APSIM is a widely used cropping system simulation model (Holzworth et al., 2014). More specifically, the APSIM sorghum module simulates phenology, crop growth, and development using a water demand and supply concept (Hammer et al., 2010). Similarly, APSIM wheat simulates winter and spring wheat daily growth and its phenological development (Zhao et al., 2014), responding to weather, soil water, soil nitrogen, and management (Zheng et al., 2015).

The APSIM model (version 7.10) was used to simulate three crop sequences: i) a monocrop sorghum, ii) a monocrop wheat, and iii) a sorghum–wheat crop sequence, i.e., two crops in the same year. Temperature and rainfall data spanning 30 years were obtained from NOAA for 194 sites in Kansas (National Oceanic and Atmospheric Administration, 2023). Radiation and relative humidity were obtained from NASA (National Aeronautics and Space Administration; NASA POWER, 2023) considering the latitude and longitude of the NOAA weather stations. All weather data were checked for errors such as the minimum temperature being lower than the maximum temperature for the day. Then, met files were created for each location and used in the simulations. The soil characteristics for each location, using the coordinates of the NOAA weather stations, were downloaded from SSURGO (Soil Survey Geographic Database; Soil Survey Staff, Natural Resources Conservation Service [NRCS], and United States Department of Agriculture [USDA], 2021), and the soil parameters were calculated employing the apsimx package (Miguez, 2022).

The simulations started 4 months before the sowing date to estimate the initial soil conditions. A sowing rule was used for both crops that included soil moisture availability and the sowing window. This is 30 mm of rainfall over three consecutive days needed to trigger a sowing event within a set sowing window. If the rule was not met, the sowing would occur on the last day of the sowing window. The sowing windows were defined based on the county recommendations ( Supplementary Table 1 ) (Shroyer et al., 1996) for sorghum; the sowing window ranged from May 15 to June 25, depending on the location, and for wheat, the sowing window ranged from September 10 to October 25. In the case of the sorghum–wheat crop sequence, if sorghum had not reached harvest moisture before the last day of the wheat sowing window, the crop was harvested on that day, and the wheat was planted. Initial conditions, i.e., soil water and soil nitrogen, were reset at the start of each crop sequence. For the sorghum–wheat sequence, the simulations were ended after the wheat crop and reset for the next year. For the monocrops, the simulations ended after the harvest of each crop.

A dry-down module was incorporated into APSIM to simulate sorghum grain dry-down after maturity using Equation 1 (Martinez-Feria et al., 2019). Sorghum dry-down parameters were obtained from Paulsen and Thompson (1973). The validation of the dry-down module is shown in Supplementary Figure 2 . The dry-down module assumed a 35% grain humidity at physiological maturity (Ciampitti et al., 2022) and triggered sorghum harvest at 14% humidity.

where M is % grain humidity at the beginning of the day, Me stands for equilibrium moisture content, k stands for proportionality drying coefficient, and x is the days since maturity.

Two previously validated sorghum hybrids for KS (Carcedo and Ciampitti, 2023) were used. An early-maturing hybrid (Pioneer_s34) was used in the sorghum–wheat crop sequence, and a late-maturing hybrid (Buster) was used in the sorghum monocrop. The difference in maturity between the early- and late-maturing hybrids was 15 days ( Supplementary Figure 3 ). The wheat variety ‘Larry’, previously validated in Kansas (Evers, 2022), was used in the wheat simulations. Crop coefficients are shown in Supplementary Tables 2 – 4 for the two sorghum and wheat genotypes. Nitrogen fertilization requirements were calculated following the recommendations described in Leikam et al. (2003). This is considering the expected yield (averaged of 10 years; USDA-NASS, 2023) and assuming a soil organic matter content of 2.5%. Recommended plant density and sowing dates followed Shroyer et al. (1996). For wheat, sowing dates ranged from September 10 to October 25 and, for sorghum, from May 15 to July 10. Plant densities were based on site rainfall, with ranges from 1,488,120 to 2,777,820 plants per hectare for wheat, and 60,000 to 170,000 plants per hectare for sorghum.

Profit calculations considered the cost of seed and fertilizer, which typically constitute 40% or more of the total input cost for both crops (Tsoodle and Li, 2023). Mean grain prices were obtained from the USDA/NASS (U.S. Department of Agriculture, National Agricultural Statistics Service) QuickStats Ad-Hoc Query Tool (quickstats.nass.usda.gov). For wheat, the reported prices for seed and fertilizer were considered representative of the central Kansas area; for the west and east areas, they were adjusted following seed and fertilization differences with central Kansas. Sorghum costs were determined based on the average for areas receiving between 508–660 and 660–812 mm of rain and adjusted to the rest of Kansas according to seed and fertilization rates. To provide a comprehensive economic analysis, three cost scenarios representing low-, intermediate-, and high-cost conditions were established. These scenarios were formulated using terciles of seed and fertilization costs spanning from 2014 to 2022 (available in Supplementary Tables 5 , 6 ). An average yield value was obtained from simulations and used to calculate gross income for the three cost scenarios. The profit for each cost scenario was obtained using a different grain price and different cost values.

The data analysis was conducted using the R software (R Core Team, 2021). A mean multiple comparison of the profit was performed between the cropping sequences and cost scenarios by fitting a linear model (package stats; R Core Team, 2021) and calculating the estimated marginal means (package emmeans; Rusell V. Rusell, 2024). Finally, the comparison between the profits was conducted using Sidak’s correlations (package multcomp; Hothorn et al., 2008). As a measure of risk, the variability in gross margins was calculated using the interquartile ratio (IQR) and standard deviation (SD) (stats package; R Core Team, 2021).

Regions having similar profits were spatially clustered. Four clusters were defined using the fuzzy C-means algorithm to classify sites based on the profits of the three cropping sequences and cost scenarios over 30 years. The number of clusters was decided based on the lowest within-cluster sum of squares, with a preference for a smaller number of defined regions (package factoextra; Kassambara and Mundt, 2020) ( Supplementary Figure 2 ). The resulting clusters were named based on the cropping sequence showing the highest mean profit, i.e., S+W or W, S+W lower, S+W higher, and W. The profit for each cluster, cropping sequence, and cost scenario was analyzed using a mean multiple comparison of the profit between the clusters, cropping sequences, and cost scenarios by fitting a linear model (stats package; R Core Team, 2021) and calculating the estimated marginal means (package emmeans; Rusell V. Rusell, 2024). Finally, the comparison between the profits was conducted using Sidak’s correlations (package multcomp; Hothorn et al., 2008). As a measure of risk, the variability in gross margins was calculated using the interquartile ratio and standard deviation (stats package; R Core Team, 2021). Each county was assigned to a cluster based on their frequency of occurrence. If the difference between the most frequent cluster and the second most frequent cluster was less than 10%, the county was defined as the W+S or W cluster, which stands for no dominance of the sorghum–wheat crop sequence or wheat monocrop. The percentage of times that each cropping sequence presented higher profit within each cluster was also calculated.

A principal component analysis (PCA) was used to identify the association between environmental covariates and their relationship with profit. Environmental covariates included the simulated average of nitrogen deficit (nfact) and crop water deficit (swdef), i.e., the ratio between crop water demand and total plant available water during the growing season, and the cumulative incoming solar radiation (rad), average minimum temperature (min), average maximum temperature (max), cumulative thermal time (TT), and cumulative rain during the growing season (rain), as well as for the pre-flowering (from sowing to flowering) (rad_pre, min_pre, max_pre, TT_pre, and rain_pre) and post-flowering (from flowering to maturity) (rad_post, min_post, max_post, TT_post, and rain_post) periods. Finally, the number of days with temperatures higher than 37.4°C and 36°C (temp_high) and lower than 10°C and 0°C (temp_low) for sorghum and wheat, respectively, were also calculated (Brown et al., 2018; Prasad et al., 2015). The number of environmental covariates was reduced by eliminating highly correlated variables (higher than 0.8) (package stats; R Core Team, 2021). Only the principal components having eigenvalues higher than one were selected, and within these, the 10 variables showing the highest loading weights were selected (package factoextra; Kassambara and Mundt, 2020).

Simulated sorghum yields were similar for the sorghum in the sorghum–wheat crop sequence and the monocrop scenarios ( Table 1 , Supplementary Table 6 ). However, simulations showed a reduction in wheat yield when wheat was grown after the sorghum crop, i.e., up to 60%. The sorghum–wheat crop sequence had higher profits than the other sequences in the low- and intermediate-cost scenarios but did not differ from wheat monocrop under the high-cost scenario ( Table 1 ). Notably, the high-cost scenario showed the largest differences among the crop sequences, with profits of 581 USD ha⁻¹ for sorghum, 733 USD ha⁻¹ for wheat, and 731 USD ha⁻¹ for sorghum–wheat. It is also noteworthy that the costs associated with the scenarios were correlated with the profits; i.e., grain prices and profit were higher for the high-cost scenario and lower for the low-cost scenario. Additionally, wheat monocrops showed the lowest variability in profit (IQR and SD) among the cost scenarios.

The profits obtained by different county-by-year combinations and cost scenarios were classified into four clusters based on the cropping sequence that had the highest profit. The sorghum–wheat crop sequence had higher profits in two clusters: one with higher incomes (S+W higher) and the other with lower incomes (S+W lower). A third cluster included instances where there was no difference between having the sorghum–wheat crop sequence or wheat monocrop (S+W or W), and the last cluster included instances where wheat monocrop had higher profits (W). Notably, the low- and intermediate-cost scenarios presented similar profits across clusters and cropping sequences (means of 454 and 481 USD ha⁻¹, respectively; Table 2 ). In cluster S+W higher, it was consistently advantageous to opt for the sorghum–wheat rotation over sorghum or wheat in monocrop, irrespective of the cost scenario (mean across cost scenarios of 872, 729, and 637 USD ha⁻¹, respectively; Table 2 ). In cluster S+W lower, the sorghum–wheat crop sequence was more profitable across cost scenarios, but the profits were lower (mean across cost scenarios of 662 USD ha⁻¹ for sorghum–wheat, 590 USD ha⁻¹ for sorghum, and 480 USD ha⁻¹ for wheat; Table 2 ). In the case of the W cluster, planting wheat was consistently more profitable across all cost scenarios (a difference of 293 USD ha⁻¹ with sorghum and 67 USD ha⁻¹ with the sorghum–wheat crop sequence; Table 2 ).

For the S+W or W cluster, the sorghum–wheat crop sequence had a difference in profit of 13 USD ha⁻¹ with wheat monocrop and 79 USD ha⁻¹ with sorghum monocrop ( Table 2 ). However, the main difference between crop sequences was observed when comparing the cost scenarios between the wheat–sorghum sequence and the wheat monocrop. In the low- and intermediate-cost scenarios, the sorghum–wheat sequence had higher profits than wheat monocrop (261 vs. 291 USD ha⁻¹), and in the high-cost scenario, wheat monocrop had higher profits (417 vs. 393 USD ha⁻¹). The standard deviation on profits and its interquartile ratio remained consistent across cropping sequences and clusters (from 83 to 216 USD ha⁻¹ and from 112 to 347 USD ha⁻¹, respectively; Table 2 ) and were consistently higher in the high-cost scenario than in low and intermediate (IQR was 235 vs. 174 USD ha⁻¹ and SD was 170 vs. 126 USD ha⁻¹ for high vs. intermediate and low, respectively).

Cluster S+W or W was mostly located in the north-east area, S+W lower was predominantly found in the south-east of Kansas, and S+W higher was found next to S+W lower in the central-west areas of Kansas ( Figure 2 ). Lastly, W concentrated in the western counties of the state. The cluster distributions had no spatial differences when comparing the three cost scenarios.

In agreement with Table 2 , the percentages of each crop sequence were similar when comparing the same clusters and cropping sequences in low- and intermediate-cost scenarios ( Figure 3 ). In all the cost scenarios, for clusters S+W lower and S+W higher, the sorghum–wheat crop sequence presented frequencies higher than 60% and 70%, respectively. The difference between those clusters is in the percentage of sorghum monocrop (between 30% and 11%). In the low- and intermediate-cost scenarios, sorghum decreased from 30% to 17% from S+W lower to S+W higher, and in the high-cost scenario, sorghum decreased from 20% to 11%, respectively. In those clusters, wheat increased from 5% to 16% when the scenarios were low or intermediate and high, respectively. In cluster S+W or W, wheat was the cropping sequence with higher frequency across all cost scenarios, but the percentage was higher in high than in low and intermediate (54% vs. 44%). In the W cluster under all the cost scenarios, wheat had a higher profit in more than 61% of the total county × year combinations followed by the sorghum–wheat crop sequence (17%–38%). In this cluster, sorghum had the lower percentage (1%).

The biplot captured 60% of the variability ( Figure 4 ). Clusters S+W lower and S+W higher were closer to each other in the biplot and mainly related to sorghum variables. The variable seasonal solar radiation for sorghum crop (sg_rad) had the highest effect (longest vector), while maximum temperature after flowering (sg_max_post), seasonal thermal time (sg_TT), the number of days with temperature lower than 10°C for sorghum (sg_temp_low), and cumulative rain for wheat (wh_rain) were also closely related to both clusters. Radiation and maximum temperature before flowering and water deficit for sorghum crop (sg_rad_pre, sg_max_pre, and sg_swdef, respectively) were correlated with both clusters, but the angles between the vectors and the clusters were larger ( Figure 4 ). The W cluster was affected by radiation after flowering (wh_rad_post) and cumulative rain before flowering for wheat monocrop (wh_pre_rain), but the angles were larger than those for the other clusters. Finally, cluster S+W or W was only affected by variables impacting wheat, which are wheat’s cumulative thermal time, radiation, and maximum temperature before flowering on the crop sequence (wh_TT_pre_r, wh_rad_pre_r, and wh_max_pre_r, respectively); radiation after flowering, cumulative thermal time, minimum, and maximum temperature after flowering (wh_rad_post_r, wh_TT_post_r, wh_min_post_r, and wh_max_post_r, respectively); nitrogen deficit and days with temperatures lower than 0°C and nitrogen deficit during wheat crop in the sorghum–wheat crop sequence (wh_nfact_r and wh_temp_low_r, respectively); and days with temperatures lower than 0°C (wh_temp_low) in wheat monocrop.