On-farm demonstration trials were conducted for two years (2012–2013) in three agroecological zones of northern Nigeria (9° 05’ to 11° 54’ N and from 6° 38’ to 8° 17’ E), particularly covering the Sudan Savanna (SS), northern Guinea Savanna (NGS), and southern Guinea Savanna (SGS) regions ( Figure 1 ). Long-term rainfall ranges from 600 to 1,000 mm (mean of 744.5 mm) in the SS, from 1,000 to 1,300 mm (mean of 1,179 mm) in the NGS, and from 1,100 to 1,400 mm (mean of 1,270 m) in the SGS (Ishaku and Majid, 2010; Umar and Bako, 2019). The extracted cumulative precipitation, average minimum, and maximum temperature are reported in Table 1 .

A total of 350 on-farm demonstration experiments were conducted across three agroecological zones in Nigeria. Those on-farm experiments were conducted using a randomized complete block design (RCBD), considering each farmer’s field as a replicate. Each plot measured 6 × 4 m², and 350 experimental fields were established in the three agroecological zones. The seeds of a soybean variety were hand-drilled at 2 cm depth at 0.75 m between rows and 0.05 m within rows, recovered with soil, and thinned to 5 cm distance between plants after 15 days to maintain a uniform population density of 266,667 plants per hectare. Four treatments (Trt) were evaluated: Trt 1: Control (farmer practice) without inoculation and no P application (non-treated); Trt 2: P-fertilizer application at 20 kg P ha⁻¹ (P) in the form of triple superphosphate (TSP) (Ronner et al., 2016); Trt 3: Rh inoculation at 5 g kg⁻¹ seed; and Trt 4: Combined application of Rh and P. Soybean seeds were treated with a commercial Rh inoculant (legume-fix) containing 10¹⁰ bacteria cells of B. japonicum strain 532c per gram of solid before sowing. The Rh inoculant was coated onto the seeds with gum arabic as a sticker and air-dried for 30 min under shade before sowing. The P fertilizer was applied by hand-broadcast within rows at sowing. The trained extensionists and farmers managed the experimental plots subsequently. Weed management was carried out through regular hand weeding every 30 days at intervals in consultation with the extensionist. Farmer groups and rural community members regularly visited the experimental plots during field days organized at the vegetative growth stage to demonstrate the treatment differences with the support of Village Promoter Agents (VPAs).

Village promoter agents (VPAs) were recruited by the area manager staff of the Notore Limited group in Nigeria to monitor the trials. The VPAs were local farmers based in the villages with previous working experience in monitoring demonstration trials, good communication skills in Hausa local language with farmers, and an interest in participatory technology dissemination to rural farmers. Notore Limited is an established private sector company based in Nigeria with a recruited area manager who daily supervises the work of VPAs in the deployed areas. Each VPA received adequate training at the early stages before the on-farm demonstration establishment of trials regarding the handling of rhizobial inoculants, coating seeds, and P applications in the respective areas. Twenty-five (25) VPAs were trained for handling rhizobial inoculants, P fertilizer applications, and general monitoring of the trials. Collaborative farmer groups and community contact persons for participatory research were registered and trained. Identified fields to establish the demonstration trials were delimited, and the geographical coordinates of each field were recorded ( Figure 1 ). Thereafter, farmer groups were subsequently trained to handle rhizobium inoculant for seed coating techniques in the respective locations, ensuring limited risks of cross-contamination. The sowing order was control, P treated, Rh inoculated, and Rh + P fertilizer plots, respectively. Farmers’ groups and VPA regularly visited the demonstration plots at various growth stages, from sowing to harvest.

Three improved soybean varieties of different maturity groups developed by the International Institute of Tropical Agriculture (IITA) in Nigeria and released by the Nigeria National Research System (https://www.seedportal.org.ng) were used for the trials. The varieties were derivatives of a tropical G. max (TGx) series of cultivars bred for their promiscuous nodulation in a wide range of environments. The soybean varieties TGx 1987-62F (reg.: NGGM 10-19) and TGx 1987-10F (reg. NGGM 10-18) were released in 2010 and are resistant to Cercospora leaf spot and bacteria pustules. The TGx 1987-62F variety is a medium maturity group (90–110 days to maturity) and was used in demonstration plots in NGS agroecology. This variety had an average grain yield of 2.1 t ha⁻¹ in on-station rainfed trials in Nigeria (https://www.seedportal.org.ng). The soybean variety TGx 1987-10F is also highly resistant to Cercospora leaf spot and bacterial pustules, with a yield range of 1.5–2 t ha⁻¹ under rainfed conditions. It is an early maturity variety (90–95 days to maturity) and was used in the experimental plots in the SS agroecology. The third variety, TGx 1448-2E, was released in 1992 and registered in 1996 under the Nigerian national code NGGM-96-15. It has an average grain yield of 2.4 t ha⁻¹, is frog-leaf resistant and belongs to the late maturity group (115–120 days); this variety was used in the SGS agroecology.

A logical framework for the model’s implementation, calibration, and training is displayed in Figure 2 . A conditional inference regression RF machine learning approach was implemented for predicting yield variability from each agroecological zone. The conditional RF captures the linear and non-linear effects of the estimator variables (soil, weather, and factor variables) on the yield response and quantifies the marginal effect of individual inputs. The inference regression RF is a powerful non-parametric decision ensemble learning method for regression classification that operates by constructing multiple artificial trees to predict and fit response variables without overfitting during the training process. To assess the model’s performance, the root mean square error (RMSE), training coefficient of determination (R²), and validation RMSE were computed for the datasets of each agroecoregion. The predicted values against the actual and variables of importance for each model were visualized. The normalized RMSE (NRMSE) was calculated using the formula:

(Eq. 2, Alabi et al., 2022),

where y_max and y_min are the maximum and minimum yield.

General statistical analysis was carried out for the three agroecological zones), and yield prediction using machine learning with 68 constructed explanatory variables and a single yield response variable was carried out. The extracted soil properties used to predict yield were tested for normality, skewness, and the kurtosis test, which reported a P value of<0.05. Descriptive statistics (maximum, median, and minimum) were computed for the yield variable. A one-way analysis of variance (ANOVA) was carried out to assess the effect of treatment on grain yield change using the JMP statistical software (JMP, 2019). The treatment mean differences were analyzed using the least significant difference (LSD) at 5% and 1% of the level of significance when the Fischer (F) value was significant from the ANOVA (P<0.05). Levels of significance are given by “ns” (not significant, P >0.05), *P<0.05, **P<0.01, and ***P<0.001. The RF analysis was computed using R Studio version 2022.12.0 (R version 4.2.1).

Descriptive statistics of extracted soil properties used for model training and validation are presented in Table 2 . Averaged across the agroecological zones, the available P ranged from 6.0 to 10.0 mg kg⁻¹ and from 6 to 9 mg kg⁻¹ in the NGS, with a right skew data distribution range ( Table 2 and Table S1 ). Similarly, for the three agroecological zones, the pH ranged from 5.1 to 6.1, 5.5–6.0 in SS, 5.3–6.1 in NGS, and 5.1–5.8 in SGS, with a left (negative) skew data distribution ( Table S1 ). The range of clay contents varied from 16% to 32% for all agroecological zones: 18%–30% in SS, 16%–30% in NGS, and 19%–32% in SGS. Similarly, the silt contents ranged from 43% to 67% across the three agroecological zones: 45%–60% in the SS, 43%–67% in the NGS, and 46%–61% in the SGS agroecology. Other extracted soil property summary statistics, such as their skewness and kurtosis values are reported in Table 2 and Table S1 .

A one-way ANOVA testing the effect of the treatment on grain yield was highly significant for the SS (F = 65.4, P<0.001), NGS (F = 86.6, P<0.001), and SGS (F = 127.3, P<0.001) agroecological zones, respectively ( Figure 3 ). The yield data for the combined application of Rh + P fertilizer was normally distributed in the SS, right-skewed in the NGS, and left-skewed in the SGS agroecological zones ( Figures 3A–C ). The soybean yield of the Rh + P fertilizer treatment was always higher than that of the control treatment in the three agroecological zones of northern Nigeria ( Figure 3 ). Average across all on-farm demonstration yield increments of 128%, 111%, and 162% were observed under the Rh + P combination compared to the control in SS, NGS, and SGS, respectively, and the overall increment for all agroecological zones of the established demonstration trial was 134% ( Figures 3A–C ). The average grain yield for the control treatment was the lowest in SGS compared to the SS and NGS agroecologies ( Figures 3A–C ). When inoculated with Rh alone, soybean yield was always higher in the Rh treatment than in the control treatment in the respective agroecological zones ( Figures 3A–C ). Similarly, the yield of the P fertilized treatment was higher than the control in the SS, NGS, and SGS agroecological zones, respectively ( Figures 3A–C ).

The results from RF models of data from the three agroecological zones and separately from each agroecological zone are presented in Table 3 and Figure 4 with their NRMSE and R² values. Among the three agroecological zones, NGS provided the highest trained R² value of 0.74 ( Table 3 ). The trained NRMSE for NGS samples was 8.8 ( Table 3 ). The validated R² and NRMSE were 0.52 and 6.0 ( Table 3 ). For the SGS, the trained R² was the lowest (0.58) and the trained NRMSE was the highest (12.7) compared to the SS, NGS, and overall samples ( Table 3 ). The validated R² and NRMSE were 0.53 and 8.9, respectively ( Table 3 ). For the overall dataset, we found trained RMSE and R² values of 8.8 and 0.64, while the validated NRMSE and R² were 6.2 and 0.57, respectively ( Table 3 ). The highest trained NRMSE was observed in SGS samples, and the reported R² was 0.58 ( Table 3 ). The validated NRMSE and R² for SGS samples were 9.9 and 0.56 ( Table 3 ). The biplots of the predicted and observed samples showed more dense points in the overall datasets and the NGS samples ( Figures 4A, C ).

The input variables of importance to predicting yield in the three agroecological zones are presented in Figure 5 . For the three agroecological zones, the top five variables (based on importance) for predicting yield include the combined application of Rh + P fertilizer, year-to-year growing conditions, silt content in the soil, rhizobium inoculation, and the minimal temperature in the month of August ( Figure 5A ). The top five predicting variables of importance to soybean yield in the Sudan Savanna were crop management practices, combined application of Rh and P fertilizer, rhizobium inoculation, sand content in the soil, and soil available P ( Figure 5B ). The top six predictor variables for yield in the NGS were Rh + P combination, P fertilizer, year-to-year soybean cultivation, crop management practices, P fertilizers, and silt content in the soil ( Figure 5C ). Similarly, the RF model found crop management practices, Rh + P combination, P fertilizer, year-to-year cultivation, and effective cation exchange capacity as the top five yield predictor variables in SS ( Figure 5D ).

The simulation using the IMPACT model showed that soybean yield increases through the combined application of Rh and P fertilizer will reduce national trade through the less imports and result in currency savings in Nigeria by 2050. We implemented the model using an average yield increase of 134% (all agroecological zones) and 111% in the NGS and two scenarios of adoption rates: low (35% adoption rate) and high (75% adoption rate) ( Figure 6A ). The model was implemented using the dataset from the NGS agroecological zone because it had the highest prediction and accuracy from the RF model. Considering the average yield increase performance of 134% (averaged across three agroecological zones), results from the IMPACT model scenario showed that the quantity of soybeans imported in the country can be reduced by −10% (35% maximum) and by −22% (75% maximum adoption scenario) if the combined application of Rh and P fertilizer technology is adopted ( Figure 6B ). With an average yield increase of 111% from the combined application of Rh + P (observed in NGS), importation can be reduced by 8.4% (under a low adoption scenario) and by 18% (under a high adoption scenario) by 2030 in the country ( Figure 6C ).

A series of on-farm demonstration experiments showed soybean yield increased through the combined application of Rh + P (always higher in under-treated conditions than in non-treated conditions), irrespective of the agroecological zones and soil types. In the absence of Rh inoculation, P fertilizer, or Rh + P combination, the average yield in control was 1,084 kg ha⁻¹ in the NGS sites, while the yield increased in the Rh + P inoculated plants by 2.3-, 2.1-, and 2.6-fold as compared to the non-treated plants ( Figure 1 ). Earlier work demonstrated increased soybean yields with the combination of Rh inoculants and P fertilizer in West African soils. The observed higher yields of 1,188 kg ha⁻¹ in SS, 1,203 kg ha⁻¹ in NGS, and 1,397 kg ha⁻¹ in SGS for the Rh + P application in West Africa (Ronner et al., 2016; Ulzen et al., 2018; Buenor et al., 2022). The authors reported an average yield increment of 815 kg ha⁻¹ from the combined application of Rh + P, along with an increment in farmers’ net profit. Several factors accounted for the higher yield under the Rh + P application, such as regular field monitoring by Notore extension agents, high-performing rhizobia microbes, and careful crop management by the engaged farmers during the implementation of the project activities. It is indicated that education, research, and extension in agriculture remain the vehicles to achieve sustainability in the modern food system. The NGS agroecological zone showed a favorable niche for rapidly increase of soybean yield using appropriate management interventions for food security in Nigeria and the sub-region. This high yield can be explained by suitable rainfall and soil fertility conditions. Suitable conditions for optimal soybean production require about 1,000 mm of water in rainfall-based production systems. The SS agroecological zone is a more drought-prone area that often limits yield. The SGS agroecology is the domain of acidic soils and low-P in Nigeria, which are limiting conditions to a high soybean yield (Jemo et al., 2015).

Farmer-managed participatory interventions and extension agents’ engagement certainly facilitated the timely establishment of on-farm demonstrations and weeding at critical crop developmental stages, inter alia. Thus, investments in information/knowledge dissemination, input fertilizers, and other technologies are crucial for the sustainable intensification of SSA.

Rhizobia inoculants are perishable commercial products, and this project secured standard and high-quality Rh inoculum with stable self-life from Legume Tech, UK. The inoculant was formulated with bacterial cell concentrations above 10¹⁰ cells g⁻¹ with lyophilized B. japonicum that was kept in the Notore stores and delivered to VPAs only a few days before soybean sowing. It is worth mentioning policy decisions aiming to accelerate the manufacturing units, the marketing of high-quality rhizobia inoculants with a satisfying minimum of bacteria cell concentration of 10⁹ cells g⁻¹, and the longer shelf-life of rhizobium to accelerate soybean production in Africa, as shown in the success study developed in Brazil (Bomfim et al., 2021). Other incentive measures to increase soybean production in SSA are the institutionalization of P fertilizers and their dissemination to rapidly address pressing food security issues.

Accurate yield prediction is of great importance to global food production. Using digitally soil-mapped properties and extracted weather and management variables, we predicted yield for the three agroecological zones using the RF machine-learning algorithm tools. The highest training R² (0.74) was achieved using samples from the NGS sites ( Table 3 ). Alabi et al. (2022) predicted soybean yield using the vegetation index and soil texture information in the RF model. We lacked a comparable study on predicting soybean yield using soil properties in Nigerian Savanna conditions. The results of this study showed that NGS is the predominant agroecology for soybean production in terms of the required soil properties for growth. A better yield prediction in NGS can be explained by symmetrical data distribution (−0.42–0.58) of the extracted soil properties in the NGS agroecological ( Table S1 ). The implications are that the soil and climatic conditions of NGS are favored for better growth and less drought effect during the growth stage. Bebeley et al. (2022) evaluated long−term seasonal analysis of soybean yield among the same three agroecological zones for deriving optimal sowing times for different soybean varieties, where yields were simulated in the NGS sites compared to other agroecological zones. In this study, the low R² values of the training dataset from SS and SGS agroecological zones could be attributed to normal data distributions of yield variables, making the yield data from SS and SGS less reliable for their good prediction using soil properties and extracted variables.

Predictions of soybean yield using datasets from the three agroecological zones (i.e., SS, NGS, and SGS) reported that the Rh + P combination has the topmost importance to increase yield under challenging environmental conditions. Also, P-fertilizer and Rh inoculation alone were also among the top variables in importance, but their relative importance varied depending on the agroecology. The available P of the soils was revealed as an important variable for soybean yield in the SS. The results imply that the supply of P fertilizers is largely required if farmers are to grow soybeans in the SS, SGS, and NGS soils. Other important soil properties, such as silt and sand contents and ECEC, were also predictors of soybean yield ( Figure 5 ). The present study extracted an average silt content of 53.3% and a sand content of 19.9% ( Table 2 ). Apart from precipitation, temperature, and macro- and micronutrients, crop yields are also dependent on soil properties such as soil texture that influence water retention at the root zones and improve nutrient diffusion and crop yield (Huang et al., 2021). Fine-textured or silty loam soil provides a higher water holding capacity and more resistance to plant water uptake in wet conditions compared to sandy soils and can be poorly drained and susceptible to waterlogging, which can lead to denitrification and yield loss (Huang et al., 2021). The interactions between physical soil properties and soybean yields are not well quantified across the agroecological zones of Nigeria and deserve further research and investigation. Such information is necessary to design key indicators to improve soil structure and carbon stocks to increase soil availability for water storage and nutrient retention and promote energy conservation around the soybean root zones.

The minimum air temperature recorded in August was among the top five predictors of importance to soybean yield. These temperatures correlated with the soybean pod filling stages and were in the range of 17–20°C, which was above the air temperature (15°C) reported to inhibit seed filling. The optimum temperatures for soybean are 15–22°C at the emergence stage, 20–25°C at the flowering stage, and 15–22°C at the maturity stage, and seed yield and yield formation of soybean are frequently reduced by temperatures below 15°C and above 30°C (Zhang et al., 2016).

In the present study, we observed that the R² for actual and predicted yields was less than 60% ( Table 3 and Figure 3 ). The results imply that all the aggregated soil and weather variables partly explained the observed yield variation. Other biotic or abiotic factors that were not aggregated in the independent variables, such as competitions with native species that were incompatible with the introduced rhizobia, impaired the nodulation and affected yield. On the other hand, the rate of P applied was only 20 kg ha⁻¹, which was insufficient to achieve optimal soybean yield. Future studies to address the “non-compatible hypothesis” and the optimal P rate for each agroecological zone will deserve further research investigations.

Linking biophysical and economic models is important in a world facing the complexities of increasing crop production under pressing climate change threats (Islam et al., 2016). We conducted a two-scenario analysis of the Rh + P combination treatment, evaluated the possibility of adoptions that could take place in the future, and assessed the impacts on Nigerian food security and soybean trade. Results from the IMPACT model showed that the Rh + P combination has the potential to reduce the current soybean importation demand by a maximum and reverse the importation trend from 2029 if maximally adopted. The scenario analysis through the adoption of promising agricultural technology on yield by 2050 has been implemented in several commodities, including rainfed maize in Africa, irrigated rice in South Asia, rainfed potato in rainfed sorghum in India, and rainfed groundnut in Africa and Southeast Asia (Islam et al., 2016). In many of these studies, the authors observed that promising technologies tested in many regions/or ecologies showed a partial to complete offset of the deleterious impacts on yield through the adoption of technology (Islam et al., 2016). In the present study, we have opted for large adoption as many demonstrations, including many participating farmers, in various steps of soybean production and training in inoculation technology with the goal of rapid adoption, were implemented to increase soybean production and improve food security.

Possible gaps and limitations in the modeling for agricultural systems as presently conducted in this work are the bias generated from the model tools and environmental conditions such as soil and climate that are heterogeneous, especially in Sub-Saharan Africa. These gaps certainly decrease statistical robustness and bias upward the values obtained for decision variables, which could often be unachievable in the real world. To avoid these aggregated biases resulting from the model, the natural conditions of the independent variables were tested for data homogeneity. To minimize the biases from human heterogeneity at on-farms, we trained the engaged farmers to use Rh inoculant and P fertilizer technology, and VPs supervised their work regularly before trial establishments in the respective areas. Overall, the present results underscore the fact that innovative interventions should be tested across a wide range of AEZ, capturing all possible variables for wider adoption. Our results strongly suggest that the application of rhizobium inoculation is affordable, and represents a low-cost agricultural intensification strategy when combined with P fertilization and VPA technical assistance.