The data used for this analysis were obtained from researchers across North America following a preliminary literature survey of peer-reviewed publications that reported N₂O emissions for North America's maize production systems to identify experiments where N uptake was possibly measured along with the reported N₂O emission in the same study. Following this survey, we requested and received from authors plot or replicate-level maize grain yield, total above ground whole-plant N uptake (TNU), and/or grain N uptake (GNU) data that were measured along with the original N₂O data. Altogether, a total of 1,375 plot-level observations (432 mean observations, averaged over replicates) of cumulative seasonal N₂O emission and their corresponding grain yield, GNU, and/or TNU data points derived from various N management systems across North America were received. A close observation of the data showed that 90% of the N₂O data received have been published in 23 peer-reviewed publications (10% unpublished, derived from 2 studies in Indiana). Similarly, 63% of the N uptake data were published either along with their corresponding N₂O data or separately in different journals, while 37% were unpublished. Details on data sources, locations and year of experiments, and N management practices are shown in Supplemental Table S1.

To be included in the final dataset, both N₂O and maize N uptake data must have originated from the same experiment conducted with ≥3 replicates for ≥2 years, and where N₂O emission was measured at least weekly for the greater part of the growing season using standard methods (vented chamber or micrometeorology procedures). However, in one instance N uptake data from one growing season was included in the dataset because the experiment involved multiple N rates and application timings (Venterea and Coulter, 2015). The data was further processed and observations from experiments that did not include control plots i.e., where no N was applied (e.g., Adviento-Borbe et al., 2007) were removed. This was because certain parameters such as fertilizer induced N₂O emission (FIE) and NRE could not be calculated for those experiments or locations. Data from experiments that involved manure applied at a N single rate (4 mean observations; Sistani et al., 2011; Halvorson et al., 2016a,b) were also excluded because they were too small a sample from which to infer N₂O consequences from an N source distinct management option. Similarly, data from Quebec City, Quebec (Gagnon et al., 2011) were removed because the N₂O values from this location were several orders of magnitude greater (mean = 17.7 kg ha⁻¹; range 3.5–39 kg N₂O ha⁻¹) than those from other locations; exploratory analysis showed them to be outliers and these were considered to be unrepresentative of the study area.

Following the above processing, the data was reduced to 379 mean observations derived across N rate, source, timing and placement and their combinations. This final dataset consisted of 94 mean observations that focused exclusively on N application rate derived from 12 side-by-side experiments (≥3 N rates, including controls), 94 mean observations that originated from 8 side-by-side comparisons of N source alone, and the remaining observations consisted of N rate and N source in various combinations with N timing and N placement. Across these N management systems, 163 observations were derived from experiments conducted under irrigated maize (Colorado, Minnesota, and Nebraska) and 216 observations were obtained from rainfed systems. The irrigation systems data from Colorado alone accounted for 80% of the observations for irrigated maize systems. Similarly, 37% of the data originated from experiments where a maize-soybean rotation was applied, and these were predominantly from Indiana and Minnesota.

For studies that reported only grain N uptake, GNU (Zebarth et al., 2008; Roy et al., 2014), total above-ground N uptake (TNU) was estimated by dividing maize grain N by a factor of 0.64 which is considered to be the N harvest index (NHI: total N in the grain as a fraction of TNU; Witt et al., 1999) that has been very stable over time as maize hybrids have changed (Ciampitti and Vyn, 2012; Mueller and Vyn, 2016). Conversely, where only TNU data was available (Venterea et al., 2011; Drury et al., 2012; Omonode et al., 2015; Venterea and Coulter, 2015; Omonode et al., unpublished), GNU was calculated by multiplying TNU by a factor of 0.64. From the available N rate and N uptake data, we calculated NRE, net N balance, NB (in terms of GNU, TNU), and surplus N (SN) as follows:

where TNU is total (grain+biomass) N uptake: TNU_N, is the TNU of N-fertilized plots, TNU₀ is the TNU of unfertilized plots, and Δ_Napplied is the differential of N applied; N_F = applied fertilizer N (kg N ha⁻¹); N_M (kg N ha⁻¹) = recoverable manure N; N_ROT = N (kg N ha⁻¹) attributed to rotation when maize followed a legume as recommended for the state/region (Kentucky, 28; Colorado, 28; Indiana, 50; Nebraska, 50; Minnesota, 30; and Quebec, 30 kg N ha⁻¹). We note here that for site-years where maize followed maize, no N credit was given to the following corn crop. Similarly, no credit was given for soybean nodules and/or N fixation; studies showed that soybean nodules and fixation are not major determinants of the soybean N credit (Bergerou et al., 2004).

Before statistical analysis, the data for management that involved N rate (N rate alone, rate + source, and rate + timing) was further grouped by 50 kg intervals (0, 1–50, 51–100, 101–150, 151–200, 201–250, 251–300; n = 7) to reduce some of the associated variability. For the rate alone data, grouping the data resulted in the following number of observations (n) for the groups: 22, 1, 13, 19, 9, 18, 2 with the following corresponding means: 0, 45, 73, 132, 174, 221, and 270 kg N ha⁻¹, respectively, for the groups.

First, the relationships between N application rate and N uptake, NRE, SN, NNB [NNB_(GNU), NNB_(TNU)] and N₂O were evaluated using single-factor regression models where N rate was considered the independent variable, and dependent variables consisted of N₂O, TNU, GNU, NRE, SN, and NNB. These relationships were assessed using data sets from experiments where management involved only rate of N application with 3 or more N levels, and included a control (zero N). The latter analysis was conducted because contrasting linear and nonlinear relationships are often reported for the relationship between N rate and N₂O, and little is known about the relationship between N rate, TNU and NRE in the context of seasonal N₂O emissions.

The relationships between N₂O (area- and yield-scaled) and N uptake parameters (TNU, NRE, NNB, and SN) in the context of multiple N management practices were also determined using single-factor regression models. In constructing these regression models, N₂O was considered the response variable and TNU, NRE, NNB, and SN constituted the independent variables. All regression analyses utilized the data points averaged over replicates for a given site-year. For analyses that assessed the relationships under N rate management systems, both the individual observations and the grouped N rate data were used in separate regression analyses for comparison. Finally, the relative significance of the contribution of the independent variables to the total variability associated with N₂O was estimated using multiple regression models. All analyses were performed using SAS statistical package (SAS Institute, 2013) by invocating the PROC REG and PROC NLIN statements, respectively, for linear and non-linear regression models. The strengths of the relationships were assessed by the value of the regression coefficient of determination (linear: r²; nonlinear: R²), and the regression model was considered significant at P < 0.05 level probability. Graphs that visualized these relationships were produced using SigmaPlot version 13, from Systat Software, Inc., San Jose, CA (www.systatsoftware.com).

Grouping N rate by 50 kg N intervals significantly improved r² values by up to 60% but did not necessarily improve the statistical significance (P-values) of the relationship. However, for easy comparison, results for the relationships obtained using both the grouped and individual observations data are presented; models using the grouped data are presented in figures, and those derived using the individual observations were presented in tables. Similarly, we present figures for the relationships between N₂O and NNB_(TNU/GNU) and SN for comparison even when the r² and P-values were similar for both parameters in some instances.

Seasonal N₂O, TNU, and NRE varied widely in distribution (data not shown) as would be expected of data aggregated across soil, management, and climate variations. Emission was generally lower for relatively drier Colorado compared to other locations. On average, cumulative N₂O was about 47% (1.67 kg N ha⁻¹) greater for rainfed maize compared to irrigated maize cropping systems (0.89 kg N ha⁻¹), perhaps because the latter was dominated by data from Colorado. Nitrogen recovery efficiency values ranged from 6 to 147%, with a mean of 56%. The NRE values exceeding 100% in the data occurred at lower N rates (<90 kg N) when TNU was significantly greater than N applied (a common response in the Midwestern United States). The average NRE observed here was similar to that reported for Indiana (Burzaco et al., 2014), but was much greater than those reported for on-farm trials (Cassman et al., 2002). Both NNB and SN ranged widely from large negative to positive values, and averaged −19.9 and −35.9 for NNB_(TNU) and SN, respectively; the latter negative values indicated that maize's TNU often exceeded fertilizer N inputs into the system.

The relationships between N application rate, maize yield, N uptake, NRE, NNB, SN, and seasonal N₂O emissions based on the grouped N data are shown in Figure 1 while the relationships derived from the individual observations are shown in Table 1. A strong, non-linear relationship existed between the N rate and maize grain yield (Figure 1A: R² = 0.87; individual observations: r² = 0.71; P < 0.001; Table 1). Grain yield generally followed a quadratic model indicating that yield increased, on average, from about 6,600 kg ha⁻¹ at zero N and plateaued at about 11,390 kg ha⁻¹ at the 225 kg N ha⁻¹ rate, beyond which grain yield was unlikely to respond to any additional increase of N application. Across these North America states or regions under consideration, N rate recommended for agronomic optimum maize yield ranges from about 150 kg N ha⁻¹ for Minnesota to 220 kg N ha⁻¹ for Indiana.

Similarly, strong and highly significant positive relationships existed between TNU and GNU and application rate (Figure 1B; relationships using point observations shown in Table 1). Overall, both linear and nonlinear models were good fits for the relationships between N rate and GNU (linear: r² = 0.99) and TNU (linear: r² = 0.94); GNU and TNU tended to increase linearly as N rate was increased up to about 225 kg N ha⁻¹ (Figure 1B). Net N balance (NNB) in terms of TNU, GNU, and SN also generally increased as rate of N application was increased (Figure 1C). At zero or low N rates, N balance was close to zero (GNU), and negative for TNU and SN, but increased exponentially as N rate was increased above 150–200 kg N, especially for GNU. The rate of increase of N balance due to increase of N rate was in the order NNB_(GNU) > NNB_(TNU) > SN.

The relationships between N rates and NRE as well as seasonal N₂O emission are shown in Figure 1D. The relationship between N rate and N₂O emission appeared to be complex and was best described by a sigmoidal model (R² = 0.96, P = 0.014) whereby the rate of increase of N₂O was relatively small for N rates up 100–130 kg ha⁻¹, followed by a sharp increase at N rates from 130 to 220 kg ha⁻¹, and then leveled off at N rates >220 kg N ha⁻¹. However, both the linear and exponential models were also good fits to the data, albeit with reduced coefficients of determinations (linear: R² = 0.91; P = 0.001; exponential: R² = 0.85; P = 0.003; graphs not shown). Overall, our model suggested that seasonal N₂O emission was likely to increase linearly by about 5 g N per kg of N applied for rates up to 220 kg ha⁻¹ (maize yield tend to plateau at 180–200 kg N ha⁻¹ across North America as indicated in Figure 1A). In contrast, a significant (P < 0.005; R² = 0.96) negative relationship existed between N rate and NRE (Figure 1D). Our model showed that maximum NRE occurred at low N rates of < 60 kg N ha⁻¹, NRE decreased rapidly to about 60% as N rates progressed to 100 kg N ha⁻¹, decreased less rapidly for rates between 130 and 150 kg N ha⁻¹, and subsequently leveled for N rates exceeding 150 kg N ha⁻¹. It is noteworthy that N₂O loss increased rapidly in the 130–200 kg ha⁻¹ N rate range, the same range of N applications at which NRE levels plateaued in these experiments.

We noted that in some locations, NRE exceeded the maximum attainable 100% (especially at lower N rates of 50–90 kg N ha⁻¹) and that these extremes will impact the regression parameters. However, we were not justified in excluding NRE values exceeding 100% as these are typical for highly productive US Corn Belt and Canadian maize producing soils at lower N rates, and are indicative of N sources other than applied fertilizer N becoming more available to the maize plants when low N rates are applied (Abalos et al., 2016). For comparison, elimination of NRE values >100% resulted in the regression model: y = 67.4 − 0.04x (r² = 0.66) which suggested that a NRE of about 64% would be expected at N rates of about 80 kg N ha⁻¹, and that NRE would decrease by about 0.04% for every kg of additional N (data not shown).

We quantified the relative influence of the N management practices on the relationships between N₂O and N uptake parameters using multiple regression models. These models showed that N₂O emission was most associated with these variables when management focused solely on N application rate, but the strength of the relationship progressively decreased in the order: rate > timing > source. When management focused only on N rate, the multiple regression model showed that all the variables associated with N uptake and N balance accounted for 40% of the variability associated with N₂O emissions. However, NNB_(TNU) and NNB_(GNU)alone accounted for 32 and 3%, respectively, of the total variability as represented by the model:

When management focused on N source, NRE was the dominant factor and accounted for 12 of the about 18% variability associated with N₂O emission, but no variable had a dominant influence when management involved N source plus timing and/or placement. Across all management systems, the multiple regression model indicated a rather weak functional linear relationship between these variables and N₂O emissions (r² = 0.046; P = 0.034) which perhaps underscored the effect of variability associated with the dataset. Nevertheless, the step-wise regression model showed that NNB_(GNU) and SN accounted for about 78% of the total variability associated with N₂O as follows:

The strong positive relationship between N application rate and N₂O emissions reported here affirmed the field-level findings of several authors who reported either a strong positive linear relationship between N application rate and N₂O (MacKenzie et al., 1998; Gagnon et al., 2011; Roy et al., 2014), or a non-linear relationship (Breitenbeck and Bremner, 1986; McSwiney and Robertson, 2005), or both, depending on timing (Venterea and Coulter, 2015). Several meta-analyses also found strong positive relationships between N application rate and seasonal N₂O emissions (Eichner, 1990; Van Groenigen et al., 2010; Decock, 2014). However, in this study, the relationship between N₂O and N rate was sigmoidal in nature and N₂O emission tended to rise sharply for N rates of 130–220 kg N ha⁻¹ (Figure 1D) that are recommended for this region, which did not support earlier suggestions by these previous authors that N application at recommended rate was likely to decrease N₂O emissions. Perhaps a reduction of N application rate within the 150–220 kg N ha⁻¹ rate window by an amount that does not significantly reduce yield (Figure 1A), but is enough to increase NRE, is a better option. This study showed that the indirect mechanism underlying such a response is perhaps because NRE tended to be greater at relatively lower N rates.

To the best of our knowledge, very few studies (whether individual experiment or meta-analysis) have reported relationships between seasonal N₂O emission and maize N uptake and N balance; therefore, comparing our results with the existing literature was rather difficult. Overall, the positive relationship between N₂O and N uptake observed here was contrary to the general expectation that an increase of N uptake will result in N₂O emission reduction. However, this positive relationship was similar to several studies where N management practices that achieved the highest recovery of fertilizer N in crop biomass also resulted in the highest N₂O emissions (Fujinuma et al., 2011; Gagnon et al., 2011). Our analysis over a multitude of N rates and environments showed that NRE dramatically decreased as N rate was increased, which conceivably made more N available for denitrification even as TNU increased.

Negative relationships between N₂O and NRE, especially when management involved rate of N application, as also reported by Van Groenigen et al. (2010) in a meta-analysis (even though these authors aggregated NRE, referred to as NUE, across different crop species), affirmed the hypothesis that an increase of NRE would result in a decrease of N₂O emissions. However, the less-than-perfect but significant relationship of N₂O emission to NRE reported for this study was probably because the periods of peak N₂O emission and plant recovery of applied N during the growing season hardly coincided, or because our analysis involved N₂O as the only source of N loss from these systems, or both. For most of North America, about 50–80% of seasonal cumulative N₂O emissions occur in 30–40 days following N application when the maize plant is at around V6 and plant N uptake is still relatively small (Omonode et al., 2011; Halvorson and Del Grosso, 2012). Several studies also found that N₂O accounted for only a small fraction of the total N that are lost from the system following N application; most N losses occurred as ammonia volatilization and/or nitrate leaching which, respectively, accounted for about 10 and 30% of applied N compared to about 3% for N₂O losses (Mosier et al., 1998; De Klein et al., 2006; Venterea et al., 2012). Similarly, the relatively strong positive relationships between N₂O emission and N balance in relation to NNB_(TNU), NNB_(GNU), and SN observed here were consistent with Van Groenigen et al. (2010) and Venterea et al. (2016).

Furthermore, our finding of strong influence of timing (in combination with N rate or source) on the relationships of N₂O to N balance and SN was generally similar to recent reports by Venterea et al. (2016). Our analysis showed that these relationships were stronger, and N₂O emissions greater, under regular sidedress timing compared to preplant/at planting, and for late sidedress relative to regular sidedress. Overall, the rate of N₂O increase per kg of N balance was greatest for SN and smallest for NNB_(GNU), especially for late sidedress application. However, at recommended N rates (150–220 kg ha⁻¹), N balance was several orders of magnitude greater for NNB_(GNU) (70–175 kg ha⁻¹ under N rate, and 50–100 kg ha⁻¹ under rate and timing combination) compared to near 0 kg for SN. Therefore, greater N₂O emission rate for SN relative to NNB_(GNU) was probably because SN from regular or late sidedress N application resulted in a greater short-term availability of N for denitrification, even as crop N uptake rate was expected to be greater at the V14 growth stage (Venterea and Coulter, 2015). However, the magnitude of NNB_(GNU) meant there is great potential for significant amounts of N₂O to be emitted later in the cropping season if available mineral N was not taken up by the maize plant. Studies have shown that grain N uptake was a major parameter that have changed over time (and across hybrids era), and grain N tended to be mostly associated with new plant N uptake during the grain filling period in modern hybrids (Ciampitti and Vyn, 2013). Thus, practices that improve grain N uptake by synchronizing availability with uptake are likely to reduce overall N losses through volatilization or leaching, and ultimately reduce seasonal N₂O emission in maize.

The published experiments from which the dataset used to examine the influence of N source on the relationships between N₂O and the N uptake dynamics showed that ESN, stabilized urea (SUPERU, AgrotainPlus) and nitrapyrin-amended UAN by themselves reduced N₂O emissions, relative to conventional urea and UAN within the location in which they were tested (Halvorson et al., 2010a,b, 2011, 2016a; Venterea et al., 2011; Drury et al., 2012; Omonode and Vyn, 2013; Burzaco et al., 2014; Decock, 2014). Our analysis of variance that used the plot-level observations aggregated over site-years for each of these locations showed that these N sources significantly affected N₂O emissions and fertilizer induced emission factor (FIEF) but had no effect on NRE and NNB_(TNU), regardless of location (Table 5). Overall, N₂O loss was greater for the conventional urea and UAN, and emission was reduced by 19–48% when nitrification and/or urease inhibitors were added to those N sources. Therefore, the rather confounding influence of N source on the relationships between N₂O and NRE, and N balance observed here suggested that N source by itself had little and/or variable effect on NRE and its relationship to N₂O emission. Table 5 showed that NRE and NNB_(TNU) were similar for all the N sources and suggested that some of the N made available from ESN, stabilized urea and nitrapyrin-amended UAN later in the growing season, following initial delay of nitrification of applied N, were probably leached out of the rooting zone and not recovered by maize plants. Therefore, the observed difference of N₂O between ESN, AgrotainPlus and nitrapyrin-amended UAN relative to UAN or urea probably resulted from high emission peaks that usually occur early in the season following fertilizer application at early maize developmental stages (Omonode et al., 2011; Halvorson and Del Grosso, 2012).

Overall, the results from this analysis confirmed that relatively strong functional relationships existed between seasonal N₂O emissions and N rate, N uptake (both GNU and TNU), and NRE (especially when N management involved appropriate timing of application). Clearly, N applications that exceeded recommended agronomic optimum N rates (ranging from about 150 kg in Minnesota to 220 kg N ha⁻¹ in Indiana) may increase TNU, but will result in reduced NRE especially in the US Corn Belt where intrinsic soil N is relatively high. Similarly, our results established that N rate and timing of application were critically important N management combinations that have the potential to influence both TNU and NRE, and their relationships to N₂O emission. Thus, application of the appropriate amount of N at the right time, especially at planting and/or early sidedress timings, was more likely to reduce N₂O emissions relative to split applications involving sidedressing at >V12 maize growth stage. However, given the large inherent variability associated with the dataset due to differences in soil, climatic conditions, and management factors, the actual size of the impact associated with N rate and timing will vary for different agroecological and/or cropping systems. The model would need to be validated to be agroecology-specific.

While N sources by themselves have been shown to result in N₂O emission differences (Halvorson et al., 2010a,b, 2011; Halvorson and Del Grosso, 2012; Burzaco et al., 2014; Vyn et al., 2016), our analyses clearly indicated that N source effect on N₂O emission was not directly related to their effect on NRE. On the contrary, N source tended to confound the N₂O versus NRE relationship; therefore, further research on N source-specific models are needed to better understand the relationship between NRE and N₂O when N management is focused on N source.

Overall, we found the strongest and most consistent relationship between cumulative N₂O and N balance (whether GNU or TNU). This was not entirely surprising because net N balance encompasses N availability in relation to both in-season fertilizer application, and the N that was carried over from the previous crop years due to practices such as rotation, cover crop, or manure application (i.e., the total size of N inputs). Thus, effective management to both improve NRE and reduce N₂O must necessarily involve evaluating and adjusting for the N balance in the cropping system. However, our model suggested that management systems achieving a net N balance of <50–60 kg N ha⁻¹ would both reduce the amount of N applied, and possibly ensure seasonal N₂O would be reduced to a minimum.

We readily acknowledge that some of the results of this study may have been constrained by the structure of the dataset (e.g., limited number of observations for some N management combinations). Similarly, our N balance estimate did not include N derived from atmospheric deposition which can vary significantly with location. However, this analysis showed that a careful selection of integrated N management practices has the potential to maximize NRE and reduce seasonal N₂O emissions. Although the numerical strength of the relationship between cumulative N₂O and either TNU or NRE was relatively small for the N rate and timing combination, the relationship was statistically highly significant, and thus indicated that optimized N application rates and timing (especially at planting or at early sidedress) has the potential to both increase NRE and reduce N₂O loss, regardless of N source. However, to further maximize the beneficial effects of rate-by-timing practices for N₂O emission reductions, closer attention should be paid to the net N balance of the cropping system.

We strongly recommend that future N₂O emissions studies incorporate a systems research approach involving N source, timing and/or placement interactions where crop N uptake and recovery efficiency parameters are also determined. This will enable scientists to better assess and understand the effects of these complex management practices on cereal grain N uptake and NRE and how they relate to N₂O emissions.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The reviewer EAM and handling Editor declared their shared affiliation, and the handling Editor states that the process met the standards of a fair and objective review.