actionable knowledge to meaningfully improve efficiency and mitigate its adverse effects, yet most cropland N application prescriptions fail to do so.

The United States (US) is a global leader in maize production, not only as the largest contributor to the global supply but also as a hub for agricultural innovation. Given this role, how the US manages N fertilizer—critical for both yield and ecological integrity—has global scale implications for the wellbeing of people and nature. The US produces approximately 30% of the global maize crop2, with over 75% of that output coming from the Corn Belt3, a region encompassing parts of Illinois, Indiana, Iowa, Michigan, Minnesota, Missouri, North Dakota, Ohio, Nebraska, and Wisconsin (Fig. 1C).

N fertilizer is a critical input for maize production worldwide. Maize grain yield has steadily increased in the US Corn Belt over the last half of the 20th century4,5, largely due to a combination of plant breeding and changes in crop management practices such as N fertilization and plant density, among other relevant technological advances6,7. The invention of the Haber–Bosch process, which converts atmospheric N into reactive forms of N8, facilitates the use of thousands of tons of manufactured N fertilizer annually for maize production in the US Corn Belt9. Therefore, maize productivity is strongly linked to N fertilization10,11, which, along with other fertilized crops, makes N fertilization key to nourishing the growing human population12. N fertilizer has unwanted impacts for society as well, as N not taken up by crops is vulnerable to oxidation and release into the atmosphere as a potent greenhouse gas nitrous oxide (N2O)13 and as a pollutant in downstream municipal and ecological water supplies14.

Indeed, upwards of 50 to 70 percent of the total N applied as fertilizer is lost through leaching and runoff (largely as nitrate, NO3-) and/or gaseous forms as N2O, NO, N2, and/or NH3 15–17 (Fig. 1A). The loss of N via NO3- to ground and surface waters drives groundwater contamination, eutrophication of aquatic ecosystems and the attendant loss of biodiversity and ecological functioning18,19, and contamination of municipal water supplies. When municipal water supplies are not properly cleaned of excess nitrate, communities experience a host of health challenges, including increased risk of cancer20, birth defects21, and overall mortality20.

Soil bacteria naturally fix dinitrogen gas into ammonium in the soil, where it is vulnerable to oxidation into NO3- and other forms of N. Under low oxygen conditions, NO3- is reduced by different soil bacteria into N2O and other N species. N2O from the soil leaks into the atmosphere, where it acts as a potent greenhouse gas (GHG) and stratospheric ozone-depleting substance22,23. Soil bacteria also release N oxide (NOx) and ammonia (NH3) gases during these processes which contribute to tropospheric ozone, formation of fine particulate matter (PM2.5), and CH4 oxidation24,25. While this cycling of N occurs in all terrestrial systems, the presence of additional N in the soil from fertilizer amendments accelerates the production of these unwanted gases. Additionally, the production of N fertilizer via the Haber–Bosch process is energetically intensive and typically relies on fossil fuel energy26. These undesirable environmental impacts of fertilizer production and use negatively affect human health, crop productivity, food security, and economic prosperity27–29.

Despite the unwanted social and environmental impacts of excess soil N, most crops are in fact N limited due to a mismatch in the timing, location, and type of N vis-a-vis plant needs30. Nitrogen limitations are well documented to decrease crop productivity, and with it, farmer and rural economic wellbeing31. Clarifying the relationship between maize grain yield and N fertilization is essential for improving N management with the goal of minimizing its adverse environmental and social consequences while optimizing yield and farmer economic return32,33. This relationship, along with maize and N fertilizer prices, determines the optimum N input needed to maximize yield (agronomic optimum N rate; AONR) or farmers’ profit (economic optimum N rate; EONR). However, fluctuations in soil moisture, soil N status, and crop growth dynamics drive considerable uncertainty on the determination of the AONR and EONR34–37. This uncertainty in the recommended N application rates can be represented by probability distributions (Fig. 1B). Left unaddressed, this uncertainty can lead to constantly recurring over or under application of N to maize crops, further exacerbating the problem of N inefficiency and its associated ills. In this study, we modeled the relationship between maize grain yield and N fertilizer rate using a quadratic-plateau model, illustrated in Fig. 1B.

Most current fertilization programs recommend a single N rate that maximizes farmers’ profit applied either to the entire field or to sub-regions within it38. However, farmers recognize the uncertainty inherent in those recommendations and typically apply more N than recommended to hedge against yield loss39,40. This practice is an insurance for farmers to make sure they can obtain excellent yields whenever weather and other conditions are favorable, with application N rates resulting in higher levels than those recommended in the US Corn Belt41,42. The uncertainty of N rate recommendations is usually overlooked in studies that evaluate the production, environmental, and social impacts of changes in N management11,43–49. Ignoring uncertainties might lead to inaccurate conclusions about yield losses when the applied N rate is reduced11. Therefore, uncertainties for defining the optimal N input should be accounted for when studying the societal and environmental impacts of this practice. A more holistic and transparent handling of the uncertainty around yield-related metrics of N efficiency resulting from this approach offers actionable insight into making marginal improvements to the N efficiency problem in agriculture.

To demonstrate the need for a more explicit accounting of uncertainty in crop N-efficiency dynamics, we analyzed different cases of N fertilizer reduction in maize across eight US Corn Belt states (Illinois, Indiana, Iowa, Minnesota, Missouri, Nebraska, North Dakota, and Wisconsin) while accounting for the uncertainty around optimal N rates and economically quantifying the savings in environmental costs to society under the most feasible case of N rate reduction (Fig. 1B). Based on the fact that farmers apply N beyond the recommendations, we explored two phases of N reduction.

The probability of losing yield, the expected yield loss, and the environmental and social costs were evaluated (Fig. 1B). In the first phase (Phase I) the reduction goes from the expected value of the AONR (E[AONR]) to the expected value of the EONR (E[EONR]) implying economic gains for farmers and positive environmental impacts (Fig. 1B). This reduction is still conservative since a high proportion of farmers apply more N than the recommended N rate, which is usually above the E[AONR]50–52. In the second phase (Phase II), four cases of N reduction were evaluated based on the quantiles of the probability distribution of the EONR. Thus, in this phase, the N cutback goes from the E[EONR] to some quantile of the EONR distribution so that farmers take the smallest reasonable risk of economic losses (Fig. 1B). Therefore, our analysis covers more than profit-maximizing scenarios, spanning from N rates maximizing grain yield to the probability distribution of optimal N rates that maximize profits. Although the risk of yield and economic losses in this Phase II is very small, farmers have the perception of being “caught short”39. Therefore, in this phase additional incentives will be needed to deal with the way farmers traditionally think50–52. By assuming that farmers apply E[AONR] in Phase I, our analysis remains both realistic and conservative relative to current N application rates50–52.

Results
Fertilizer N rates: point and uncertainty estimations
The quadratic plateau model fitted to the data captured different shapes on the maize grain yield response to N fertilization in the 49 sites analyzed in the database (Fig. S1). Out of these sites, 17 were removed because of poor convergence of the AONR and/or EONR, and/or yield plateau was achieved at a N rate (E[AONR]) greater than the highest rate implemented in the studies (Table S2).

To facilitate the interpretation of the results, we first describe the calculations for point and uncertainty estimations considering a particular site and then summarize the general results across all sites. As an illustrative example, we selected site T18, corresponding to a field experiment conducted in Lewis, Iowa, during the 2015 season. For this site, the estimated E[AONR]—the mean of the posterior probability distribution of the AONR—was 149 kg ha⁻¹ (Fig. S2). The 0.025 and 0.975 quantiles of this posterior distribution, which define the 95% credible interval and thus the uncertainty of the estimate, were 114 and 191 kg ha⁻¹, respectively. The difference between these two quantiles determines the uncertainty of the AONR estimation, which resulted to be 77 kg ha⁻¹, representing ~52% of the E[AONR] (Fig. S2). The same procedure was applied to all sites to estimate both the point values (expected values) and the associated uncertainties of the AONR and EONR.

Across all sites, the E[AONR] ranged from 108 to 291 kg ha−1 with an average of 198 kg ha−1 (Fig. S2). The difference between the 0.025 and 0.975 quantiles (95% credible interval) determine the uncertainty of the AONR estimations. The uncertainty of the AONR had an average of 97 kg ha−1 with a minimum of 54 kg ha−1 and a maximum of 163 kg ha−1 (Fig. S2). Proportional to the E[AONR], the uncertainties on the estimations of the N rates that maximized maize grain yield were between 27 and 87%. The expected value of the N rate that maximizes farmers’ profit, i.e., E[EONR], had a mean of 180 kg ha−1 with a minimum of 101 kg ha−1 and a maximum of 261 kg ha−1 (Fig. S3). The EONR uncertainty was, on average, 46% (range from 26 to 74%), with a minimum of 49 kg ha−1 and a maximum of 138 kg ha−1. These numbers highlighted a substantial uncertainty for the N rate that maximizes grain yield (AONR) and farmers’ profit (EONR) in maize production across different sites of the US Corn Belt region (Figs. S2 and S3).

Feasibility of Nitrogen fertilization reductions
To facilitate interpretation, we first describe the calculations of the expected grain yield loss and its associated probability in Phase I, where the N rate was reduced from E[AONR] to E[EONR]. For each iteration of the Markov Chain Monte Carlo algorithm (Bayesian model fitting), E[AONR] and E[EONR] were estimated, and their corresponding yields were predicted. Because these predictions were functions of random variables (model parameters and optimal N rates), they generated two probability distributions—one for yield at E[AONR] and another for yield at E[EONR]. The difference between these two distributions yielded a third distribution representing yield change, from which we derived the expected yield loss (the mean), its 95% credible interval, and the probability of yield loss. To express yield losses as proportions, the expected yield loss was divided by the expected yield at E[AONR]. Further methodological details are provided in the “Conceptual framework” subsection of the Methods.

As an illustrative example, we visit site T18, a field experiment conducted in Lewis, Iowa, during the 2015 season. For this site, the expected yield loss was –24 kg ha⁻¹, with a 95% credible interval from −159 to 272 kg ha⁻¹ (Fig. S4). The probability of yield loss was 59%, i.e., P(yield at E[AONR] > yield at E[EONR]) = 0.59, and by complement, P(yield at E[EONR] > yield at E[AONR]) = 0.41. The expected yield at E[AONR] was 11,711 kg ha⁻¹, corresponding to a relative yield loss of 0.20% in Phase I (Fig. S4). The same procedure was applied to all sites in both Phases I and II, regarding the changes in optimal N rates according to the studied Phase.

Across all sites, In Phase I, the N reduction was evaluated as the change from the E[AONR] to E[EONR]. In this phase, on average, there was 62% chance of losing between 11 to 68 kg ha−1 of maize grain yield across the evaluated sites (Fig. S4). This reduction was observed with an expected grain yield ranging from 8507 to 16,537 kg ha−1 at E[AONR]. Therefore, in Phase I, there was 53 to 0.71% probability of losing between 0.08 and 0.49% of maize grain yield (Fig. S4). Thus, there were two implications in this phase. First, the N rate was reduced from the expected value of the N rate that maximizes maize grain yield to the expected value of the N rate that maximizes farmers’ profit, meaning that farmers would earn money due to reducing N application. Second, there was a probability smaller than 71% of losing less than 0.49% of yield (economically not relevant), i.e., yield losses in this Phase I were disregarded.

In Phase II, the expected yield losses and their corresponding probabilities increased from case 1 to case 4 (quantiles 0.4 and 0.1 of the EONR distribution, respectively) (Fig. S5). The expected yield loss among the different cases substantially changed depending on the type of maize grain yield response to N fertilization (sites). However, changes in probability among the different scenarios were similar regardless of the site (Fig. S5).

The combination of the probability of losing yield with the expected yield loss can be thought of as the risk taken by farmers when reducing the N rate. In all of the sites, case 2 (quantile 0.3 of the EONR probability distribution) was a low risk or the safest zone since it implied, on average, 74% chances of expected yield loss between 39 to 132 kg ha−1. In case 2, the estimated expected value of yield at E[EONR] had a maximum of 16,708 kg ha−1 and a minimum of 8438 kg ha−1. Therefore, the previously mentioned yield losses (ranging between 39 to 132 kg ha−1) represented grain yield reductions between 0.45 and 1.06% relative to yield at E[EONR]. This means that, under case 2, there was a 70 to 79% probability of losing between 0.45% and 1.06% of grain yield (Fig. S5). These numbers highlighted case 2 as a feasible case for reducing N rates in the US Corn Belt, independently of the maize grain yield response to N fertilization.

Finally, when considering the two phases of N reduction altogether, the N reduction was from E[AONR] to the quantile 0.3 of the EONR distribution (case 2). In the total N cutback from fertilization, there was 71% probability of losing between 64 and 158 kg ha−1 relative to the yield at E[AONR] (Fig. 2). In other words, considering the total N reductions suggested in this study, there was 64 to 79% probability of losing between 0.48 and 1.43% of grain yield (Fig. 2). The probability of yield loss was similar across the evaluated phases and when combining Phases I and II, but there was a little increase in the proportion (and the amount) of expected yield loss. The results shown here depict the absence of (Phase I) or low risk (Phase II) of economic losses and should be considered when dealing with farmers’ perception of being caught short of N when fertilizing maize with this nutrient.

Nitrogen rate reduction: representative scenarios
Considering the uncertainty of the AONR and EONR (Figs. S2 and S3), three sites were selected as representative scenarios of high, medium, and low uncertainty of N rate recommendations for evaluating the environmental and social impact of N fertilization reductions suggested in Phases I and II. The sites “T10” (Troth, Missouri, in 2014 season), “T46” (Kyes, Nebraska, in 2016 season), and “T5” (Loam, Indiana, in 2014 season), were selected and named “Scenario A” (high uncertainty), “Scenario B” (medium uncertainty), and “Scenario C” (low uncertainty), respectively.

The maize grain yield response curves to N fertilization for the three selected scenarios are presented in Fig. 3A. The crop rotations over the previous four years consisted of continuous soybean in Scenario A and maize–soybean rotation in Scenarios B and C. Scenario A represented high uncertainty in the N rate recommendations (163 and 138 kg ha−1 for the AONR and EONR, respectively), Scenario B an average uncertainty (103 kg ha−1 in the AONR and 85 kg ha−1 in the EONR), and Scenario C low uncertainty (56 and 49 kg ha−1 for the AONR and EONR, respectively) (Fig. 3B and Figs. S2 and S3). The range of expected values for the AONR was between 174 kg ha−1 (Scenario C) and 254 kg ha−1 (Scenario A), with a middle value of 205 kg ha−1 (Scenario B). Furthermore, E[EONR] ranged from 161 kg ha−1 to 231 kg ha−1, with a middle value of 182 kg ha−1 for Scenarios C, A, and B, respectively (Figs. 3A and 2B).

In Phase I, the N reduction from E[AONR] to E[EONR] was 19 kg ha−1 in Scenario B, with a maximum of 22 kg ha−1 and a minimum of 14 kg ha−1 in Scenarios A and C, respectively (Fig. 3B, C). Proportional to the E[AONR], these reductions represented 9% (Scenario A) and 8% (Scenarios B and C). In the second phase, the N reduction from E[EONR] to the 0.3 quantile of the EONR had a maximum of 19 kg ha−1, middle of 12 kg ha−1, and a minimum of 7 kg ha−1 observed in Scenarios A, B, and C, respectively (Fig. 3B, C). Proportional to the E[EONR], these N cutbacks constituted 7% (Scenarios A and B), and 4% (Scenario C).

Considering the reductions in Phases I and II, a total N reduction between 21 and 41 kg ha−1 (with middle of 31 kg ha−1) could be achieved (Fig. 3C). That is, it was possible to reduce the N rate between 12 and 16% (Fig. 3C) without (Phase I) or with minor risk (Phase II) of yield losses in the US Corn Belt when uncertainties are properly accounted for defining N input for maize.

As the AONR and EONR uncertainties increased (Fig. 3B), the N reductions in Phases I and II also increased (Fig. 3C). Furthermore, as the expected value of the optimum N rate increased the uncertainty increased (Fig. S6). These results indicate that it should be expected that sites with higher optimum N rates have higher uncertainty and a greater potential to reduce the N fertilization rates with no (Phase I) or small risk (Phase II) of yield losses.

Environmental and social gains
The N fertilization reduction was translated into environmental and social benefits. In Phase I, the NO3-–N leaching was reduced by an average of 1.42 kg ha-1 (Fig. 4A). The maximum NO3-–N leaching reduction was 1.84 kg ha−1 (Scenario A) and the minimum 0.90 kg ha−1 (Scenario C). This represented a cutback of NO3-–N leaching between 10 to 6% with an average of 8% (Fig. 4A). The N fertilization cutbacks found in Phase II reduced the NO3-–N leaching by 0.83 kg ha−1 (0.41 kg ha−1 – 1.38 kg ha−1) (Fig. 4A), representing an additional 5% (3–7%) reduction with respect to the emissions at the E[EONR]. In the case of N2O–N, the reductions in Scenario A, B, C were 0.15 kg ha−1 (7%), 0.13 kg ha−1 (7%), and 0.08 kg ha−1 (5%), respectively in Phase I (Fig. 4A). While in Phase II, the average N2O–N emission reduction was 0.08 kg ha−1, with a minimum of 0.04 kg ha−1 and a maximum of 0.12 kg ha−1 (Fig. 4A). Lastly, the CO2 emissions associated with fertilizer manufacturing and transport were reduced between 37 and 58 kg ha−1 in Phase I, and between 18 and 50 kg ha−1 in Phase II (Fig. 4A).

In summary, overall reductions were up to 17% for the NO3-–N leaching, 13%, for N2O–N emissions, and 16% for the CO2 emissions associated with both Phases with minor impact on crop productivity and economic returns for farmers.

For economically quantifying the social benefits of reducing the N rate in maize, the equivalent CO2 and N leaching reductions were scaled to the maize planted area across the eight US states. Considering a price of 18.54 $/kg N leaching and 50 $/t CO2 (see Methods section), the N fertilization cutbacks resulted in a social benefit between $156M and $298M (average of $234M) in Phase I and between $74M and $231M (average of $148M) in Phase II (Fig. 4B). Therefore, properly accounting for the uncertainty in the N rate recommendations to farmers brought a social benefit of up to $529M with the absence of (Phase I) or low risk (Phase II) of economic losses in the US Corn Belt. This social benefit was likely underestimated since the social benefit of reducing NOx and NH3 emissions was not considered.

Methods
Database description
In this study, we utilized the open dataset from the Performance and Refinement of N Fertilization Tools (PRNT), a public–industry partnership project presented by refs. 78,79.

This database contains 49 site-years combinations of plot research studying the maize grain yield response to N fertilization. The experiments were conducted during the 2014, 2015, and 2016 growing seasons across eight states in the US Corn Belt (Iowa, Illinois, Indiana, Minnesota, Missouri, North Dakota, Nebraska, and Wisconsin) (Fig. 1). Hereafter, the site-year combinations are referred to as “site”. The same experimental protocol was carried out at each site. For this study, we filtered the cases in which the N rates were applied at planting (broadcast to the soil surface). A total of 8 N rates from 0 to 315 kg ha−1 were applied in increments of 45 kg ha−1. A randomized complete block design with four repetitions was implemented in each site. For crop sampling, the maize grain yield (kg ha−1) was obtained in each experimental unit, and it was adjusted at 155 g kg−1 moisture. Furthermore, the grain N content (kg ha−1) was also obtained in each experimental unit by multiplying the grain N concentration and the grain dry matter. At 96% of the sites, a maize–soybean rotation was implemented, while the remaining 4% consisted of continuous maize or soybean.

Soil characteristics and prevailing weather conditions exert a strong influence on maize yield responses to applied nitrogen80. To capture this variability, two contrasting sites were selected within each of eight US states for each of the three study years (2014–2016): one site located on a highly productive soil and a second site characterized by comparatively lower soil productivity. Collectively, these locations spanned a substantial portion of the US Corn Belt and encompassed a broad range of soil types and climatic regimes78. The selected sites were broadly distributed across the three dominant soil orders in the region—Alfisols, Mollisols, and Entisols.

Mean annual precipitation exhibits considerable spatial variability across the study region, increasing by nearly a factor of two from the northwestern to the southeastern areas. In addition to this spatial gradient, precipitation shows a pronounced seasonal pattern, with ~70–80% of total annual rainfall occurring during the spring and summer months of the maize growing season (April–October)78. Mean annual air temperatures also vary substantially across the region, generally increasing along a north–south gradient. As a consequence of this temperature variability, the length of the growing season differs markedly among sites.

To account for site-specific differences in growing season duration, maize hybrids were selected to ensure appropriate comparative relative maturity ratings and other agronomic traits suited to each location. This selection strategy aimed to maximize yield potential while reducing the risk of frost damage at individual sites. The hybrids used in the study ranged in comparative relative maturity rating from 89 to 115 days.

Conceptual framework
The grain yield response to N fertilization curves is affected by crop management, soil, and weather factors. Different curves can be obtained across seasons, even within the same location32. Therefore, the “optimal” N rate has considerable uncertainty34–37. Our uncertainty attributed to estimating the response curve, and consequently on the AONR and EONR, for a specific season in a given site can be represented by the posterior distribution of curves using Bayesian inference. We fitted a quadratic plateau model to the grain yield response to N fertilization via Bayesian inference. Therefore, instead of having a point estimation of the model parameters (with its respective uncertainty on the estimation), we had a probability distribution of the parameters. This allowed us to obtain a probability distribution of the optimum N rates (i.e., AONR and EONR) (Step 1–Fig. 5). In Phase I, the N reduction was from E[AONR] to E[EONR], that is, from the red vertical line to the blue vertical line, as represented by the horizontal black arrow in Step 1–Fig. 5. In Phase II, four cases of N reduction were created based on the EONR distribution. Furthermore, the posterior predictive distribution for grain yield was obtained for each case (Step 1–Fig. 5). These distributions were used to compute the probability of losing yield and the expected yield loss with respect to yield at the E[EONR] in a given curve within a given site (Step 2–Fig. 5).

These steps enabled us to evaluate the feasibility of reducing the recommended N rates considering the AONR and EONR uncertainties, i.e., regarding that at planting it is not known which is the appropriate N rate for a specific season.

Steps 1 and 2 were repeated in each of the studied sites presented in this article. In Phase II, the most feasible case for N reduction across sites was identified based on the probability of losing yield and the expected yield loss. After this, we selected representative sites based on the amount (kg ha−1) and the proportion (%) of N reductions in Phases I and II. In those sites, we translated the N rate reduction into savings in air (NO3-–N leaching) and water (NO3-–N leaching) pollution (Step 3–Fig. 5). Finally, the sustainability of the change in the N fertilization practice was estimated by computing the social benefit (Step 4–Fig. 5).

Statistical analysis
Bayesian inference was used in this study to perform probabilistic inference while accounting for the uncertainty in the parameter estimation, and to easily obtain the uncertainty of model predictions.

A quadratic plateau model (see its shape in Step 1–Fig. 5) was fitted to data for the relationship between maize grain yield (response variable; y) and N rates (predictor variable; x). This model allowed us to analytically obtain the AONR by taking the first derivative of the model, equating it to zero, and solving for x. Then

AONR = β1 / (2β2), (1)

where β1 is the slope of the model, and β2 is the quadratic term. Following a similar procedure, but equating the first derivative of the model to the price ratio (PR), the EONR (Step 1–Fig. 5) can be obtained as

EONR = (β1 - PR) / (2β2) (2)

The PR is calculated as PR = N price ($/kg N) / maize price ($/kg maize), i.e., PR represents the kg of maize needed to pay for 1 kg of N fertilizer. The PR was calculated for each year included in the search. Based on PR mean (5.34 kg maize/kg N) and variance (1.87 kg maize2/kg N2), it was assumed that PR ~ gamma(15.2, 2.8). Where 15.2 and 2.8 are the shape and the rate of the distribution, respectively. That is E[PR] = 15.2/2.8, var(PR) = 15.2/2.8^2. Therefore, the EONR was calculated as the PR was sampled from gamma(15.2, 2.8).

The quadratic plateau model fitted to the grain yield and N rate data in this study was:

yij ~ normal(μij, σε), (3)

μij = β0 + τj + β1xi - β2xi^2, if xi < AONR
μij = β0 + τj + β1AONR - β2AONR^2, o:w: (4)

β0 ~ gamma(αβ0, ββ0), (5)

β1 ~ gamma(αβ1, ββ1), (6)

β2 ~ gamma(αβ2, ββ2), (7)

τj ~ normal(0, σb), (8)

σb ~ uniform(0, 5000), (9)

σε ~ gamma(ασε, βσε), (10)

where yij is the grain yield (kg ha−1) for the ith observation in the jth block, xi is the ith observation of the N rate (predictor variable), μij is the underlying process, β0 (intercept) represents grain yield when no N is applied, β1 (slope) is the parameter modeling the linear response of maize grain yield to N rate, β2 is the parameter modeling the quadratic effect of the N rate on maize grain yield. Finally, τj is the random effect of the jth block on β0, σ2b is the variance of τj, and σ2ε is the variance of maize grain yield. This model was fitted to the data for each of the six sites within the selected states. The Eqs. (5–10) are the prior distribution of the model parameters, which were set so that their influence on the posterior distributions was reduced as much as possible.

The hyperparameters, except those for σ2b in Eq. (9), were obtained by fitting a quadratic plateau model to the data utilized in ref. 34 for maize grain yield versus N rate relationship. The model was fitted to Iowa, Illinois, Indiana, Minnesota, Missouri, North Dakota, Nebraska, and Wisconsin separately. The model was also Bayesian, and the priors were set as wide uniform distributions to reduce their influence on the posterior distribution of the model parameters. The same priors were used in each state. Subsequently, the expected value and the variance of each parameter were obtained from their posterior distributions and utilized to build the hyperparameters for the model fitted in the current study. Therefore, the hyperparameters in Eqs. (5–8) and Eq. (10) changed according to the states and those can be found in Table S1. From Eqs. (1–10), it can be seen that the AONR and EONR are functions of the model parameters (β1 and β2), which are considered as random variables in the Bayesian framework. Therefore, the AONR and EONR are derived quantities and Monte Carlo integration can be used to approximate their probability distributions.

In addition, to estimate the GHG emissions and NO3-–N leaching at different N rates, it was necessary to determine the N exported in maize grains at a given N rate (Step 3–Fig. 5). Therefore, a quadratic or quadratic plateau model was fitted to the relationship between the grain N content (kg ha−1) and N rates in each site. These models can be written as

yij ~ normal(μij, σε), (11)

μij = β0 + τj + β1xi - β2xi^2, (12a)

μij = β0 + τj + β1xi - β2xi^2, if xi < β1/(2β2)
μij = β0 + τj + β1^2/(4β2), o:w: (12b)

β0 ~ uniform(0, 300), (13)

β1 ~ uniform(0, 5), (14)

β2 ~ uniform(0, 2), (15)

τj ~ normal(0, σb), (16)

σb ~ uniform(0, 1000), (17)

σε ~ uniform(0, 1000), (18)

In this case yij is the grain N content (kg ha−1) for the ith observation in the jth block, xi is the ith observation of the N rate (predictor variable), μij is the underlying process, β0 (intercept) represents grain N content without N application, β1 (slope) is the parameter modeling the linear effect of the N rate on grain N content, β2 is the parameter modeling the quadratic effect of the N rate on grain N content. Lastly, τj is the random effect of the jth block on β0, σ2b is the variance of τj, and σ2ε is the variance of grain N content. Equations (13)-(18) are the prior distribution for the model parameters, which were set so that their influence on the posterior distributions was reduced as much as possible.

The plots for the models fitted in Eqs. (3–10) and Eqs. (11–18) are shown in Figs. S1 and S7. The posterior predictive distribution of each model presented in Eqs. (3–10) and Eqs. (11–18) was studied to evaluate model performance (Figs. S8 and S9). The posterior predictive distribution represents the uncertainty in the model parameters and the ability of the model to make accurate predictions of the data82.

The models were fitted to the data to obtain the posterior distributions of the parameters using a Markov Chain Monte Carlo (MCMC) algorithm. Four chains were run in parallel with a total of 60,000 iterations and a warm-up period of 30,000 iterations. After warm-up, 1 in 10 draws was saved (i.e., thinning = 10) to reduce autocorrelation among draws before making inference. The convergence of the models was explored via trace plots and Gelman–Rubin diagnostic83. The models were fitted in R program84 (version 4.3.3), using the rjags package85. The code to fit the models is available at ref. 86. All the data implemented in this study is freely available in different repositories (see Data availability).

Assessing N reduction feasibility
Assuming farmers apply N so that yield is maximized, i.e., AONR41–43, the feasibility of reducing the N fertilization rate in the US Corn Belt was analyzed by a probabilistic assessment of different cases. The uncertainty on the AONR, the EONR, and on maize and fertilizer prices were considered (Step 2–Fig. 5).

After fitting the models to the data, the model parameters, AONR, and EONR (derived quantities) convergence were analyzed. Furthermore, the E[AONR] was obtained and considered as the most likely N rate at which yield was maximized in each site. We assumed convergence when the Gelman–Rubin diagnostic < 1.02. Additionally, if yield plateau was achieved at a N rate (E[AONR]) greater than the highest rate implemented in the studies, the site was not considered as selectable to avoid extrapolating results beyond the range of N rates explored in the studies. These criteria also allowed us to avoid relying on the values of N reduction from the E[AONR] to the E[EONR] in the 49 sites where the yield plateau was reached beyond the tested N rates required extrapolation to estimate the optimal rates, thereby inflating uncertainty and producing unrealistically large N reductions with minimal yield risk. However, a high proportion of such uncertainty would arise from limitations in experimental design or data quality rather than from inherent variability in weather, soil, or crop demand. Similarly, sites with Gelman–Rubin values above 1.02 typically exhibited no response or a linear yield response, indicating model non-convergence and unreliable estimates of optimal N rates. Therefore, these sites were excluded to provide a more conservative and realistic assessment of potential N rate reductions and their associated risk of yield loss.

In the 32 remaining sites, the N rate reduction from the E[AONR] to the E[EONR] were computed. Moreover, to determine the feasibility of further N reductions, the probability distribution of the EONR was considered to represent its uncertainty. Four cases of N reduction were created based on different quantiles of the EONR distributions (Step 1–Fig. 5). For cases 1, 2, 3, and 4, the grain yield posterior predictive distribution at quantiles 0.4, 0.3, 0.2, and 0.1 were obtained, respectively. Since the posterior distribution of the EONR was symmetric in all sites, quantile 0.5 ≈ E[EONR], then an incremental N reduction was considered from case 1 to case 4. Afterward, the posterior predictive distributions at each quantile were implemented to compute the probability of losing yield at each case with respect to yield at the E[EONR] in a given curve within a given site. The most feasible case for N fertilization reduction was defined based on the probability of losing yield and the expected yield loss (Step 2–Fig. 5). After this, three sites (out of the 32) were selected as the most representative based on the amount (kg ha−1) and the proportion (%) of N reduction from E[AONR] to E[EONR] (Phase I) and from E[EONR] to some quantile of the EONR (Phase II) representing the most feasible case of N reduction. The selected sites were referred to as “scenarios” (Scenario A, B, and C).

Environmental and social impact
More efficient N utilization creates multiple material benefits for society. In the US Corn Belt, farmers almost universally hedge their risk by over-applying, which means more efficient utilization is almost invariably achieved via N rate reduction in this region—when the suitable model for the grain yield response to N fertilization has a decreasing slope. The N rate reduction was translated into a social benefit under the “safest” case of N rate reduction in the selected scenarios (Step 4–Fig. 5). For calculating the social benefit (SB), we considered the social cost of N fertilization associated with GHG emissions and water pollution from N loss to ground and surface water. According to ref. 44, the SB was calculated as:

SB ($ ha−1) = GHGΔN2O + GHGΔfert P GHG + ΔN leaching P leaching, (19)

Where GHGΔN2O is the N2O–N emission reduction (kg ha−1), GHGΔfert is the CO2 emission reduction from fertilizer manufacturing (kg ha−1), P GHG is the social cost of GHG emissions ($/t CO2-e), ΔN leaching is the reduction in N leaching, and P leaching is the social cost for N leaching ($/kg N). McLellan et al87 and Eagle et al65 proposed models to estimate N leaching (NO3-–N) and N2O–N emissions in agricultural fields based on the relationship between soil N balance with NO3-–N leaching and with N2O–N emissions (Step 3–Fig. 5). It was assumed that NO3-–N leaching and N2O–N emissions followed gamma distributions with expected value α=β and variance α=β2. The models proposed by refs. 87,65 were implemented to model the expected values as

E[N2O–N] (kg ha−1) = e^(0.339 + 0.0047 N balance), (20)

E[NO3-–N] (kg ha−1) = e^(2.459 + 0.0061 N balance), (21)

where

N Balance (kg ha−1) = total N applied (kg ha−1) - grain N content (kg ha−1) (22)

The total N applied (kg ha−1) is the N from mineral fertilizer and other N inputs such as manure, N-fixing cover crops, irrigation water, etc. Since the other N inputs beyond N from mineral fertilizer were not present in the experiments considered in this study, total N applied = N rate. The grain N content (kg ha−1) is the N removed in maize grains. In this study, the grain N content was obtained from the posterior predictive distribution of the models for grain N content vs N rate evaluated at the E[AONR] and at the N rate for the selected case in each of the three scenarios (i.e., N rate for the 0.3 quantile of the EONR distribution). Then, the N balance, the E[NO3-–N] leaching, and the E[N2O–N] emissions were estimated for the E[AONR] and for the selected case in each of the three scenarios. These estimations were computed for each value in the posterior predictive distribution of the models for grain N content vs N rate.

We conducted a literature review to retrieve information about N2O–N emissions and NO3-–N leaching in the US Corn Belt. The search was conducted through Web of Science®. The 31 of June 2024 was selected as a cut-off date, after which literature searches were no longer conducted. The implemented keywords were: “fertilizer”, “nitrogen” OR “N“, “agriculture”, “nitrous oxide”, “emissions”, “nitrate”, and “leaching”. The selection criteria were: (i) the experiment was conducted in the studied states within the United States of America (Iowa, Illinois, Indiana, Minnesota, Missouri, North Dakota, Nebraska, and Wisconsin); (ii) the experiments were performed in field conditions; (iii) only corn-based systems were considered; (iv) the implemented N rates were between 50 kg N ha-1 and 300 kg N ha−1 because N2O–N emissions and NO3-–N leaching were calculated at the E[AONR], E[EONR], and the 0.3 quantile of the EONR; and (v) manure were not included because of uncertainty and variability in nutrient composition. Out of the retrieved articles, a total of 31 studies were considered to summarize N2O–N emissions and NO3-–N leaching in the US Corn Belt (Table S3).

The variances for NO3-–N leaching and N2O–N emissions in the US Corn Belt were obtained from a literature review (Table S3) and it was assumed fixed over the scenarios. The E[NO3-–N], the var(NO3-–N), the E[N2O–N], and the var(N2O–N) were implemented to calculate the parameters of the gamma distribution as α0 = E[:]^2 / var(:) and β0 = E[:] / var(:). The parameters α0 and β0 were obtained for each of the calculated values of E[NO3-–N] leaching and E[N2O–N] emissions. Then, the uncertainty in NO3-–N leaching and N2O–N emissions was estimated using the gamma distribution with parameters α0 and β0. To estimate the benefit of N2O–N emission reduction (GHGΔN2O), we normalized emissions into CO2 equivalent (CO2-e)88. Furthermore, for the P GHG in Eq. (19), it was assumed a price of 50 $/t CO2-e based on Interagency Working Group’s central estimate89,90. For computing GHGΔfert, we based on the fact that the Haber–Bosch process is the most commonly utilized ammonia production method for N fertilization manufacturing26,64. The fact that the Haber–Bosch process emits 2.16 kg CO2 kg NH3−126 was also considered. Finally, for the P leaching in Eq. (19), it was assumed a price of 18.54 $/kg N91.

For the selected case, the equivalent CO2 reduction, the N leaching reduction, and the SB were obtained in terms of kg ha-1 or $ ha−1 for each scenario were scaled to evaluate potential benefits at the Corn-Belt level. The equivalent CO2 reduction, the N leaching reduction, and the SB were calculated per state by multiplying their values and the area planted with maize for each of the considered states. We took the average maize planted area in the last five years (2019−2023) from the USDA-National Agricultural Statistics Service3. Finally, aggregated estimations for the US Corn Belt were obtained by assuming that the eight states studied followed simultaneously the same maize yield response to N fertilization. This mean that maize planted in the area of the states behaved as each of the selected scenarios simultaneously. This assumption allowed us to provide potential cases of equivalent CO2 reduction, N leaching reduction, and SB in the US Corn-Belt (Step 4–Fig. 5).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "General Comments: This manuscript presents an interesting approach for analyzing existing nitrogen response curves to\nidentify an appropriate nitrogen fertilizer application rate for maize production. The unique aspect of the approach is to\nconsider the uncertainty in the rate recommendations based on the maximum return to nitrogen (MRTN) with\nimplications for yield, as well as environmental and societal costs. While the manuscript\nis well conceived and would be of interest to the\nreadership Nature Communication, there\nare few aspects of the approach that need to be addressed including the crop\nrotations\nthat were evaluated as well as how the uncertainty could take into account response\ncurves that do not fit the\nMRTN approach. Specific comments as well as a number of\ngrammatical suggestions are as follows:\nLine 53: and throughout the manuscript: be consistent with the abbreviation of nitrogen – use N.\nLine 56: delete as (…to the soil in the form…\nLine 63: Start a new paragraph with “Soil bacteria…”\nLines 128-129: revise: … will be needed to deal with the way farmers traditionally think.\nLines 193-201: It is unclear if all these scenarios are continuous corn or some other rotation like corn-soybean. It would be\nuseful to indicate what rotations are being considered.\nLine 241 and throughout the manuscript: Are you expressing leaching load as nitrate or do you really mean nitrate-N. Since\nthis manuscript is looking at N rates it would make more sense to express the amount of nitrate leached as nitrate-N. Same\ncan be said about N2O – are the emissions N2O as N or as simply as N2O gas?\nLine 244: … reduced NO3- leaching by 0.83….\nLine 271: … was not considered.\nLines 279-281: See comments below for methods, but the data set used only considered N responses that fit the MRTN\nmodel i.e. with a plateau. Based on the data used, about 1 in 3 or one third of the sites showed a linear or non-plateau\nresponse and were disregarded. It is understandable why this was done for this study as the true N rate required is not\nknown when a plateau is not attained or it could skew the MRTN to a much higher N rate. More discussion about this\nproblem is warranted as this linear response is a likely reason why growers tend to over apply. While the analysis shows N\nrates can be reduced based on the uncertainty analysis, this is only true when a plateau response is achieved (about 66% of\nthe time). As far as I could tell, the linear response data is not included in the uncertainty analysis.\nLine 326: This may offset potential economic yield loss, but how does the farmer recoup this loss? There is some discussion\nbelow about this, but this statement still needs to be qualified, like through an incentive program.\nLine 367: …providing a significant yield decline….\nLine 370-73: some rewording needed: In our study, we found that reducing the N application rate by 12% to 16% resulted in\n7% to 13% reductions in N2O emissions and 9% to 17% in (cid:1)(cid:2)3− leaching with no or negligible risk (low probability and low\nexpected value) of yield losses when accounting for the uncertainty of the N rate recommendations to farmers.\nLine 400: do you mean the hectares of maize plated relative to hectares of soybeans has been altered? If so how, has it\nbeen altered higher or lower?\nLines 421-422: This is not entirely true. Many states give an “acceptable range”\nLines 447-449 and 459-461: How is previous crop taken into account? Does it matter for this analysis?\nLine 483: was estimated…\nLine 581: Define MCMC and add reference number.\nLines 597-602: See comments above. It is understandable why these sites were not included but these linear or non-plateau\nsites further add to the uncertainty of N rates. This could be addressed in the discussion section.\nLines 619-621: This is only the case when conditions are not conducive for N losses. There is a 1 in 3 chance that a plateau\nis not reached, hence a tendency to over-apply.\nLine 650: The variances for…\nLines 663-665: revising needed: The fact that the Haber-Bosch process emits 2.16 kg CO2 kg NH3-1 26 was also\nconsidered.", "reviewer_3": "The U.S. Corn Belt faces a severe problem of excessive nitrogen fertilizer application. This study quantifies the uncertainty\nembedded in current nitrogen rate recommendations to assess how much fertilizer can be reduced while keeping yield risk\nwithin an “acceptable yield risk” threshold. Results indicate that, by fully accounting for uncertainty, the Corn Belt could\nachieve a 12–16% reduction in N fertilizer application with negligible yield impacts, generating up to $530 million in net\nsocial benefits. The work provides robust, probability-based evidence for designing \"low-risk, high-benefit\" nitrogen-\nmanagement policies.\nOverall, I find the paper innovative and policy-relevant. However, several revisions are necessary to meet publication\nstandards:\n1. The Abstract is structurally incomplete. Please add a concluding sentence that clearly summarizes the policy implications\nor the principal finding's significance for future research.\n2. Reconsider figures selection, arrangement, and formatting, for instance:\nConsider moving Fig. 1 to the Results section, insert sub-panel labels (a, b, c) and revise the title;\nGiven the extensive referencing of Supplementary Figures in the main Results section, consider merging key\nSupplementary Figures into the main text to enhance the clarity.\nLine 267 references \"FIG. 3B,\" yet Figure 3 lacks proper subfigure labels. Please standardize all figure and subfigure\ncaptions across the manuscript (e.g., Figure 2 currently has captions, while others do not).\n3. Several expressions require clarification:\nLines 89-91: “Current fertilization programs, whether variable or non-variable rate, recommend the N rate that maximizes\nfarmers' profit as a single (i.e., exact and unique value) N rate for the entire field or for a sub-region within a field.”\nDoes the subsequent analysis only reference profit-maximizing scenarios? Does the study exclude the goal of production-\nmaximizing recommendations? Clarify whether the two-phase approach (starting with AONR) implies that farmers in the\nstudy area have already adopted NONR?\nLine 265: The rationale for selecting the two specific price points needs justification. Citations might be needed here.\nLine 356-358: The reference to \"Soil organic C\" appears without sufficient preceding or following context. Please add\nbackground or explanation to justify its inclusion at this point in the discussion.\nAdditionally, I would like to know what factors EONR considers. Does it incorporate environmental costs into farmers'\nproduction costs? Please explicitly discuss why the shift from AONR to EONR inherently yields environmental benefits (e.g.,\nis it solely because it represents a reduction in applied N relative to the maximum possible yield?).\nSome detailed suggestions as follows:\nLine 151: This paragraph's formatting differs from others;\nLine 154&156: “therefore” is used twice consecutively;\nLine 330: The abbreviation “SB” is used without prior defination;\nLine 380: Consider adding references;\nLine 403: it should be BMPs;\nLine 626: Does the formula require multiplication symbol?", "reviewer_4": "A major source of nitrogen leaching into surface and ground waters is, in general, agriculture, and maize production is a\nprimary contributor within agriculture. Extensive studies have been conducted to develop nitrogen rate recommendations for\nmaize. These recommendations have been made historically for a state or a region within a state. The advent of precision\nagriculture has enabled recommendations to be implemented at finer spatial scales. However, variability in maize fields,\nweather, management, and other factors make it impossible to publish precise regional or state nitrogen recommendations.\nThe authors consider the uncertainty associated with nitrogen rate recommendations. They suggest an approach to reducing\nthe use of nitrogen with a quantifiable amount of risk in terms of yield loss for the producer and the associated societal\nbenefit. This review focuses on the statistical aspects of the paper.\nThe statistical analysis is creative, strong, and well presented. The following comments focus on helping the reader\nunderstand the results.\nIt would be helpful to present, or at least point to, the form of the quadratic plateau model prior to equation (1). Otherwise,\nreaders, including this one, may spend time wondering why there is no negative sign present in (1), only to learn on the\nfollowing page that the quadratic term in the model has a negative sign.\nAs measures are introduced in the results section, illustrations could improve the readability. Three specific examples are\nprovided, and the authors should consider others:\n1. In the paragraph beginning on line 138, basic measures that are then used throughout the paper are provided. It would be\nhelpful to present, for one field, the estimates of E[AONR] and E[EONR] followed by the computations of the uncertainties,\nboth in terms of N rates and proportions.\n2. In the paragraph beginning on line 151, the processes behind estimating the probability of losing a percentage of grain\nyield need to be better explained, again preferably with an illustration, especially since the related figure is in the\nsupplementary materials.\n3. Beginning on line 170, the case 2 reduction in grain yield was “an expected grain yield of 16,708 kg/ha – 8,438 kg/ha at\nthe expected value of the EONR.” Again, helping the reader understand each of the numbers would be nice. This reader\nassumes that 16,708 kg/ha is the EONR and 8,438 kg/ha is the reduction. If that is not correct, perhaps it will help the\nauthors understand where improvements in clarity can be made. If it is correct, then the authors should realize that this is not\nevident from the presentation.\nThis is excellent work, and the authors are to be commended. Others will benefit more from reading the paper if the authors\nhelp them by providing illustrations (using only a sentence or two in each case) and a few clarifying words. Thank you for the\nopportunity to read the paper."}, "author_response": "Response to reviewers' comments\nReviewer #1 (Remarks to the Author):\nGeneral Comments: This manuscript presents an interesting approach for analyzing\nexisting nitrogen response curves to identify an appropriate nitrogen fertilizer application\nrate for maize production. The unique aspect of the approach is to consider the uncertainty\nin the rate recommendations based on the maximum return to nitrogen (MRTN) with\nimplications for yield, as well as environmental and societal costs. While the manuscript\nis well conceived and would be of interest to the readership Nature Communication, there\nare few aspects of the approach that need to be addressed including the crop rotations\nthat were evaluated as well as how the uncertainty could take into account response\ncurves that do not fit the MRTN approach. Specific comments as well as a number of\ngrammatical suggestions are as follows:\n1) Line 53: and throughout the manuscript: be consistent with the abbreviation of nitrogen\n– use N.\nResponse: Thank you for noticing this, and for providing this suggestion. We have changed the\nword “nitrogen” by “N” in all the document, after defining the meaning of N in line 34. We kept the\nword “nitrogen” in titles and in figure captions (to make figures self-explanatory).\n2) Line 56: delete as (…to the soil in the form…\nResponse (line 59): Thank you. We deleted “…to the soil as in the form …”. We made further\nchanges to improve the grammar of the sentence after erasing that fragment.\n3) Line 63: Start a new paragraph with “Soil bacteria…”\nResponse (line 67): Thank you for this suggestion. This comment was very helpful in improving\nthe reading of the manuscript. We have split the original paragraph starting a new one with “Soil\nbacteria…”.\n1\n4) Lines 128-129: revise: … will be needed to deal with the way farmers traditionally think.\nResponse (lines 138 and 139): Thank you for your recommendation. We have changed the\noriginal sentence. The new version is much clearer, thank you.\n6) Lines 193-201: It is unclear if all these scenarios are continuous corn or some other\nrotation like corn-soybean. It would be useful to indicate what rotations are being\nconsidered.\nResponse (lines 251 and 252): Thank you for noticing this. It will be helpful for readers to have\nthis information when it comes to interpreting the results. There was just one site in entire data\nbase with continuous soybean in the four seasons previous to the analyzed maize experiment.\nThis was Scenario A. Scenarios B and C had corn-soybean rotations. We have added this\ninformation in the main text.\nFor a more complete background, among the 49 site-year combinations in this open database\nused in our study, there was one site (trial 10, in Troth, MO, year 2014) with continuous soybean\nin the four years previous to the corn experiment analyzed in our study. Furthermore, there was\none site (trial 12, in Durbin, ND, year 2014) with continuous corn in the four years previous to the\ncorn experiment analyzed in our study. The rest of the site-year combinations in the database\ncorrespond to corn-soybean rotations in the four previous seasons. This means 96% of the\nanalyzed experiments corresponded to corn-soybean rotations.\n7) Line 241 and throughout the manuscript: Are you expressing leaching load as nitrate or\ndo you really mean nitrate-N. Since this manuscript is looking at N rates it would make\nmore sense to express the amount of nitrate leached as nitrate-N. Same can be said about\nN2O – are the emissions N2O as N or as simply as N2O gas?\nResponse: Thank you for noticing this detail. The equations we have used to estimate nitrogen\nlosses through leaching and nitrous oxide emissions considered nitrogen balance as the predictor\nvariable. The scale of the obtained predictions (response variable), for both leaching and gas\nemission, was in kilograms of nitrogen per hectare (kg N ha-1). Therefore, in all the manuscript we\nexpress leaching load as nitrate-N ( ) and nitrous oxide emissions as . We\n−\nmodified this in the entire article. We replaced by to make it clear that we are\n𝑁𝑂3 −𝑁 𝑁2𝑂−𝑁\n− −\nreferring to nitrogen losses from nitrate when dealing with leaching. We have also replaced N O\n𝑁𝑂3 𝑁𝑂3 −𝑁 2\n2\nby N O–N to clarify that we refer to nitrogen losses from nitrous oxide when dealing with nitrogen\n2\noxide gas emissions.\n8) Line 244: … reduced NO3- leaching by 0.83….\nResponse (line 305): Thank you. We have replaced “in” with “by”.\n9) Line 271: … was not considered.\nResponse (line 333): Thank you for highlighting this grammar error. We changed “were” to “was”.\n10) Lines 279-281: See comments below for methods, but the data set used only\nconsidered N responses that fit the MRTN model i.e. with a plateau. Based on the data\nused, about 1 in 3 or one third of the sites showed a linear or non-plateau response and\nwere disregarded. It is understandable why this was done for this study as the true N rate\nrequired is not known when a plateau is not attained or it could skew the MRTN to a much\nhigher N rate. More discussion about this problem is warranted as this linear response is\na likely reason why growers tend to over apply. While the analysis shows N rates can be\nreduced based on the uncertainty analysis, this is only true when a plateau response is\nachieved (about 66% of the time). As far as I could tell, the linear response data is not\nincluded in the uncertainty analysis.\nResponse (lines 359-366 and 700-708): Thank you for bringing this very interesting point. You are\ncorrect; the flat and linear responses sites were not included in the uncertainty analysis. We have\nacknowledged this by adding two sentences into the manuscript.\nTo complete our response, we did not consider the sites when: (i) the yield plateau was achieved\nat a N rate (E[AONR]) greater than the highest rate implemented in the studies and (ii) the sites\nshowed Gelman-Rubin diagnostic greater than 1.02 for the AONR and/or EONR.\nIf we had considered the sites where the yield plateau was achieved at a N rate (E[AONR]) greater\nthan the highest rate implemented in the studies, then we would have been making an\nextrapolation to find the optimal N rates. This would have led to larger uncertainty estimation on\nthe predicted value of the optimal N rates, and consequently, a larger N reduction would have\n3\nbeen possible with small risk of yield losses. However, this scenario would not represent a case\nin real life, since our inability to find the optimal rates precisely would not be highly related to the\nuncertainty attached to weather, soil, and crop demand variability (which is the real uncertainty),\nbut it would be attached to a poor experimental design (lack of exploring more N rates) or data\nquality. Therefore, we opted for a more conservative approach by removing those sites.\nOn the other hand, as the reviewer mentioned, the sites where the Gelman-Rubin diagnostic was\ngreater than 1.02 for the AONR and/or EONR had either no response (flat horizontal line) or a\nlinear response. To give a better perspective, 11 sites (out of 49 studied, i.e., ~22% of the sites)\nshowed a flat response (North Dakota: T12, T27, T28, T44, T45; Nebraska: T30, T47; Wisconsin:\nT31, T32, T48, T49). On the other hand, 6 sites (out of 49 studied, i.e., ~12% of the sites) showed\na linear response (Illinois: T3; Minnesota: T39; Missouri: T25, T26; Nebraska: T13, T29).\nIn both cases (flat and linear responses), the optimal nitrogen rates could not be determined. This\nmeant that although we were able to compute an expected value and its associated uncertainty,\nwe could not trust those values because the model did not converge for the computation of the\noptimal N rates. Therefore, in those cases, we would have had considerably high under- or over-\nestimations of the expected values of the optimal N rates with high uncertainty, leading (once\nagain) to big, unreal N reduction with small risk of yield losses. However, as the reviewer\nmentioned, these two alternatives do not have the same effect on farmers’ decision making\nprocess. When there is a flat response, farmers, extensionists, and crop advisors recognize that\nthere is no need to apply N. However, in linear responses farmers, extensionists, and crop\nadvisors realized that more N would lead to higher yields, but the appropriate optimal N rate\ncannot be precise and accurately estimated. Therefore, linear responses (~12% of the sites)\nwould increase the uncertainty of N rates leading to overapplications by farmers.\nAs a summary, we have considered these two approaches for not including the sites having these\ncharacteristics to make a more conservative and realistic analysis of potential N fertilizer rate\nreductions and their associated risks of yield loss (probability of losing yield and its expected yield\nloss).\nWe have not explained this clearly and connected the linear and flat responses as reasons behind\npotential increases in the uncertainty of the N rate recommendations leading farmers to overapply\nN fertilizers. Now, in the Methods section under the subtitle “Assessing N reduction feasibility” we\nhave mentioned the reasons explaining why we have removed the sites that were not included in\nthe final analyses of potential N rates reductions and their associated risk of yield loss (lines 700-\n4\n708). Furthermore, in the discussion section (under the subtitle “Uncertainty on the fertilizer N rate\nrecommendations”), we have suggested the linear responses as potential reasons for increasing\nthe uncertainty of N rates leading to overapplications by farmers (lines 359-366).\n11) Line 326: This may offset potential economic yield loss, but how does the farmer\nrecoup this loss? There is some discussion below about this, but this statement still needs\nto be qualified, like through an incentive program.\nResponse (lines 408-410): Thank you for this suggestion. We completely agree with reviewer’s\ncomment; a statement was needed to better preset the idea in that paragraph (lines 410-412).\n12) Line 367: …providing a significant yield decline….\nResponse (line 455): Thank you. We have made that correction.\n13) Line 370-73: some rewording needed: In our study, we found that reducing the N\napplication rate by 12% to 16% resulted in 7% to 13% reductions in N2O emissions and 9%\nto 17% in 3− leaching with no or negligible risk (low probability and low expected value)\nof yield losses when accounting for the uncertainty of the N rate recommendations to\n𝑁𝑂\nfarmers.\nResponse (lines 459-462): Thank you for pointing out these changes for clarity. We have applied\nthe suggested rewriting.\n14) Line 400: do you mean the hectares of maize plated relative to hectares of soybeans\nhas been altered? If so how, has it been altered higher or lower?\nResponse (lines 489-490): Thank you for this comment; that statement needs to be clarified. As\nthe reviewer mentioned, we referred to modifications in the hectares of maize planted relative to\nthe hectares of soybeans. This maize:soybean ratio has decreased, i.e., more farmers decided\nto plant soybean due to a considerable increment in N fertilizer prices. We have clarified that in\nlines 491-492.\n5\n15) Lines 421-422: This is not entirely true. Many states give an “acceptable range”\nResponse (lines 511-513): Thank you for noticing this. The reviewer is completely right; many\nstates following the MRTN approach provide farmers with a range of optimal N rates. However,\nthe limits of the range are arbitrarily defined by considering 1 $/acre below and above the MRTN\nvalue. Therefore, the MRTN is subjectively defining a “most profitable range” within 1 $/acre\nMRTN. In our study, we suggest the use of true (objective) statistical ranges of most probable\nvalues for optimal N rates based on the probability distribution of these quantities. This approach\nenabled us to analyze different cases of N rate reductions and their potential yield losses in a\nprobabilistically way. We have modified the statement to consider the MRTN approach where a\nrange of optimal N rates is subjectively provided based on profits.\n16) Lines 447-449 and 459-461: How is previous crop taken into account? Does it matter\nfor this analysis?\nResponse: Thank you for pointing this out. It is well known that the previous crop can influence\nthe optimum N rate required in a region. However, we hypothesize that the difference in optimal\nN rates between corn and soybean as previous crops is small compared to the overall uncertainty\nin the estimates, making the effect of crop rotation less relevant compared to the level of\nuncertainty to define the optimal N rate for corn. This idea can be roughly seen (though not fully\nstatistically accurate) in the box sizes shown in Baum et al. (2025). Therefore, with all due respect,\nwe believe that considering the crop rotation is not particularly critical for the specific analysis in\nour study. Still, we have added a note about this as a direction for future research in the discussion\nsection (line 521-523). We have also clarified in the methods section that 96% of the studied sites\nare all derived from the same type of crop rotation, corn-soybean rotations (lines 551-553), and\nthus, the potential effect of crop rotation is not a relevant aspect for our analyses.\n17) Line 483: was estimated…\nResponse (line 580): Thank you. We replaced “were” by “was”.\n6\n18) Line 581: Define MCMC and add reference number.\nResponse (line 678): Thank you. We have addressed this comment.\n19) Lines 597-602: See comments above. It is understandable why these sites were not\nincluded but these linear or non-plateau sites further add to the uncertainty of N rates. This\ncould be addressed in the discussion section.\nResponse: Thank you for these comments. We have addressed them and provided a response\nin comment number 10. We appreciate the reviewer bringing this topic, since now an extra source\nof uncertainty potentially explaining N fertilizer overapplications was added in different sections\nof the manuscript.\n20) Lines 619-621: This is only the case when conditions are not conducive for N losses.\nThere is a 1 in 3 chance that a plateau is not reached, hence a tendency to over-apply.\nResponse: Thank you for your comment. The reviewer is completely right. When the grain yield\nresponse to N is accurately described by a model with a decreasing slope (e.g., quadratic-plateau\nfunctions), reduction on the N rate lead to an increase in the secant slope between yield at zero\nN application and yield at a given N rate, i.e., the agronomic use efficiency of the fertilizer.\nTherefore, under these conditions, reducing N rates inherently improves fertilizer use efficiency.\nIn contrast, when the yield response to N is best represented by a model with a constant slope\n(e.g., linear response, which represented 12% of the analyzed sites in our study), reduction on\nthe N rate does not lead to changes in the secant slope between yield at zero N application and\nyield at a given N rate. In such cases, reducing N does not increase fertilizer use efficiency and\nmay considerably increase the risk of yield loss. Consequently, these conditions introduce greater\nuncertainty, which might lead to N overapplications. We illustrated this in the plot below.\nuse efficiency is not universally true, but when the slope of the fitted model is decreasing.\nFurthermore, we have added a paragraph to the discussion section based on this comment (lines\n367-376).\n21) Line 650: The variances for…\nResponse (line 757): Thank you. We have added the letter “s”.\n8\n22) Lines 663-665: revising needed: The fact that the Haber-Bosch process emits 2.16 kg\nCO2 kg NH3-1 26 was also considered.\nResponse (lines 771-772): Thank you. We have moved “was also considered” from the beginning\nto the end of the sentence.\nCo-reviewed\nThe U.S. Corn Belt faces a severe problem of excessive nitrogen fertilizer application. This\nstudy quantifies the uncertainty embedded in current nitrogen rate recommendations to\nassess how much fertilizer can be reduced while keeping yield risk within an “acceptable\nyield risk” threshold. Results indicate that, by fully accounting for uncertainty, the Corn\nBelt could achieve a 12–16% reduction in N fertilizer application with negligible yield\nimpacts, generating up to $530 million in net social benefits. The work provides robust,\nprobability-based evidence for designing \"low-risk, high-benefit\" nitrogen-management\npolicies.\nOverall, I find the paper innovative and policy-relevant. However, several revisions are\nnecessary to meet publication standards:\n1) The Abstract is structurally incomplete. Please add a concluding sentence that clearly\nsummarizes the policy implications or the principal finding's significance for future\nresearch.\nResponse (lines 29-32): Thank you. We have added a sentence summarizing the policy\nimplications of our results and conclusions.\n2) Reconsider figures selection, arrangement, and formatting, for instance:\n2.1) Consider moving Fig. 1 to the Results section, insert sub-panel labels (a, b, c) and\nrevise the title;\nResponse (lines 110-117): Thank you for this comment. We have added sub-panel labels to\nhelp readers focus on the key points mentioned in the main text, and we have changed the\nfigure title. We have also added references to each panel in the main text. Regarding moving\nthe figure to the Results section, with all due respect, the figure is a schematic representation.\nIn other words, it does not present any results from our study, but helps to frame the main issue\nthat the paper is bringing forward. We believe that placing it in the Results section could be\nconfusing for readers, since the figure does not actually contain any study results.\n11\n2.2) Given the extensive referencing of Supplementary Figures in the main Results\nsection, consider merging key Supplementary Figures into the main text to enhance the\nclarity.\nResponse (lines 228-239): Thank you, we have moved supplementary figure 6 to the main text\nto enhance clarity. This is a figure without sub-panels. Therefore, no letters were added for\nreference. Although we would like to move more relevant figures from the supplementary\nmaterials to the main text, we believe this is not possible due to the size of the figures and due\nto the fact that if Fig. S2 is moved then Fig. S3 should be, and if Fig. S4 is moved then Fig. S5\nshould be, because each figure in those pairs are equally important. On the other hand, the\nsupplementary figures 2, 3, 4, and 5 depict the results for all sites analyzed in the study. Three\nsites were selected as representative of the main different scenarios encountered for the entire\ndataset (called Scenarios A, B, and C), and the main findings are based on the representative\nsites. Otherwise, it would be very difficult and unclear to transmit the results and conclusions\nof our study.\nOn the other hand, based on reviewer’s number 4 comments, to ensure clarity and facilitate\nreaders’ interpretation of the results, we have added a paragraph illustrating the calculations\nof the results for one particular field study. These descriptions were added in the subsections\nthat rely the most on supplementary materials, which are “Fertilizer N rates: point and\nuncertainty estimations” and “Feasibility of Nitrogen fertilization reductions” within the Result\nsection.\n2.3) Line 267 references \"FIG. 3B,\" yet Figure 3 lacks proper subfigure labels. Please\nstandardize all figure and subfigure captions across the manuscript (e.g., Figure 2\ncurrently has captions, while others do not).\nResponse: Thank you for this comment. We have made these changes in the figures and in\nthe main text when corresponding.\n3) Several expressions require clarification:\n3.1) Lines 89-91: “Current fertilization programs, whether variable or non-variable rate,\nrecommend the N rate that maximizes farmers' profit as a single (i.e., exact and unique\nvalue) N rate for the entire field or for a sub-region within a field.”\nmake it clearer.\n3.2) Does the subsequent analysis only reference profit-maximizing scenarios? Does\nthe study exclude the goal of production-maximizing recommendations? Clarify\nwhether the two-phase approach (starting with AONR) implies that farmers in the study\narea have already adopted NONR?\nResponse: Thank you for this comment; it helped to clarify some points. In lines 85-87 we\nmentioned that the AONR and EONR are the nitrogen rates maximizing grain yield and\nfarmers’ profit, respectively. Then, in the paragraph starting in line 126, our analysis proposes,\nin Phase I, N reductions going from the expected value of the AONR to the expected value of\nthe EONR. In Phase II, the suggested reductions go from the expected value of the EONR to\nsome quantile of the probability distribution of the EONR (studied by analyzing four cases of N\nreduction). Therefore, our subsequent analysis does not refer only to profit-maximizing\nscenarios, but it starts with grain yield maximization and ends in some value of optimal N rate\nwithin the probability distribution of the rates maximizing farmers’ profit (EONR). We have\nadded a new sentence in lines 134-136 to clarify that our analysis encompasses both, grain\nyield and profits maximizations.\nRegarding whether the two-phase approach (starting with AONR) implies that farmers in the\nstudy area have already adopted AONR; in lines 129-131, we have mentioned that a high\nproportion of farmers apply more N than the recommended N rate, and the actual applied N\nrate is usually above the E[AONR]. This is supported by previous studies mentioned below in\nthis response. Then, as reviewer said, in our analysis we assume (or imply) that farmers have\nalready adopted AONR. Although we are missing the farmers that apply more than the AONR\n(which is a high proportion), assuming they apply AONR is the middle ground in between those\napplying the recommended rates (i.e., EONR) and those applying more than AONR. Therefore,\nassuming farmers apply the expected value of the AONR allowed us to be realistic and\nconservative in our analysis. We have added an extra sentence in lines 139-140 hoping to\nmake this implication/assumption clearer.\nReferences:\ndetriment of the environment? Environ Resource Econ 9, 323–340 (1997).\nHouser, M. Farmer Motivations for Excess Nitrogen Use in the U.S. Corn Belt. Case Studies\nin the Environment 6, 1688823 (2022).\nSellars, S. C., Schnitkey, G. D. & Gentry, L. F. Do Illinois Farmers Follow University-Based\nNitrogen Recommendations? (2020)\n3.3) Line 265: The rationale for selecting the two specific price points needs justification.\nCitations might be needed here.\nResponse: Thank you. We agree with the reviewer about the fact that citations might be\nneeded here. However, line 265 was in the Result section, unless results are blended with\ndiscussion, scientific writing theory does not recommend adding citations in the Result section.\nThis does not mean that the use of these two specific price points does not need to be justified,\nbut the justification and citations are in the Methods section. Since these prices come from\nother studies and we use them to calculate new variables in our study, readers should refer to\nthe Methods section. We cited the studies that justify the use of these prices in the Methods\nsection in lines 767 and 773. We have added clarification in between parentheses to refer\nreaders to the Methods section for more information (line 327).\n3.5) Line 356-358: The reference to \"Soil organic C\" appears without sufficient preceding\nor following context. Please add background or explanation to justify its inclusion at\nthis point in the discussion.\nResponse (lines 439-444): Thank you for catching this. We have added information to clarify\nthat soil organic carbon is connected to capturing carbon from the atmosphere, helping to\nreduce global warming. This is to highlight that we are proposing changes in N fertilization\nmanagement to reduce greenhouse gas emissions without affecting other agriculture-related\nalternatives to reduce greenhouse gases concentrations in the atmosphere. We have added\nbackground and explanation to justify the inclusion of soil organic carbon at that point of the\ndiscussion (lines 439-444).\n14\n3.6) Additionally, I would like to know what factors EONR considers. Does it incorporate\nenvironmental costs into farmers' production costs? Please explicitly discuss why the\nshift from AONR to EONR inherently yields environmental benefits (e.g., is it solely\nbecause it represents a reduction in applied N relative to the maximum possible yield?).\nResponse: Thank you. Regarding the factors EONR considers, we have explained this in the\nMethods section, under the subtitle “Statistical analysis” (lines 602-616). There, it can be seen\nthat the EONR does not consider environmental costs into farmers’ production costs.\nOn the other hand, we have clarified in lines 446-448 within the discussion section that, as you\nsaid, the shift from the E[AONR] to E[EONR] inherently yields environmental benefits just\nbecause it represents a reduction in the N rate relative to that maximizing grain yield.\n4) Some detailed suggestions as follows:\n4.1) Line 151: This paragraph's formatting differs from others;\nResponse (line 191): Thank you. We have corrected the formatting.\n4.2) Line 154&156: “therefore” is used twice consecutively;\nResponse (line 196): Thank you. We have changed the second one by a synonym.\n4.3) Line 330: The abbreviation “SB” is used without prior defination;\nResponse (line 413): Thank you. We have made corresponding corrections.\n4.4) Line 380: Consider adding references;\nResponse (line 469): Thank you. We have added references.\n4.5) Line 403: it should be BMPs;\nResponse (line 493): Thank you. We have added the letter “s”.\n15\n4.6) Line 626: Does the formula require multiplication symbol?\nResponse: Thank you for catching this. In mathematics, there is a method known as “implied\nmultiplication”. According to this method, we can express multiplications without a symbol by\nplacing one number or variable next to parentheses, or by writing variables and numbers next\nto each other. According to this method, for the equation the reviewer mentioned (equation\nnumber 19), there is no need to place a multiplication symbol since we are using general\nvariable notation and parentheses. We have applied the implied multiplication method\nconsistently in all the equations in our manuscript. For example, in equations 20 and 21, no\nmultiplication symbol is needed because we wrote numbers and variables next to each other.\nA major source of nitrogen leaching into surface and ground waters is, in general,\nagriculture, and maize production is a primary contributor within agriculture. Extensive\nstudies have been conducted to develop nitrogen rate recommendations for maize. These\nrecommendations have been made historically for a state or a region within a state. The\nadvent of precision agriculture has enabled recommendations to be implemented at finer\nspatial scales. However, variability in maize fields, weather, management, and other factors\nmake it impossible to publish precise regional or state nitrogen recommendations. The\nauthors consider the uncertainty associated with nitrogen rate recommendations. They\nsuggest an approach to reducing the use of nitrogen with a quantifiable amount of risk in\nterms of yield loss for the producer and the associated societal benefit. This review\nfocuses on the statistical aspects of the paper.\nThe statistical analysis is creative, strong, and well presented. The following comments\nfocus on helping the reader understand the results.\n1) It would be helpful to present, or at least point to, the form of the quadratic plateau model\nprior to equation (1). Otherwise, readers, including this one, may spend time wondering\nwhy there is no negative sign present in (1), only to learn on the following page that the\nquadratic term in the model has a negative sign.\nResponse: Thank you for catching this detail. The reviewer is completely right, as the quadratic\n(or quadratic plateau) model is usually written, the first derivative of the model with respect to is\n𝑥\n𝛽m1a+xim2𝛽u2m𝑥 (or minimum), we end up with . However, c𝑥onsidering previous knowledge on\n𝛽1\nthis area of study, we wrote the model suc𝑥h= th a−2t 𝛽w2e obtain a flat line or a concave downward line.\nThis means that the parameter can be very close to zero or negative. Therefore, by adding this\nrestriction to the mod𝛽e2l, the maximum is achieved at instead of a maximum or a minimum\n𝛽1\nat . However, as the reviewer mentioned,𝑥 th=e 2r𝛽e2striction imposed over the model is\n𝛽1\npre𝑥se=n te−d2𝛽 b2elow the AONR and EONR equations.\nin the Introduction section (i.e., before equation 1), this is in lines 92-93. In the Methods section,\nwe have added reference to the Step 1 in Fig 5, where the shape of the quadratic plateau model\ncan be seen (line 597). We have also added the minus symbol in the calculations of the AONR\nand EONR, since these would be the result when expressing the model without restrictions (lines\n601 and 605). Then, when readers see the restriction imposed in the model will automatically\nknow that is negative, so the final version of equations 1 and 2 would be and\n𝛽1\n𝛽2 . 𝐴𝑂𝑁𝑅 = 2𝛽2\n𝛽1−𝑃𝑅\n𝐸𝑂𝑁𝑅 = 2𝛽2\n2) As measures are introduced in the results section, illustrations could improve the\nreadability. Three specific examples are provided, and the authors should consider others:\n2.1) In the paragraph beginning on line 138, basic measures that are then used\nthroughout the paper are provided. It would be helpful to present, for one field, the\nestimates of E[AONR] and E[EONR] followed by the computations of the uncertainties,\nboth in terms of N rates and proportions.\nResponse (lines 149-159): Thank you for this comment. We appreciate it because the changes\nwill facilitate readers’ interpretation of the results. We have added a paragraph illustrating the\ncalculations for one particular field study.\n2.2) In the paragraph beginning on line 151, the processes behind estimating the\nprobability of losing a percentage of grain yield need to be better explained, again\npreferably with an illustration, especially since the related figure is in the supplementary\nmaterials.\nResponse (lines 173-190): Thank you for this suggestion. We believe the interpretation of the\nresults should improve after adding this illustration. We really appreciate reviewer’s comment.\n18\n2.3) Beginning on line 170, the case 2 reduction in grain yield was “an expected grain\nyield of 16,708 kg/ha – 8,438 kg/ha at the expected value of the EONR.” Again, helping\nthe reader understand each of the numbers would be nice. This reader assumes that\n16,708 kg/ha is the EONR and 8,438 kg/ha is the reduction. If that is not correct, perhaps\nit will help the authors understand where improvements in clarity can be made. If it is\ncorrect, then the authors should realize that this is not evident from the presentation.\nResponse (lines 209-214): Thank you once again for helping us to facilitate the interpretation\nof the results of this study. We have clarified this by rewriting the fraction of the text the reviewer\nhighlighted. The changes can be seen in lines 209-214.\nWe did consider other sections of the results where illustrations or rewriting could improve the\nreadability. In connection with reviewer 2, for improving the interpretation and readability of the\n“Feasibility of Nitrogen fertilization reductions” sections within the Results, we have moved Fig\nS6 to the main text. Furthermore, we have carefully read the results section looking for more\nsections where illustrations or rewriting could improve readability. However, based on\nreviewer’s 3 suggestions, we found a cascade effect in the sense that the changes made for\nillustrating calculations automatically facilitated the interpretation of the rest of the results.\nTherefore, we greatly appreciate the recommendations of illustrating calculations and pick one\nsite for showing them.\nThis is excellent work, and the authors are to be commended. Others will benefit more\nfrom reading the paper if the authors help them by providing illustrations (using only a\nsentence or two in each case) and a few clarifying words. Thank you for the opportunity to\nread the paper.\nResponse: Thank you. We honestly appreciate reviewer’s comments; they helped to facilitate the\ninterpretation of the results in our study and to provide a better understanding of the statistics\nimplemented.\nwork. Looking forward to a positive outcome.\nBest regards,\nAuthors.\n20"}, {"round": 2, "reviewer_comments": {"reviewer_1": "I read through the rebuttal and the revised manuscript and the authors addressed my comments thoughtfully and thoroughly.\nThey should be commended for a job well done. In my opinion, the revised manuscript now is acceptable for publication.", "reviewer_3": "The authors have done an excellent job of addressing our previous questions. After reviewing the refined manuscript,\nwe have some remaining minor comments.\nLine 30: Does “their” refer to the “Additional N reduction”?\nThe statement that the practice leads to a “high” risk of yield loss seems to contradict the expression that the proposed\nreduction is possible “with negligible risk of maize yield losses.” The authors should clarify the source and extent of this\n\"high\" risk.\nThe term “unsustainable” might be less precise than \"unacceptable\" in describing the induced farmer behavior.\nPlease consider rewriting the sentence, perhaps as: “the potential risk of yield loss makes this practice unacceptable for\nfarmers”.\nLine 260: The subtitle formatting for Figure 3 appears to be different from the others.", "reviewer_4": "The authors have carefully considered each comment on the initial review of the paper. This revision is more readable and\nprovides increased clarity to the methods as well as the strengths and weaknesses of the work.\nThank you for the opportunity to read your work."}, "author_response": "Response to reviewers' comments\nReviewer #1 (Remarks to the Author):\nI read through the rebuttal and the revised manuscript and the authors addressed my\ncomments thoughtfully and thoroughly. They should be commended for a job well done.\nIn my opinion, the revised manuscript now is acceptable for publication.\nResponse: Thank you. We appreciate reviewer’s time devoted to reviewing our research article.\nTheir comments have been really helpful to improve the quality of the manuscript.\nReviewer #2 (Remarks to the Author):\nCo-reviewed\nReviewer #3 (Remarks to the Author):\nThe authors have done an excellent job of addressing our previous questions. After\nreviewing the refined manuscript, we have some remaining minor comments.\nResponse: Thank you. We appreciate the reviewer’s time and helpful comments, which have\nimproved our manuscript.\nLine 30: Does “their” refer to the “Additional N reduction”?\nResponse (lines 30-31): Thank you for noticing. Yes, “their” refers to the “additional N reductions”.\nWe have clarified this by replacing “their” by “the high risk of yield loss associated with additional\nN reductions makes this practice unsustainable for farmers”.\nThe statement that the practice leads to a “high” risk of yield loss seems to contradict the\nexpression that the proposed reduction is possible “with negligible risk of maize yield\nlosses.” The authors should clarify the source and extent of this \"high\" risk.\nResponse (lines 30-31): Thank you. The reviewer is right. However, with the modification we made\nbased on the previous comment, now it is clear that the high risk is associated with additional N\nreductions beyond the ones proposed in this study. That is, the ones proposed in this study have\nlow risk, but the additional ones have high risk.\nThe term “unsustainable” might be less precise than \"unacceptable\" in describing the\ninduced farmer behavior.\nPlease consider rewriting the sentence, perhaps as: “the potential risk of yield loss makes\nthis practice unacceptable for farmers”.\nResponse (line 32): Thank you. We have replaced the word “unsustainable” by “unacceptable”.\nLine 260: The subtitle formatting for Figure 3 appears to be different from the others.\nResponse: Thank you. We have checked this. The formatting was the same as the others.\nReviewer #4 (Remarks to the Author):\nThe authors have carefully considered each comment on the initial review of the paper.\nThis revision is more readable and provides increased clarity to the methods as well as\nthe strengths and weaknesses of the work.\nThank you for the opportunity to read your work.\nResponse: Thank you. Reviewer’s comments have been really helpful to improve the quality of\nthe manuscript. We appreciate reviewer’s time devoted to reviewing our research article."}]

Decision letter