Evaluation and application of the CROPGRO-soybean model for determining optimum sowing windows of soybean in the Nigeria savannas

Soybean production is limited by poor soil fertility and unstable rainfall due to climate variability in the Nigeria savannas. There is a decline in the amount and duration of rainfall as one moves from the south to north of the savanna zones. The use of adapted soybean varieties and optimum sowing windows are avenues to increase productivity in the face of climate variability. Crop simulation models can be used as tools for the evaluation of alternative management options for a particular location, including fertilizer application rates, plant density, sowing dates and land use. In this study, we evaluated the performance of the Cropping System Model (CSM)-CROPGRO-Soybean to determine optimum sowing windows for three contrasting soybean varieties (TGX1835-10E, TGX1904-6F and TGX1951-3F) cultivated in the Nigeria savannas. The model was calibrated using data from ten field experiments conducted under optimal conditions at two sites (BUK and Dambatta) in Kano in the Sudan savanna (SS) agro-ecology over four growing seasons. Data for model evaluation were obtained from independent experiment for phosphorus (P) response trials conducted under rainfed conditions in two locations (Zaria and Doguwa) in the northern Guinea savanna (NGS) zone. The model calibration and evaluation results indicated good agreement between the simulated and observed values for the measured parameters. This suggests that the CROPGRO-Soybean model was able to accurately predict the performance of soybean in the Nigeria savannas. Results from long-term seasonal analysis showed significant differences among the agro-ecologies, sowing windows and the soybean varieties for grain yield. Higher yields are simulated among the soybean varieties in Zaria in the NGS than in Kano the SS and Jagiri in the southern Guinea savanna (SGS) agro-ecological zones. Sowing from June 1 to July 5 produced optimal yield of TGX1951-3F and TGX1835-10E beyond which yield declined in Kano. In Zaria and Jagiri the simulated results show that, sowing from June 1 to July 12 are appropriate for all the varieties. The variety TGX1951-3F performed better than TGX1904-6F and TGX1835-10E in all the agro-ecologies. The TGX1951-3F is, therefore, recommended for optimum grain yield in the savannas of northern Nigeria. However, the late maturing variety TGX1904-6F is not recommended for the SS due to the short growing season in this zone.

Nigeria savannas were laid out as a single factor experiment in a randomized complete block design with three replications. The experiments were conducted under optimum management practices with no water and nutrients stress. Prior to land preparation, 4 tonnes ha −1 of poultry manure was applied to the plots to increase soil fertility. The experimental field was disc-harrowed and ridged before sowing. Each plot contains four 5 m-long rows with spacing of 0.75 m between rows. Each plot received a basal application of 40 kg ha −1 each for K 2 O in the form of Muriate of Potash and P 2 O 5 in the form of Triple Super Phosphate (TSP). Before sowing, a Nodumax inoculant containing rhizobia was used to inoculate the seeds. Seven seeds were planted at intra-row spacing of 10 cm, and later thinned to four plants per hill to give a final population of 533,333 plants ha −1 . Although the experiments were conducted in the rainy season, supplementary irrigation was carried out when necessary to keep the plots well-watered.
The experiments for model evaluation were conducted at the International Institute of Tropical Agriculture (IITA) experimental stations at Zaria (11° 11′ N, 7° 38′ E, 686 m a.s.l) and Doguwa (10° 45′ N, 8° 44′ E, 466 m a.s.l) in the northern Guinea savanna (NGS) zone. The experimental fields were disc-harrowed and ridged. The sowing was done on 20th and 24th June in 2016 at Zaria and Doguwa, respectively and 7th July in 2017 and 22nd June in 2018 at Zaria only. The experiments were design using split-plot design with three replications. The main plot treatments consisted of three P fertilization rates (0, 20, and 40 kg P 2 O 5 ha −1 ). The subplot treatments were three soybean varieties (TGX 1835-10E, TGX1951-3F and TGX 1904-6F). The sub-plot size was 3 × 5 m with four 5-m rows spaced at 0.75 m. The harvest area was 1.5 × 4.5 m. Soybean was planted at the same plant population as for model calibration. All the experiments were carried out in compliance with relevant guidelines and regulations.
Weather and soil data. WatchDog weather station (manufactured by Spectrum Technologies Inc, USA) was used to monitor daily weather conditions at experimental sites. The stations monitored daily rainfall, minimum and maximum air temperature, and solar radiation used for model calibration and evaluation. For the longterm simulation of soybean response to sowing window, a 30-year weather data  was obtained from the Nigeria Meteorological Agency (NIMET) for Kano representing Sudan savanna (SS) and Zaria representing northern Guinea savanna (NGS). For Jagiri representing southern Guinea savanna (SGS), thirty years' records of daily precipitation were sourced from downscaled CHIRPS rainfall at 5.5 km resolution 35 , then merged with data (daily minimum and maximum air temperatures, and daily solar radiation) from National Aeronautics and Space Administration (NASA) database for Climatology Resource for Agro-climatology (http:// power. larc. nasa. gov/). R scripts were created to append data for CHIRPS and NASA power. The weatherman utility software in the DSSAT v4.7 was used to input the weather data for the 2 sites in order to check for errors before use.
Before the trials were established, a detailed soil characterization and profiling was done at each experimental site and the long-term simulation sites. FAO guidelines were used to classify the generic horizons of the soil profile and types 36 . The modified Walkley and Black chromic acid wet chemical oxidation and spectrophotometric method was used to measure total soil organic carbon (total OC) 37 . Total nitrogen (total N) was determined by the micro-Kjeldahl digestion method 38 . Soil pH in water (S/W ratio of 1:2.5) was measured using a glass electrode pH meter and followed by the particle size distribution using the hydrometer method 39 . Available phosphorus was extracted using the Bray 1 method 40 . Phosphorus in the extract was determined colorimetrically by the molydo-phosphoric blue method using ascorbic acid as a reducing agent. K was analysed based on Mehlich 3 extraction procedure 41 . The soil utility software (SBuild) of DSSAT was used to input the soil profile information. The P soil test information was entered into the model in the soil analysis layer and the P balance turned on in the simulation option. For each soil layer, the model estimated bulk density, drained upper limit (DUL), saturated upper limit (SAT), lower limit of plant-available soil water (LL), saturated hydraulic conductivity (Ksat) and root growth factor (RF) using the soil data tool SBuild in DSSAT. The Soil parameters used in the model is presented in Table 1.
Plant measurements. Field data were collected from the net plot leaving the outside rows and a distance of 25 cm at the end of each row to serve as borders. Parameters measured include phenology dates, total dry matter m −2 , and grain yield (kg ha −1 ). At full podding, a quadrat measuring 1 m × 1.5 m was placed across the two middle rows of the net plot; all the plants in the quadrat were sampled to determine dry matter. Leaves were collected from the quadrat on a daily basis until harvest. At harvest, all plants from the quadrat were removed and separated into pods, stem and leaves. The pods that contain seeds were threshed and separated from seeds. All plant parts including leaves collected from the quadrat were dried in an oven at 60 °C for 76 h to constant weight, weighed and combined to give a total dry matter. Grain yield was determined according to Kamara et al. 42 . Pods on plants from the two middle rows were harvested, sundried, and hand threshed. The grains obtained from the quadrat were added to those from the two middle rows and weighed to calculate grain yield. The moisture content of grain samples from each plot was determined using portable moisture meter (Farmex MT-16). Grain yield kg ha −1 was calculated based on 13% moisture content.
Crop model overview. DSSAT shell allows the users to organize and manipulate crop, soil and weather data, to run crop models in various ways, and to analyze their outputs 43,44 . CROPGRO-Soybean which is one of the models running under DSSAT, is a generic physiological process-oriented legume crop model 45 . The CSM-CROPGRO-Soybean model within the DSSAT suite simulates plant growth and development from sowing to maturity using a daily time step, and ultimately predicts yield 24,26,46 . The basic structure of the model, including underlying equations, has been published by several authors [47][48][49] . The model accounts for vegetative and reproductive development; photosynthesis, respiration and partitioning; and transpiration, root water uptake, soil evaporation, soil water flow, infiltration and drainage 45  www.nature.com/scientificreports/ the crop's response to the major weather factors, such as temperature, rainfall and solar radiation, and to soil characterizations such as the amount of extractable soil water and nutrients 26 . The CROPGRO-Soybean model includes detailed soil and plant nitrogen balance components which simulate nitrogen uptake, nitrogen fixation and nitrogen mobilisation 49 .

Methods of model calibration and evaluation.
Model calibration is the adjustment of certain model parameters to make the model work for any desired location. The CROPGRO-Soybean model requires genetic coefficients that describe durations of phases of the crop life cycle for vegetative growth and reproductive traits unique to a given cultivar 50 . These coefficients allow the model to predict differences in development, growth and yield among cultivars when planted in the same environment as well as the differences in the behaviour of a single cultivar when planted in different environments 27 . The soybean model was calibrated by determining the cultivar coefficients for the three cultivars TGX 1835-10E, TGX1951-3F, and TGX 1904-6F using the experimental data. Fifteen cultivar coefficients are required by the CROPGRO-Soybean model. The cultivar coefficient describes the growth and development of the crop. As these were not available for the cultivars used in these experiments, the existing cultivar coefficients for the maturity group (MG) 7 were used for the cultivar TGX 1835-10E; while Jupiter 10 was used for the other cultivars at the start of the calibration to represent the characteristics of a tropical soybean varieties. The cultivar coefficients for each cultivar were determined through trial and error of the model and by comparing simulated and observed data, following the procedures described by Hoogenboom et al. 51 . To obtain the critical short-day length (CSDL) hour, and photoperiod sensitivity (PPSEN) 1/h, the simulated annealing was used by matching the simulated and observed flowering date. The cultivar coefficients EMFL (the duration from emergence to flowering) photo thermal days (Pd), FLSH (flowering to beginning pod) Pd, FLSD (flowering to beginning seed) Pd and SDPM (beginning seed to physiological maturity) Pd, were adjusted for the simulated and observed data to match the life cycle of the crop. The value for maximum leaf photosynthesis rate (LFMAX) mg CO 2 /m 2 /s, was modified using trial and error to obtain a good agreement between simulated and observed dry matter accumulations. The specific leaf area coefficient (SLAVR) cm 2 /g, the time to cessation of leaf expansion Table 1. Soil physical and chemical properties of pedons used for calibration, evaluation and model applications in the Sudan savanna and northern Guinea savanna of Nigeria. LL lower limit, DUL drained upper limit, SAT volumetric water content at saturation, BD bulk density, OC organic carbon content, N percent Nitrogen content, P available phosphorus.  www.nature.com/scientificreports/ (FLLF) Pd, and maximum size of full leaf (SIZLF) cm 2 , were adjusted to minimize the difference between the observed and simulated leaf growth. The average number of seeds per pod (SDPDV) #/pod, duration of pod addition (PODUR) Pd, maximum weight per seed (WTPSD) g, and seed filling duration for a pod cohort (SFDUR) Pd, were also adjusted to match the simulated and observed pod weight.
The performance of the model was evaluated with the four independent data sets from the P response trials as described in 2.1. Model performance was evaluated using statistical indicators of root mean square error (RMSE) and the index of agreement (d value) 52 between observed and simulated variables. Data used for evaluation included days to flowering and maturity and final grain yield. Statistical evaluation of model performance. The model statistics used to evaluate model performance including RMSE, normalize RMSE (nRMSE) and d statistic 12,15,53 .
P is the predicted, O is the observe, N is the number of observations within each treatment.

J O is the overall mean of observed values
The simulation is considered excellent when the nRMSE is < 10%, good if the nRMSE is > 10% and < 20%, fair if the nRMSE is > 20% and < 30%, and poor if the nRMSE is > 30% 54 . The d statistic is recommended for making cross-comparisons when the d value is both relative and has bounded measures 52 . Sowing was carried out based on the treatments with conditions set to sow when a total rainfall is above 10 mm within the last three days before sowing in each simulation year. Generally, the sowing density was 53.3 plants m −2 , planted at a soil depth of 4 cm. The model was set to supply 40 kg P 2 O 5 at sowing using TSP fertilizer material. The model was set to harvest at harvest maturity. The standard deviations, the mean maximum and minimum yields for 30 years were calculated for each variety and location. The results of simulated grain yield over 30-year period were presented using cumulative frequency plots.

Results
Soil and weather. The results of soil chemical and physical properties for model calibration, evaluation, and application are shown in Table 1. Soil data from the study sites showed wide variability in major properties on the top layer, with soil pH ranging from 4.7 at Zaria to 6.6 at Kano, and the available phosphorus from 2.7 at Kano to 7.0 mg kg −1 at Jagiri. Soil total nitrogen (total N) content was very low across the study areas, ranging from 0.1 g kg −1 at Doguwa to 0.8 g kg −1 at Zaria. All sites, except at Jagiri had low available P below the critical value for soybean of 7 mg kg −155 . Soils in Dambatta, Jagiri and Kano were sandy, with a sand content of above 67% in the top layer, whereas Doguwa and Zaria were loamy soils with a low sand content of below 40%. Soil organic carbon was < 1% (10 g kg −1 ) in all the study sites and ranged from 3.6 g kg −1 at Dambatta to 5.4 g kg −1 at Jagiri. The average bulk density for all the study sites was below 1.6 g cm −3 which was best for root growth and aeration 41 . The soil hydraulic parameters (LL, DUL and SAT) showed high variability among the various soil layers in the study areas (Table 1)  www.nature.com/scientificreports/ Result from long-term weather data of 30-years (1985-2014) monthly variations of rainfall, rainy days (RD), minimum and maximum air temperatures are shown in Table 2. The results revealed that rainfall increases southwards with a mono-modal pattern indicating a short growing season (May-Oct) for Kano and Zaria while Jagiri indicates growing season between April and October.
Model calibration. Table 3 shows the values of calibrated parameters for the three soybean cultivars. The cultivar coefficients for the soybean cultivars TGX1951-3F, TGX1904-6F and TGX1835-10E were estimated through trial and error and comparison of model simulated and observed values. The CROPGRO-Soybean model adequately simulated all the measured parameters of all the varieties using the generated cultivar coefficients (Fig. 1).
The average predicted days to flowering, days to physiological maturity and grain yield of soybean varieties range from 47 to 59 days, 99 to 122 days and 2815 kg ha −1 to 3496 kg ha −1 respectively (Fig. 1). The values of RMSE and NRMSE ranged from 0.89 to 1.95 days and 1.5 to 3.5% for days to flowering, respectively. The values of RMSE and NRMSE ranged from 1.18 to 2.21 days and 1.1 to 1.9% for days to physiological maturity, respectively. For grain yield the RMSE values ranged from 126 to 198 kg ha −1 and NRMSE (%) ranged from 4.5 to 5.7%. The d-index values for days to 50% flowering ranged from 0.8 to 0.93, days to physiological maturity 0.9-0.97, total dry matter 0.6-0.8 and grain yield 0.75-0.85 for all the varieties (Fig. 1). The statistical indices Table 2. Long-term (1985-2014) Monthly variation of rainfall, number of rainy days (NRD), minimum temperature (Tmin) and maximum temperature (Tmax) in Kano (Sudan Savanna), Zaria (northern Guinea savanna) and Jagiri (southern Guinea savanna). The bold represents sowing months used for the simulation.

Kano
Zaria Jagiri    Table 4. Except for grain yield with variety TGX1904-6F, the model simulated days to 50% flowering, physiological maturity and grain yield reasonably well across P levels as indicated by low nRMSE (< 20%) and high d-index values (0.73-0.99) for the three varieties in the two locations. The values of RMSE were low < 2 days for days to 50% flowering and physiological maturity and < 300 kg ha −1 for grain yield for all the varieties in both locations. www.nature.com/scientificreports/    www.nature.com/scientificreports/

Seasonal analysis of soybean grown under different sowing windows. The simulated grain yields
for the ten (10) sowing windows (SWs) using 30-year weather data (1985-2014) for the three soybean varieties are presented in Tables 5, 6, 7. Generally, the simulation outputs revealed that soybean varieties respond to varying SWs and sites across the agro-ecological zones. The results showed higher grain yields for the soybean varieties in northern Guinea than in southern Guinea and Sudan savanna agro-ecological zones. The least grain yields were simulated in the southern Guinea savanna despite higher rainfall than for the other zones. In addition, higher yield was simulated for the variety TGX1951-3F than for TGX1904-6F and TGX1835-10E. In Kano representing Sudan savanna (Table 5), simulated mean grain yields ranged from 453 to 1763 kg ha −1 for TGX1835-10E, 383-1590 kg ha −1 for TGX1904-6F and 474-1714 kg ha −1 for TGX1951-3F depending upon the sowing window (SWs). The result revealed that simulated yield decreases with delay in sowing. The mean simulated grain yield for sowing between SW1 and SW6 was above 1000 kg ha −1 except for TGX1904-6F (SW1-SW5) compared to SW7-SW10 for which the simulated yield was below 1000 kg ha −1 . The most suitable SWs for stable grain yield were SW1 to SW5 for TGX1835-10E beyond which mean simulated yield declined by 13-67%. For TGX1904-6F and TGX1951-3F stable grain yields were simulated for SW1-SW4 beyond which yield decline significantly by 12-70% (TGX1904-6F) and 10-66% (TGX1951-3F) respectively.
The CPD plot in Zaria in the northern Guinea savanna zone showed that sowing TGX1835-10E from early June (SW1) to early-July (SW5) resulted in higher and marginal grain yield ranging from 1434 to 1550 kg ha −1 in 75% of the years simulated (Fig. 3A). However, delaying sowing of this variety to SW6 and SW7 reduced grain yield by 12 and 34%, respectively. At this level of probability, delaying sowing of TGX1835-10E to late July (SW8) and beyond produced yields below 900 kg ha −1 . Sowing TGX1904-6F from SW1 to SW5 and TGX1951-3F from SW1 to SW6 produced the highest grain yield above 1500 kg ha −1 in 75% of the years in Zaria (Fig. 3B,C). Delaying sowing beyond SW5 significantly reduced yield by 10-116% for TGX1904-6F and 18-83% for TGX1951-3F when sowing was delayed beyond SW6.
At Jagiri in the southern Guinea savanna, the CPD plot shows that sowing TGX1835-10E from early-June to early-July (SW1-SW5) will produce a guaranteed yield of over 1000 kg ha −1 in 75% of the years. Sowing this variety beyond early-July (SW5) will reduce yield by over 18-69%. (Fig. 4A). Sowing the variety TGX1904-6F from June 1 (SW1) to late-July (SW8) will produce a yield of 1000-1372 kg at ha -1 with high level of probability (P = 0.75) beyond which yield will reduce by 14% for SW9 and 50% for SW10 (Fig. 4B). For TGX1951-3F sowing from early June (SW1) to early August (SW9) will produce yield of 1041-1420 kg ha -1 but when sowing is delayed to SW10, the yield reduced by 27% at 75% probability (Fig. 4C).

Discussion
Soybean is increasingly becoming an important economic crop in the savannas of northern Nigeria. Its yield is however, limited by poor soil fertility and variable rainfall due to climate change. The determination of optimum crop management practices such as optimum sowing windows can provide useful information for strategic planning in the country. However, this process is time consuming and expensive. The use of a dynamic crop simulation model can be an alternative option to estimate yield levels under different growing conditions. Variation in crop yield associated with genotype, environment and management practices can be explained through the use of crop models 27 .
In this study, the statistics for calibration and evaluation of CROPGRO-soybean model indicated good agreements between the model simulated and observed values for soybean phenology and grain yield. This is indicated by low nRMSE and RMSE as well as high d-index values for all measured parameters. Based on these results, it can be concluded that the model was very robust in predicting the critical phenological growth stages and yield of the soybean varieties. This suggests that the CROPGRO-soybean model is a reliable tool for decision making in the production of soybean in the savannas of Nigeria. The accuracy of CROPGRO-soybean model in the study area supports previous research findings in similar environments in Kenya 25 , Nigeria 56 , and Mozambique 57 in Sub Saharan Africa, which showed good agreement between observed and predicted values for soybean growth and yield using the CROPGRO-Soybean model.
The phenological parameters were accurately predicted with less than 2 days between the simulated and observed values. Wang et al. 58 suggested that predicting days to flowering is among the important stage for model simulation as time between emergence to flowering determines plant size thereby influencing dry matter  www.nature.com/scientificreports/ production and final crop yield. Robertson et al. 59 stated that all genotypic variations affecting leaf area development, total dry matter and grain yield will be captured by the model when the phenology is accurately calibrated. The model also performed well in simulating grain yield of all the varieties in the diverse savannas of Nigeria with higher average d index above 0.95 for each variety across the two locations. Talacuece et al. 57 also reported high d-index values of 0.96 and 0.99 for grain yield of the tropical soybean cultivars in Mozambique. The result of the evaluation shows that the accuracy of prediction of all the measured parameters were better with applied P-rates compared with no P application. This agrees with the findings of Naab et al. 60 who observed high accuracy of prediction with high P-fertilizer rate and lower prediction accuracy under low or no P-fertilizer application when simulating for groundnut growth using CROPGRO-Peanut. The inter-annual variability for early SWs showed low variability ranging from 6 to 15% compared to delayed SWs which are estimated above 15% of the average grain yield, among the soybean varieties and sites except for Kano site. Our results revealed that early SWs simulated high grain yield while delay SWs led to low yield, which varied among the agro-ecozones. For instance, in Kano, the length of optimal sowing period was estimated at 35 days for the soybean varieties. Sowing from June 1 to July 5 (SW1-SW5) could be more favourable to attain reasonable yields (1366-1763 kg ha −1 ) of the extra-early maturing TGX1835-10E, and early maturing TGX1951-3F (1266-1714 kg ha −1 ). Optimum planting window for TGX1904-6F is late June (SW4) when yields of 1261-1590 kg ha −1 can be obtained.
In Zaria (northern Guinea savanna) and Jagiri (southern Guinea savanna) the trend in sowing window was found to be similar with simulated yields showing that, sowing could be extended to July 12. This implies that the length of the optimal sowing window in these two locations is 42 days. Despite the stable and higher rainfall in Jagiri during the growing seasons (Table 2), the simulated average yield in Zaria was higher across the sowing window compared to this location. Generally, the yields in Jagiri were found to be lower which could be attributed to high sand content of the soil resulting to low water holding capacity and nutrient retention. From the results, Zaria was found to be more favourable for soybean production. The soils in Zaria have higher organic matter and clay contents resulting to high water retention (0.543 cm 3 cm −3 ) and high nutrient content. Tofa et al. 15 also simulated higher yield of maize in Zaria in the northern Guinea savanna than in Kano in the Sudan savanna and Abuja in the southern Guinea savanna.
The study showed that in Sudan savanna, there is a high probability that higher yields will be obtained when extra-early (TGX1835-10E) and early (TGX1951-3F) maturing soybean varieties are planted between early June to early-July. Because of short planting window and the uncertainty in rainfall at the beginning of the season coupled with the narrow window of sowing, it is not advisable to plant the medium-maturing variety, TGX1904-6F in Kano in the Sudan savanna. This suggests that farmers in this zone should plant extra-early and early maturing varieties to avoid drastic yield reduction. In northern Guinea savanna, there is a high probability that higher optimum yields will be obtained when all the varieties were sown between early June to early-July except for TGX1951-3F, which also gave optimum yield when sowing was delayed to mid-July because of its high yield potential. TGX1835-10E and TGX1951-3F were found to have less yield reduction than TGX1904-6F when planted beyond mid-July. This is attributable to the moderate amount of rainfall in the northern Guinea savanna and the long growing season, which allows the earlier maturing varieties to complete their growth cycles when planted late in the season. Although the crop performance in the southern Guinea savanna was lower than in the Sudan savanna and northern Guinea savanna probably due to poor soil fertility, the probability of obtaining optimal yield with later sowing windows was high. Average yields of 1 t ha −1 for the extra-early maturing TGX1835-10E and 1.38 t ha −1 for the early-maturing TGX1951-3F can be obtained if planting is delayed to July 12 while an average yield of 1.3 t ha −1 can be obtained if planting of TGX1904-6F is delayed to July 5. The results also indicated that late sowing beyond mid-July is risky and can leads to a higher yield reduction or crop failure in all the agro-ecologies.
For all the agroecological zones, sowing soybean beyond mid-July significantly reduced grain yield. This may be due to drought stress arising from moisture deficit before the soybean crop complete its life cycle. Rainfalls towards the end of the growing season in the Nigeria savannas are not stable 15 . The rains can cease in September or October before the crops reach maturity which can significantly reduce the yield and yield components of soybean. Drought stress has been reported to significantly reduce the yield of soybean. Therefore, information on suitable planting window that will help farmers plant their crops and avoid end of season drought will be useful.
Using the CERES-Maize model, Tofa et al. 15 reported reduced grain yield of maize as a result of delay in sowing dates beyond late July for medium-maturing maize in the Nigeria savannas. Beah et al. 61 used the APSIM model to simulate optimum sowing window of early and medium-maturing maize varieties in the Nigeria savannas. Their results showed that for optimum grain yield for both early and medium maize varieties, sowing should be done between June 15 to 28 in all the agro-ecologies.
Sowing date is an important factor influencing soybean growth and yield. The growth and yield responses of soybean to sowing date depend on the cultivar, environment and management practice 62 . There was variation in the performance of soybean among the agro-ecologies in the study area. This could be attributed to variation in the maturity periods, soil and weather conditions (temperature, rainfall and solar radiation) in the study area. Lin et al. 63 stated that soil, climate and crop variety are the most important factors that affect crop production. For all the varieties, averaged mean grain yield across sowing windows were generally higher in the northern Guinea savanna than the other agro-ecologies irrespective of the length of growing season. This is probably due to the good soil conditions in this agro-ecology where the clay and organic carbon contents are higher (Table 1) than in the other agro-ecologies where the soils were sandy. Due to the variability in onset of rainfall in the Nigeria savannas, sowing window recommendations should be made with caution. Most often establishment of rains vary significantly between first week of June to early July due to climate change. This variability influences commencement of sowing of crops in the region. www.nature.com/scientificreports/

Conclusion
The DSSAT CROPGRO-Soybean model was calibrated and evaluated for the simulation of sowing windows of three tropical soybean varieties in the Nigeria savannas. The model calibration and evaluation results showed that there was good agreement between the simulated and observed values for phenology, growth, and yield parameters of the soybean varieties This suggests that the CSM-CROPGRO-Soybean model was able to accurately simulate the growth and yield of soybean in the Nigeria savannas. This study also showed the potential of the model to serve as a tool for determining optimum sowing window for soybean in the savannas. The simulation results show significant differences among the agro-ecologies and the soybean varieties in terms of grain yield. The results revealed higher yields are simulated among the soybean varieties in northern Guinea than in southern Guinea and Sudan savanna agro-ecological zones probably due to the high clay content in the northern Guinea savanna leading to high water and nutrient retention capacity. The least grain yields were simulated for the southern Guinea savanna than for the other zones despite higher rainfall and longer growing season probably due to the poor soil fertility in this zone. In addition, higher yield was simulated for the variety TGX1951-3F than for TGX1904-6F and TGX1835-10E in all the agro-ecozones. Our results revealed that length of sowing windows is dependent on agro-ecology and soybean variety. Sowing from June 1 to July 5 (SW1-SW5) produced optimal yield of TGX1951-3F and TGX1835-10E in Kano in the SS zone. Delaying sowing beyond July 5 will results in significant yield loss for all the varieties. The cultivation of TGX1904-6F is not recommended for the Sudan savanna zone because of its late growing cycle. In Zaria (northern Guinea savanna) and Jagiri (southern Guinea savanna) the simulated results show that, sowing could be extended to July 12 for all the varieties. Generally sowing beyond July 12 for all the varieties significantly reduced grain yield in all the agro-ecozones which may be due to drought stress at the end of growing season which coincided with grain-filling period.

Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request. www.nature.com/scientificreports/