Introduction

Increasing soil carbon sequestration is a top priority for mitigating climate change1. The largest carbon input to cultivated soils comes from crop residue, the biomass remaining in the field after grain harvest2. Historically, crop yields have been increasing, especially in the US Corn Belt3,4. Residue carbon inputs have been historically increasing2, but a comprehensive evaluation of residue carbon inputs across temporal and spatial scales is missing, limiting our ability to estimate carbon budgets and credits at scale.

Residue carbon input can be estimated using grain yield data and the harvest index (HI), the ratio of grain yield to the above-ground biomass5. This approach is promising because in the US Midwest, historical grain yield data at scale are readily available6 and currently can be estimated at even higher spatial resolution from satellite imagery7. Accurate estimation of HI at scale is a key to this approach. Recent studies have provided new information on HI, which could be synthesized across temporal and spatial scales8,9,10,11.

The quality of the residue, represented by its chemical composition, is equally important for soil carbon sequestration12,13,14. The quality of the residue carbon is typically assessed with the carbon-to-nitrogen (CN) ratio. Maize, a C4 species, is known for having a higher residue CN ratio than legume crops15. Maize residue CN ratio can substantially vary from field to field and year to year (range 40–136) due to different management practices, environmental conditions, and genetics10,16,17. Yet, whether the CN ratio has changed over the years and across regions in the US Corn Belt remains unknown.

Management of residue in the field, such as tillage, influences residue decomposition patterns and residue carbon stabilization in soils. The US Corn Belt has an increasing trend towards low tillage systems as a solution to climate change18,19. Low tillage practices maintain the soil surface covered longer, prevent soil erosion, and alter soil carbon-nitrogen-water processes20. However, large amounts of residue could constrain the adoption of low tillage practices, especially in cool, humid regions and in fine-textured soils21,22, because large surface residue amounts prevent soils from warming up and drying adequately, resulting in planting delays and hence grain yield loss23. Other interventions to manage residue in the field include residue decomposition promoters and partial residue harvest. Residue decomposition promoters (e.g., residue chopping, biological products, nitrogen fertilizer applications) have been shown to have a limited effect in the US Corn Belt24,25. Conversely, rationale residue harvest can enhance crop productivity and nitrogen use efficiency, but excessive residue removal may reduce soil organic carbon and promote soil erosion26,27,28.

Despite the paramount impact of maize residue carbon on soil carbon, currently, we don’t know how the quantity and quality of the maize residue have changed during the last half-century across the US Corn Belt. A baseline is missing, and this knowledge gap may affect how we manage production fields to maximize ecosystem services. Here, we aim to comprehensively estimate maize residue carbon inputs and quality across temporal and spatial scales in the US Corn Belt. This quantification will provide actionable data to decision-makers, enabling them to prioritize research and develop initiatives in agriculture to mitigate climate change and to identify regions with high potential for soil carbon sequestration or residue removal.

To develop spatiotemporal residue quantity and quality estimates, we first analyzed field experiments distributed across the US Corn Belt (Supplementary Fig. 1) to develop scalable HI and CN ratio models that account for genetics, management, and environmental factors (Supplementary Fig. 1; Eqs. 2 and 4; Supplementary Table 1). The derived models were first validated using independent datasets showing adequate performance and reasonable estimates (Supplementary Fig. 2), and then used along with historical county maize grain yield data6 to estimate historical changes in residue quantity and quality in the US Corn Belt. Our analysis spanned 40 years and 708 US counties, which account for 85% of US maize production.

Results

Across the US Corn Belt, maize grain yield has increased by an average of 109 kg dry matter ha−1 yr−1 over the past 40 years6 (Fig. 1). The rate of increase was different across the landscape. Eastern South Dakota, eastern Nebraska, northwestern Iowa, and northwestern Illinois realized the highest increase (152 kg dry matter ha−1 yr−1), while western Kansas and Nebraska realized the smallest (5 kg dry matter ha−1 yr−1). Field experiments across the US Corn Belt testing hybrids released over different eras (breeding effect) indicated an average grain yield increase of 86 kg dry matter ha−1 yr−1 (Fig. 1) together with an increased HI of 0.0016 yr−1 from 1980 to 2020 (Fig. 2). The increase in yield and HI was similar for different relative maturity hybrids (Figs. 1 and 2). The developed regional HI model, which considers genetics, management, and environmental factors (see Eq. 2), revealed an overall maize HI increase from 0.46 in 1980 to 0.54 in 2020 (0.0020 yr−1; Fig. 2). Breeding accounted for 80% of the increase in HI, while earlier planting dates and increased grain yield accounted for the remaining. The rate of HI increase followed an east-to-west gradient, with the largest increases to be realized in Nebraska and South Dakota.

Fig. 1: Historical changes in maize grain yield in the US Corn Belt.
Fig. 1: Historical changes in maize grain yield in the US Corn Belt.The alternative text for this image may have been generated using AI.
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Grain yield is reported at 0% grain moisture. A Maps represent county-level yields in 1980, in 2020, and the difference between 2020 and 1980 (source USDA-NASS6). B Regional scale, G × E × M effects, illustrates temporal trends in USDA-NASS yields across the US Corn Belt: red line indicates the counties’ weighted average value, the internal dashed lines represent the 1st and 3rd quartiles, and external dashed lines represent the 5th and 95th percentiles. C Field experiments, Breeding effect, illustrates grain yields versus year of hybrids release from field experiments (54 hybrids released from 1980 to 2020 across 31 locations, see Supplementary Fig. 1 for the distribution of the experiments). Blue circles and orange squares represent short-maturity (100–105 days) and long-maturity (109–115 days) hybrids, respectively.

Fig. 2: Estimated historical changes in maize harvest index in the US Corn Belt.
Fig. 2: Estimated historical changes in maize harvest index in the US Corn Belt.The alternative text for this image may have been generated using AI.
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A Maps represent county-level harvest index estimates in 1980, in 2020, and the difference between 2020 and 1980 using Eq. 2. B Regional scale, G × E × M effects, illustrates temporal trends in harvest index estimates across the US Corn Belt: red line indicates the counties’ weighted average value, the internal dashed lines represent the 1st and 3rd quartiles, and external dashed lines represent the 5th and 95th percentiles. C Field experiments, Breeding effect, illustrates observed harvest index versus year of hybrids release from field experiments (54 hybrids released from 1980 to 2020 across 31 locations, see Supplementary Fig. 1 for the distribution of the experiments). Blue circles and orange squares represent short-maturity (100–105 days) and long-maturity (109–115 days) hybrids, respectively.

The combination of HI and yield data allowed us to estimate residue quantity at scale (Eq. 3). Results indicated that maize residue quantity has increased by 34% over the past 40 years, from 6.1 to 8.1 Mg ha−1 (Figs. 3 and 4). The rate of increase averaged 51 kg dry matter ha−1 yr−1 across the US Corn Belt. This increase is half that of the grain yield increase and varies across the landscape (-30 to 100 kg dry matter ha−1 yr−1). Top maize-producing states like Iowa and Illinois today produce, on average, 8.5 Mg of residue ha−1 (HI = 0.56), while highly productive maize fields can produce over 11 Mg of residue ha−1 (HI = 0.59; Fig. 4). South Dakota and Ohio had the largest maize residue inputs increase from 1980 to 2020 (3.0 Mg ha−1, Fig. 3). South Dakota’s increase was driven by the grain yield increase, while Ohio’s increase was due to a moderate increase in grain yield and a delay in planting dates in recent years29,30. Counties in western Nebraska and Kansas had the smallest increase (<1.0 Mg ha−1) since they already had high maize residue inputs in the 1980s due to irrigation.

Fig. 3: Estimated historical changes in maize residue quantity in the US Corn Belt.
Fig. 3: Estimated historical changes in maize residue quantity in the US Corn Belt.The alternative text for this image may have been generated using AI.
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Residue quantity is reported at 0% moisture. A Maps represent county-level residue quantity estimates in 1980, in 2020, and the difference between 2020 and 1980 using Eq. 3. B Regional scale, G × E × M effects, illustrates temporal trends in residue quantity estimates across the US Corn Belt: red line indicates the counties’ weighted average value, the internal dashed lines represent the 1st and 3rd quartiles, and external dashed lines represent the 5th and 95th percentiles. C Field experiments, Breeding effect, illustrate observed residue quantities versus year of hybrids release from field experiments (54 hybrids released from 1980 to 2020 across 31 locations, see Supplementary Fig. 1 for the distribution of the experiments). Blue circles and orange squares represent short-maturity (100–105 days) and long-maturity (109–115 days) hybrids, respectively.

Fig. 4: Maize residue production for different grain yield levels.
Fig. 4: Maize residue production for different grain yield levels.The alternative text for this image may have been generated using AI.
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Grain yield levels reflect four scenarios: US Corn Belt in 1980, US Corn Belt in 2020, Iowa in 2020, and rain-fed high-yielding field56. Values on top of the bar represent the estimated harvest index. Grain yield is reported at 15% grain moisture, and residue quantity is reported at 0% moisture.

We estimated that across the US Corn Belt, maize residue carbon inputs have increased by 46%, from 70 in 1980 to 103 million Mg C in 2020 (Fig. 5). Overall, this increase was driven by a 33% increase in residue quantity per area, alongside a 10% expansion in the area planted with maize. While residue carbon input increased in all US states, the cause of the increase differed across states. In some states, such as Iowa and Illinois, the increase was caused by the increased residue productivity; in Kansas was due to maize area expansion, while in South Dakota due to both factors (Fig. 5, Supplementary Table 2).

Fig. 5: Changes in maize residue carbon inputs from 1980 to 2020 in the US Corn Belt.
Fig. 5: Changes in maize residue carbon inputs from 1980 to 2020 in the US Corn Belt.The alternative text for this image may have been generated using AI.
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A Maize residue quantity estimated using USDA grain yields6 and harvest index (HI) values from Eq. 2, and also using a fixed HI of 0.50. B Maize planted area. C Estimates of carbon inputs in the US Corn Belt using maize cropland area, residue quantity, and carbon concentration of 43%. D Maize residue carbon inputs by state. E Changes in maize planted area and residue quantity by state between 1980 and 2020.

The estimated residue carbon input increase in the US Corn Belt (Fig. 3) is directionally consistent with field experiments, but the magnitude was higher because of the combined factors (genotype × management × environment). Field experiments revealed that maize breeding has not only increased residue production, but also altered the residue composition towards more cob and leaf and less stem biomass (Supplementary Fig. 3). Cobs and stems have a lower quality (high CN ratio) than leaves (Supplementary Fig. 3). Breeding for high yields has indirectly increased cobs and stem CN ratio in the long-season hybrids. This resulted in an overall increase in the residue CN ratio in long-season hybrids, which was not evident in the short-season hybrids (Supplementary Fig. 4).

Estimates from the regional-scale CN ratio model (Eq. 4) showed that the residue CN ratio has remained relatively stable at about 62 over the years in the US Corn Belt (Table 1, Supplementary Fig. 4). This is likely due to the compensatory effects between maize breeding and changes in agronomic management. Modern hybrids have greater nitrogen use efficiencies16, are planted at higher plant populations, and have greater grain yields than old hybrids, and hence have residues with a higher CN ratio than older hybrids. On the other hand, nitrogen fertilizer rates have, on average, increased by 32 kg N ha−1 from 1980 to 201831, which could reduce the CN ratio.

Table 1 Estimated historical changes in maize residue carbon-to-nitrogen ratio (CN ratio) for central (Iowa, Illinois, Indiana) and North US Corn Belt (Michigan, Minnesota, South Dakota)
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Discussion

Our work enhances the predictability and explainability of HI across temporal and spatial scales, which can stimulate analyses in other environments or crop species (beyond the US Corn Belt) toward developing a robust global dataset with crop residue input. The HI comprises a major plant characteristic routinely used across disciplines2,17,32,33, and its value has a substantial impact on carbon budgets. Without this current knowledge, previous studies used constant HI values2,34,35, which led to the misestimation of residue carbon inputs. For example, using a 0.5 fixed value for HI in the US Corn Belt would have underestimated the residue carbon inputs by 11 million Mg in 1980 and overestimated the carbon inputs by 18 million Mg in 2020 (Fig. 5). Our approach to estimating HI across temporal and spatial scales accounts for the effects of genetics, environment, and management factors (see Eq. 2), which are known to affect HI9,10,16,17,36,37. Furthermore, the developed scalable HI model (Eq. 2) considers easily obtainable input data such as year of hybrid release, grain yield, planting date, and longitude, and has the potential to be enhanced further and applied beyond the US Corn Belt towards robust estimates of global maize residue carbon inputs.

We estimated maize residue production to linearly increase from 1980 to 2020 by, on average, 51 kg dry matter ha−1 yr−1 in the US Corn Belt (Fig. 3), about half the rate of grain yield increase (Fig. 1). This translates to 32.5 million Mg more carbon inputs in recent years than 40 years ago (46% increase; Fig. 5). Today’s maize residue production in the US Corn Belt is worth $14.7 billion in carbon markets, assuming a price of $38 per Mg CO2 (California price in 2024; https://carbonpricingdashboard.worldbank.org/). However, a recent study shows that the social cost of carbon should be much higher ($185 per Mg CO2)38. For reference, the economic value of maize grain production in 2020 was $55 billion according to USDA-NASS records. This signifies the importance of residue production for the US Corn Belt. There are several initiatives to remove maize residue from the field, and use it for construction (CornBoard™ developed by the University of Illinois; CornCrete developed by Colorado State University) or bioenergy (Bioethanol Verbio, https://www.verbio-north-america.com/). Our regional estimates, which directionally agree with field studies8,10,17, can be leveraged to enhance sustainability through improved site-specific management strategies. This is necessary because handling large residue amounts in the field may limit the progress of conservation practices such as reduced tillage or the adoption of cover crops18,21,22,39.

We attributed 77% of the historical residue carbon input increase to greater maize productivity and 23% to area expansion (Fig. 5). Results indicated large residue increases in the high-yielding areas, like east Nebraska, Iowa, and Illinois (Fig. 3). A common characteristic of these areas is the control of water, either via subsurface tile drainage40,41 or irrigation systems42 and produce over 8.5 Mg ha−1 of maize residue, while individual fields can produce over 11 Mg ha−1 (Fig. 4). In certain areas, such as Kansas, the increase in maize residue is primarily due to area expansion, as maize replaced sorghum because of its higher-yielding capacity under drought conditions11. In South Dakota, the historical increase in maize residue resulted from both greater productivity and conversion of grassland and wetland areas into cropland43.

Our 31 field experiments were strategically distributed to capture major environmental and management gradients across the US Corn Belt (Supplementary Fig. 1). Previous studies have shown that many regions within the US Corn Belt share similar weather and soil conditions44. However, we acknowledge that we did not have experiments in some states, such as South Dakota, where crop relative maturity typically ranges from 95 to 105 days45. This may have introduced errors in extrapolation (Fig. 2) since we mostly explored 100–115-day hybrids (Supplementary Table 346). Still, our study represents the most comprehensive collection of maize HI and residue CN ratio data available in the US. Our framework can be further refined and expanded as more data becomes available, improving spatial coverage and predictive accuracy. In addition, future studies should also focus on developing models to estimate spatial and temporal residue inputs from other major crops in the US Corn Belt.

The increased maize residue production may limit the implementation progress of conservation practices such as cover crops and no-tillage, which are highly recommended for increased soil carbon18,21,22. Currently, areas with cover crops comprise a small fraction of the maize cropland area, contributing 2.7 million Mg carbon year−1 in the US Corn Belt (Supplementary Table 2)47,48. Of interest, the annual rate of residue carbon inputs increase is 0.9 million Mg carbon year−1 [(106 million Mg carbon year−1 − 71 million Mg carbon year−1)/40 years; Supplementary Table 2], representing one-third of the total annual carbon input provided by cover crops in the US Corn Belt. While maize residue represents the largest source of soil carbon input, only a small fraction of it ends up in stabilized soil organic carbon form (about 11%)49. Therefore, current maize residue production may represent 11.6 million Mg of carbon sequestration and 7% of the annual CO2 from the US agricultural sector, equivalent to 634 million metric tons of CO2. If residue production continues to increase, there is a possibility that soil will eventually reach saturation, resulting in no further CO2 sequestration, although this is debatable50,51.

The increase in maize residue poses one of the greatest challenges for adopting low-intensity tillage practices in the US Corn Belt, especially in fields without subsurface drainage40. Tillage remains a standard practice in regions with the highest maize residue production, such as Iowa and as well as in colder environments like Minnesota18,47, because tillage helps to warm and dry the soil for planting, reducing the risk of economic yield loss23,52,53. No or low tillage practices are more prevalent in water-limited environments like Nebraska and Kansas18,47,54,55.

Highly productive maize fields56 can yield over 18 Mg ha−1, generating over 11 Mg ha−1 of maize residue (Fig. 5). Large residue amounts of low quality would require increased N-fertilizer rates27,57, which could increase the risk for N2O emissions because approximately 1% of the applied N fertilizer is emitted as N2O58. Large residue amounts can also compromise the early planting of soybeans, which is recommended to increase yields53,59. Residue removal has the potential to increase soybean and maize yield60 and also to reduce N2O emissions61, however, residue inputs of 6–7 Mg ha−1 per year are necessary to maintain soil organic carbon stocks in Iowa soils28,62. Future research should invest more into optimizing residue management practices, such as residue removal rates, tillage systems, and residue chopping practices, in combination with other management practices, such as fertility programs and planting dates, to maximize productivity and sustainability63. Emerging remote sensing technologies that can detect soil cover and estimate residue amount per field could assist site-specific residue management recommendations7,64.

We anticipate maize residue production to continue increasing in the future, but at a slower rate than in the past 40 years. This is because the current maize HI is above 0.50, meaning further increases in grain yield will result in a less-than-proportional increase in residue. If maize grain yield and HI continue to increase at the same rate as in the past 40 years, by 2050, the average US Corn Belt grain yield could reach 12.9 Mg dry matter ha−1 with a HI of 0.60, producing about 8.6 Mg ha−1 of residue, similar to current levels (Supplementary Fig. 5). A regional average HI of 0.6 is feasible. Elite modern hybrids already have HI of 0.60 or even higher at the plot level9,11. Furthermore, commercial maize breeding companies are developing reduced-stature hybrids with higher HI than conventional hybrids65,66. Our future projection for residue carbon input is conditional on factors including the future of maize breeding, policy, and climate patterns67. Climate change will indirectly influence crop residue production due to the direct impact on grain yields and planting date68,69,70. In addition, heat stress can significantly affect pollination and kernel set, affecting not only grain yield, but also HI and residue production37,71. Future modeling studies can build on present results and explore residue production and management scenarios for maximizing productivity, profitability, and environmental sustainability.

In addition to residue quantity, we developed spatiotemporal patterns for residue CN ratio, an important measure of residue quality. Present findings suggest that the residue CN ratio has remained unchanged over the last 40 years in the US Corn Belt (Table 1 and Supplementary Fig. 4) and we attribute this to the following compensatory effects of: (1) breeding efforts and historical increases in plant density tend to increase residue CN ratio10,72,73 (Supplementary Fig. 4); and (2) increases in N-fertilizer rate tend to decrease residue CN ratio10,15,72. These driving factors occur simultaneously, resulting in stable residue CN ratios throughout the US Corn Belt, with a few exceptions in the northern Corn Belt.

Another important finding of this research is that maize breeding has indirectly changed the composition of maize residue and its chemical composition (Supplementary Figs. 3 and 4). The increase in cob and leaf biomass accounted for 72% of the increase in residue quantity, which is expected as grain yield per plant is highly correlated with ear biomass74,75. We also found that modern long-maturity hybrids have a higher CN ratio than old hybrids (Supplementary Fig. 4), in agreement with previous findings16. We attribute this to reduced organ N concentration caused by greater N allocation to grain and increased N remobilization from stems to grain16,32. While we were expecting a similar pattern for the short-maturity hybrids or an even higher CN ratio change than the long-maturity hybrids due to less soil N mineralization in the northern latitudes caused by low temperatures, that was not the case (Supplementary Fig. 4). We believe the primary reason for this is the applied N-fertilizer, which was not similar across experimental locations and secondary due to the lower grain yields of the short-maturity hybrids compared to long-maturity hybrids, which implies less N in the grain and hence more N availability for other plant organs76. A previous study highlighted the substantial impact of the N-fertilizer rate on the residue CN ratio10.

Materials and methods

Field experiments to estimate maize breeding impacts on harvest index, residue quantity, and residue CN ratio

Thirty-one field experiments were conducted across the US Corn Belt in 2021 and 2022 (Supplementary Fig. 1). We studied 54 Bayer Crop Science Legacy hybrids commercialized between 1980 and 2020, representing various brands (Supplementary Table 3). Hybrids were selected based on their commercial relevance and correspond to two relative maturities: 24 hybrids with relative maturity between 100 and 105 days (short-maturity) and 30 hybrids with relative maturity ranging from 109 to 115 days (long-maturity). Each field experiment involved testing 18 to 24 hybrids, with each hybrid being evaluated at a minimum of 7 locations (Supplementary Table 3). Further details about the field experiments can be found in previous studies9,46,76.

Crop planting date, plant density, and N-fertilizer rate for each experiment followed regional practices, except for four locations that were fertilized with a low N rate. Planting dates ranged from April 14 to May 22, and plant populations ranged from 6.5 to 8.6 plants m−2 across locations. The applied N-fertilizer rates ranged from 45 to 274 kg N ha−1, excluding the low N rates, the range is 132 to 274 kg N ha−1. The previous crop was soybean in most locations, except for 2021 Dyersville, 2022 Dyersville, and 2022 Mount Zion, where the previous crop was maize. All locations were rainfed except for 2021 Beatrice, 2022 Beatrice, and 2022 Eustis, which received 89, 225, and 152 mm of irrigation, respectively. Twenty-six out of the thirty-one locations had shallow water table influence. Mean temperature, mean vapor pressure deficit, total rainfall, and total net radiation were retrieved from a gridded weather dataset77 and analyzed for the growing season (April to September) and summer (June to August). Across environments, cumulative in-season rainfall and irrigation ranged from 333 to 679 mm, cumulative solar radiation from 3000 to 3495 MJ m−2, and mean growing season temperature from 18.2 to 21.8 °C. Most locations experienced near-normal weather conditions compared to the historical average, with some slightly warmer and drier. Some locations experienced no heat stress during flowering, while others had up to 11 days with maximum temperatures exceeding 35 °C. Across the landscape, our experiments captured a range of weather and soil conditions and different farmer management practices, providing a good representation of the US Corn Belt (Supplementary Fig. 1, Supplementary Table 4).

At the end of the crop cycle (R6), we measured above-ground plant biomass and its distribution between grains and residue. From each plot, we harvested five plants. The residue samples were further separated into leaf, cob, stem, and husk/shank in seven out of the thirty-one locations. After determining organ dry weights, we analyzed the samples from all sites for N and carbon concentrations using a CHNS Elemental Analyzer (Elementar Americas). Further details can be found in previous study9. Plot-level grain yield estimates were derived from combine harvesters (two middle rows per plot). Above-ground biomass from each plot was estimated by dividing the plot-level grain yield by the harvest index obtained from the five plants. Residue production from each plot was obtained by subtracting the grain yield from the above-ground biomass. Grain yield and residue quantity are reported at 0 g kg−1 moisture, unless otherwise indicated.

Genetic gain estimations

Grain yield, harvest index, residue quantity, and residue CN ratio genetic gains were estimated by fitting linear mixed effects models (lmer function, lme4 package78 from R software version 4.2.179) across hybrids commercialized between 1980 and 2020 in thirty-one environments:

$${Y}_{{ij}{kl}}= \, {\beta }_{0}+{\beta }_{1}{{{{\rm{YORC}}}}}_{i}+{{{{\rm{\mu }}}}{{{\rm{LOC}}}}}_{j}+{\mu ({{{\rm{LOC}}}}\times {{{\rm{YORC}}}})}_{{ij}}+{{{{\rm{\mu }}}}{{{\rm{HYB}}}}}_{k} \\ +{{{{\rm{\mu }}}}({{{\rm{BLO}}}}/{{{\rm{LOC}}}})}_{{jl}}+{\varepsilon }_{{ij}{kl}}$$
(1)

where Yijkl represents the variable of interest for the hybrid year of release i, the environment j, the hybrid k, and the block l; β0 is the fixed intercept parameter, β1 is the fixed effect for the continues variable hybrid year of release YORC (centered by the mean of 2001.5), µLOCj represents the random effect of environment j, µ(LOC × YORC)ij represents the random interaction effect of environment j and year of release i, µHYBk is the random effect of hybrid k, μ(BLO/LOC)jl is the random effect of the block l nested within the environment j, and εijkl represents the residual error term. All random terms and residuals were assumed independent and normally distributed with a mean of zero and constant variance. Model estimates were obtained using REML (restricted maximum likelihood). The same methodology was used to assess organ biomass and CN ratio genetic gains in seven locations. Genetic gain (β1) significance was tested using the emmeans function from the emmeans package80.

Development of scalable harvest index and residue CN ratio models

We explored different management and environmental variables as covariates to develop the HI and CN ratio models (Eq. 1). We followed a top-down four-step modeling strategy81,82. In Step 1, we generated a loaded random and mean structure model, with different management and environmental predictors. We explored 20 potential variables to explain site-to-site variability in HI and residue CN (μLOCj and μ(LOC × YORC)ij; Supplementary Table 4), and we used Pearson correlation and linear ANOVA analyses to evaluate multicollinearity among predictors. This analysis identified grain yield, planting date, latitude, longitude, net radiation, soil productivity index, and temperature as the top predictors for HI and N-fertilizer rate, grain yield, and longitude for residue CN ratio. These results aligned well with previous literature on the effects of individual factors on HI and residue CN ratio10,16,17,36,83. We determined multicollinearity among predictors (i.e., longitude, summer net radiation, and soil productivity index were autocorrelated), so longitude was considered in the HI model to simplify the models. The final models from Step 1 included as many predictors as possible in the fixed component (loaded random and mean structure). In Step 2, we determined the optimal structure of the random component. For that, we used REML-based likelihood ratio tests to determine which random effects to keep in the model and the optimal covariance structure for the residuals. In Step 3, we determined the optimal fixed structure based on ML-based likelihood ratio tests. Because yield predictors were in different units and scales, we also performed this analysis using standardized variables (z-scores) and obtained the same fixed structure. Finally, in Step 4, we used REML estimations to determine the final models (Eqs. 2 and 4):

$${{{\rm{Harvest}}}} \, {{{{\rm{index}}}}}_{{ijklmn}}= \, {\beta }_{0}+{\beta }_{1}{{{{\rm{YOR}}}}}_{i}+{\beta }_{2}{{{{\rm{GY}}}}}_{j}+{\beta }_{3}{{{{\rm{PD}}}}}_{k}+{\beta }_{4}{{{{\rm{LON}}}}}_{l} \\ +{\beta }_{5}{{{\rm{YOR}}}}\times {{{{\rm{LON}}}}}_{{il}}+{{{{\rm{\mu }}}}{{{\rm{LOC}}}}}_{m}+{{{{\rm{\mu }}}}{{{\rm{HYB}}}}}_{n}+{\varepsilon }_{{ijklmn}}$$
(2)
$${{{\rm{Residue}}}}\,{{{{\rm{quantity}}}}}_{{ijklmn}}={{{{\rm{GY}}}}}_{j}/{{{{\rm{HI}}}}}_{{ijklmn}}{-}{{{{\rm{GY}}}}}_{j}$$
(3)
$${{{\rm{Residue}}}}\; {{{\rm{CN}}}}\,{{{{\rm{ratio}}}}}_{{ijklmn}}= {\beta }_{0}+{\beta }_{1}{{{{\rm{YOR}}}}}_{i}+{\beta }_{2}{{{{\rm{GY}}}}}_{j}+{\beta }_{3}{{{{\rm{N}}}}}_{k}+{\beta }_{4}{{{\rm{GY}}}} \\ \times {{{{\rm{N}}}}}_{{jk}} {{{{\rm{\mu }}}}{{{\rm{LOC}}}}}_{l}+{{{{\rm{\mu }}}}{{{\rm{HYB}}}}}_{m}+{{{{\rm{\mu }}}}({{{\rm{BLO}}}}/{{{\rm{LOC}}}})}_{{ln}}\\ +{\varepsilon }_{{ijklmn}}$$
(4)

where harvest index was estimated by Eq. 2. Fixed effects were the intercept parameter (β0), the continuous variable hybrid year of release, (β1YORi), the continuous variable grain yield (β2GYj), the continuous variable plating date (β3PDk), the continuous variable longitude (β4LONl), and the interaction between hybrid year of release and longitude (β5YOR × LONil). Random effects were location (μLOCm), hybrid (μHYBn), and the residual error term (εijklmn). Residue quantity was estimated using Eq. 3, using a HI previously estimated with Eq. 2. Residue CN ratio was estimated by Eq. 4. Fixed effects were the intercept parameter (β0), the continuous variable hybrid year of release (β1YORi), the continuous variable grain yield (β2GYj), the continuous variable fertilizer N rate (β3Nk), and the interaction between grain yield and fertilizer N rate (β4GY × Njk). The YORi was 2001.5, the mean (YOR, 2001.5), and the actual YOR for relative maturities shorter, equal, or longer than 105-day maturity, respectively. Random effects were location (μLOCl), hybrid (μHYBm), block nested in site (μ(BLO/LOC)ln), and the residual error term (εijklmn). All random terms and residuals were assumed independent and normally distributed with a mean of zero and constant variance. We checked the Gaussian distribution and homoscedasticity assumptions for the standardized model residuals with graphical analysis for model validation.

The R2 of adjusted models was obtained following the methodology described in Nakagawa and Schielzeth84 for generalized linear mixed models. Marginal R2 (R2m) represents the variance explained by fixed effects, while conditional R2 (R2c) represents the variance explained by the entire model (fixed and random effects). Equation 2 had an R2m of 0.48 and an R2c of 0.78, while Eq. 4 had an R2m of 0.31 and an R2c of 0.67. We evaluated the performance of the models using two techniques: (1) independent datasets and (2) leave-one-site-out cross-validation. We tested Eq. 2 against literature-era studies in North America, summarized in a previous study9, and Eq. 4 against genotype × management × environment data10. The prediction capacity of Eqs. 2 and 4 was deemed sufficient (Supplementary Fig. 2). The leave-one-site-out cross-validation technique confirmed the robustness of the developed new models. The relative root mean square error (RRMSE) averaged 6% for Eq. 2 and 18% for Eq. 4 (Supplementary Fig. 2).

Regional-scale estimations of residue quantity and CN ratio

We estimated harvest index, residue quantity, and CN ratio for each county (n = 708) and year (1980–2020) in the US Corn Belt using the fixed effects coefficients (βn) estimated in Eqs. 2–4. We used the following inputs: county-level grain yields6, longitude, year, state-level planting date data6, county-level data on hybrid relative maturity (Bayer Crop Science data; Supplementary Fig. 1), and state-level N-fertilizer rate data31. We also estimated residue inputs by utilizing county-level planting date data for the period from 2000 to 202029, and these estimates showed a high degree of consistency (RRMSE = 0.06, n = 14080) with those derived from state-level planting dates. We used linear regression across 40 years for each county to estimate values for 1980 and 2020, instead of comparing specific past and current residue inputs using the specific values for those years, in order to minimize year-to-year variability11,55. We did not see evident signs of nonlinearity for most traits and counties. Detailed estimated values for each county and year are available in the data repository. We used R software79 to visualize results and perform a multi-year regression analysis to estimate the regional-scale rate of change.