Maize is a major crop in Sub-Saharan Africa (SSA) that is grown under diverse growing conditions. Mean grain yields are low, generally 10–30% of potential rainfed yield (Wortmann et al. 2016; www.yieldgap.org). But annual variation in grain yield is high, often with coefficients of variation (CV) greater than 40% while the CV for irrigated maize in the US is typically about 7% (www.yieldgap.org). Numerous biotic and abiotic constraints contribute to the low means and high CVs of maize yield in SSA and the most limiting constraint for a field typically varies by year. Among the constraints is the inadequate availability of some soil nutrients essential to crop growth and the relatively low capacity of financially constrained smallholder farmers to manage constraints. The mean yield response to applied nutrients is limited by other biotic and abiotic constraints and these constraints contribute to high response CV.

The goal of the OFRA project was to improve farmer profitability with respect to fertilizer use, especially for financially constrained smallholder farmers (Kaizzi et al. 2017). Crop nutrient response functions, which are essential to the efficient application of economics to fertilizer use decisions, were developed from past and recent field research results using a curvilinear to plateau asymptotic response function of the form Y = a − bcr where a is the projected yield at plateau, b is the estimated maximum yield gain resulting from application of the nutrient, c is a curvature coefficient and r is the rate of nutrient application. The database had 5500 geo-referenced crop nutrient response functions at the time of this analysis, 33% of which were for maize and the remaining for 33 other crops (Table 1) (http://agronomy.unl.edu/OFRA). Results from 16 countries were included. Forty, 37 and 23% of the results were from 191 publications, recent OFRA supported research and other sources, respectively, and 48% were from research done in 2010 or later. Background information for the trials such as soil test information is included in the database when available. The 1817 maize response functions included N (43%), P (29%), K (9%), S (3%) and Zn (1%) treatments. The points in Fig. 1 represent research sites for which maize nutrient response functions were determined on a site-year basis but most sites have numerous years of results and corresponding individual response functions.

Table 1 Numbers (n) of compiled nutrient response functions for sub-Saharan Africa by crop and country
Full size table
Fig. 1
figure 1

Distribution of sites with research results used to determine maize response to applied nutrients

Full size image

It is expected that results from areas of homologous growing conditions can be used to make decisions at a similar location of interest (Aiken et al. 2001). This can be done according to established zones or dynamically through geospatial queries based on environmental criteria. Climate variation is captured in Harvest Choice’s agroecological zonation (HC-AEZ) (HarvestChoice 2010) (Fig. 1) and in the narrower more specific recommendation domains of the Global Yield Gap Atlas (GYGA-RD) project (http://wwws.yieldgap.org/web/guest/download_data) (Van Wart et al. 2013). Countries have delineated their own AEZs (Wortmann et al. (2017), http://agronomy.unl.edu/OFRA) often incorporating local soils and physiographic information.

OFRA-IT (Wortmann and Milner 2015; Wortmann et al. 2017) is an ArcGIS 10.3 ArcPy script tool. It identifies crop nutrient response functions associated with areas that share similar growing conditions to those found at a point of interest (http://agronomy.unl.edu/OFRA). The tool defines similarity by querying seven rasters: aridity index (AI) (Zomer et al. 2007, 2008); temperature seasonality (TS) (Hijmans et al. 2005), elevation as a proxy for annual growing degree day accumulation (Lehner et al. 2008); distance from the equator (as degrees latitude times 1000) to distinguish between bimodal and unimodal precipitation regimes; soil pH (as pH times 10); sand content; and organic content (SOC) (Hengl et al. 2014, 2015). The three soil properties were for the 5–15 cm depth. The OFRA-IT default queries were determined in agronomic consideration of environmental effects on crop adaptation and distribution. The default queries were: if the selected point’s AI value is <6000, then similarity equals the selected AI value ±1000, else similarity equals AI values >5000; temperature seasonality similarity equals the selected value ±1000; if the selected SOC value is ≤35 g kg−1, then similarity equals the selected SOC value ±10, else similarity equals SOC > 25; if the selected pH × 10 value is <54, then similarity equals the selected pH × 10 value ±4, else similarity equals pH × 10 values >50; if the selected sand value is >75, then similarity equals the selected sand value ±20, else similarity equals sand values <80; if the selected elevation value is >700 m, then similarity equals the selected elevation value ±250, else similarity equals elevation <1000; and distance from equator (|degrees| × 1000) similarity equals the selected distance value ±3000. Research locations that meet all the criteria fall in the inference, or recommendation, domain of the selected point.

The objectives of this research were to: compare the use of HC-AEZ, GYGA-RD, and OFRA-IT inference domains for determining representative maize nutrient response functions; apply spatial information to determine location specific S and Zn response functions; and to evaluate the sensitivity of OFRA-IT criteria ranges.

Materials and methods

The georeferenced maize crop nutrient response functions associated with each of the study’s HC-AEZs, GYGA-RDs and OFRA-IT inference domains were extracted using ArcMap 10.3. Due to the number and distribution of maize response functions, analysis was restricted to N, P and K and to four tropical HC-AEZ and four GYGA-RD. The four HC-AEZ were warm semi-arid (312), warm sub-humid (313), cool sub-humid (323), and cool humid (324) (Table 2). The four GYGA-RDs were 6701, 7501, 9501, and 10,301 where the first one or two numbers (6, 7, 9, 10) represent annual growing degree day accumulation, the next number (7, 5, 5, 3) represents AI with lower numbers representing more aridity, and the rightmost number (1) represents TS (Van Wart et al. 2013). Nine sites were selected within the study’s HC-AEZ and GYGA-RD boundaries for determination of OFRA-IT inference domains (Table 3).

Table 2 The number of response functions available for selected Global Yield Gap Atlas recommendation domains (GYGA-RD) and Harvest Choice agroecological zones (HC-AEZ)
Full size table
Table 3 Locations used for query with the OFRA Inference Tool
Full size table

The sensitivity of OFRA-IT query criteria was evaluated by comparing the representative response functions determined from different ranges of criteria. Wider and narrower ranges resulted in larger and smaller inference domain, respectively. The three sets of plus and minus values, relative to the site value, were: 800, 1000, and 1200 for both AI and TS (e.g. for site AI of 7000, the respective ranges would be 6200–7800, 6000–8000, and 5800–8200 for narrow, intermediate and wide queries); 8, 10 and 12 g kg−1 SOM; 0.3, 0.4, and 0.5 for pH; 16, 20, and 24 g kg−1 sand; 200, 250, and 300 m elevation; and 2, 3, and 4 degrees latitude. The analysis was done at Farako-ba, Achefer, Wenchi, Siaya, and Kapchorwa (Table 3).

The yield response for each selected response function was determined for six nutrient levels using 25, 5, and 10 kg ha−1 increments for N, P, and K, respectively, using Excel. Non-linear regression analyses were done for the datasets created by the HC-AEZ, GYGA-RD, and the OFRA-IT selection methods according to Y = a − bcr as defined above using Statistix 10 (Analytical Software, Tallahassee FL). Since the analysis was for response to applied nutrient only, coefficient a and b were equal. Standard errors and standard deviations of the b and c coefficients, the estimated R2 values, and differentiation of response functions were considered in the comparisons of selection methods and criteria ranges.

Results

Nutrient application did not result in increased yield in some cases. The percent of cases with yield changes for applied N, P, K, S, and Zn, were respectively: for increases of >0.1 Mg ha−1, 87, 69, 57, 87, and 84%; for positive or negative yield changes of <0.1 Mg ha−1, 12, 27, 24, 13, and 11%, and for yield decreases of >0.1 Mg ha−1, 1, 4, 18, 0, and 5%. The frequent negative response to K is not well understood but the negative responses often occurred even with rates of 10 kg ha−1; salt effects of KCl placed too close to the seed may have been a factor.

Use of soil test results may improve prediction of response to applied nutrients. Soil pH of <5.3, 5.3–7.3, and >7.3 occurred in 25, 74, and 1% of the cases. Soil organic matter of <13, 13–25, and >25 mg kg−1 occurred in 23, 22, and 54% of the cases. Soil Mehlich-3 and Bray-1 P distribution include 80 and 20% of cases with <15 and >15 mg kg−1, respectively, with many of the high P sites being from research centers. Exchangeable K was >130, 80–130, and <80 mg kg−1 for 14, 76, and 12% of the cases, respectively, with most cases of <80 occurring with sandy soils in the Sahel. The low soil pH may inhibit response to applied nutrients, especially in cases of Al toxicity. Soil organic matter may contribute to prediction of response to N and other nutrients but the very low levels are mostly from areas of severe soil water deficits and a large proportion of soil organic matter is resistant to decomposition as indicated by evidence of low release of N (Kaizzi et al. 2012, 2013). The probability of low soil test P with smallholder annual crop fields is very high unless near the household and livestock holding areas. Exchangeable K is high enough on most smallholder fields that not much response to applied K should be expected in most maize production areas of SSA. Therefore, soil test results may not account for much variation in crop nutrient responses.

Comparison of HC-AEZ, GYGA-RD, and OFRA-IT inference domains

The OFRA-IT sites, Wenchi and Mlingano, are in the same GYGA-RD (9501) and HC-AEZ (313) although separated by about 4700 km (Table 3). The inference domain selection for each was associated with response functions from Ghana, Nigeria and Tanzania, but Wenchi’s inference domain also encompassed a few functions from Mali and Togo. The remaining 7 OFRA-IT sites are located in unique GYGA-RD and HC-AEZ combinations. The Nyakunguru and Siaya OFRA-IT queries selected response functions from the same four countries with some much overlap in response functions.

The overall potential yield response to applied N (coefficient b) was 1.38 Mg ha−1 but values ranged from 0.91 to 2.28 Mg ha−1 for GYGA-RD 9501 and the Achefer inference domains, respectively (Table 4). Mlingano and Wenchi, both under GYGA-RD (9501) and HC-AEZ (313), had b values of 0.99 and 1.14 Mg ha−1, respectively. Bougouni, Mlingano, Nyakunguru and Wenchi were in HC-AEZ 313 which had a b value of 1.28 Mg ha−1 while the respective values determined from the OFRA-IT queries were 1.86, 0.99, 1.25, and 1.14 Mg ha−1. Similarly, Mwanza, Nyakunguru, and Siaya were in GYGA-RD 7501 which had a b value of 1.60 Mg ha−1 while the respective values determined from the OFRA-IT queries were 2.14, 1.25, and 1.47 Mg ha−1. The overall coefficient c value was 0.970. The c value was relatively low for the GYGA-RD 6701, HC-AEZ 324, and Kapchorwa inference domains. The GYGA-RD had greater differentiation compared with HG-AEZ, both for response at low and at high N rates (Fig. 2a). GYGA-RD 6701 and GYGA-RD 10301 had similarly steep yield response at low N rates. Kapchorwa, Nyakunguru and Siaya which were within 1.5 degrees of the equator had low c values but only intermediate b values for N response compared with higher latitude query points. This indicated more yield response, N uptake and N recovery efficiency at low N rates for low latitudes with bimodal rainfall distribution compared with higher latitudes. However, high latitude Achefer and Mwanza with high b values, also had large responses to low N rates (Fig. 2b). The mean R2 values were 31, 23, and 33% for GYGA-RD, HC-AEZ, and OFRA-IT inference domains, respectively. The mean standard deviation for b was 1.00, 1.09, and 0.96 and the mean standard deviation of c was 0.056, 0.063, and 0.051 for the GYGA-RD, HC-AEZ, and OFRA-IT inference domains, respectively. The maximum differences in b values were 8.6, 5.7 and 10.4 times the mean associated SE for GYGA-RD, HC-AEZ, and OFRA-IT inference domains, respectively.

Table 4 Maize N response function results for selected Harvest Choice (HC) AEZs, Global Yield Gap Atlas (GYGA) recommendation domains and OFRA Inference Tool domains in Sub-Saharan Africa
Full size table
Fig. 2
figure 2

Maize response to N by inference domains in Sub-Saharan Africa

Full size image

The overall potential yield response to applied P (coefficient b) was 0.65 Mg ha−1 but values ranged from 0.29 to 1.85 Mg ha−1 for HC312 and Achefer, respectively (Table 5). Bougouni, Mlingano, Nyakunguru and Wenchi had b values of 0.32, 0.59, 1.10, and 0.67 Mg ha−1, respectively, although all were in HC313 which had a b value of 0.61 Mg ha−1. Similarly, Mwanza, Nyakunguru, and Siaya were in GYGA7501 which had a b value of 0.52 Mg ha−1 while the respective OFRA-IT values were 0.50, 1.10, and 1.14 Mg ha−1, respectively. The overall coefficient c value was 0.90. The c value was relatively low for GYGA7501 but within the SE of the mean. The GYGA-RD had less differentiation compared with HG-AEZ inference domains for responses at both low and high P rates (Fig. 3a). The differences in response were much greater for the OFRA-IT compared with GYGA and HC domains ranging from 0.32 to 1.52 Mg ha−1 with 30 kg ha−1 P applied. With the exception of GYGA6701, HC324, and HC312, responses to P were very similar for GYGA-RD and HC-AEZ. As with N, the Achefer query resulted in a great response to P (Fig. 3b). The three low latitude OFRA-IT sites had the next greatest responses to P. The mean R2 values for P compared with N response were less and were 16, 11, and 14% for GYGA-RD, HC-AEZ, and OFRA-IT inference domains, respectively. The mean standard deviation for b was 0.80, 0.95, and 1.10 and the mean standard deviation of c was 0.28, 0.46, and 0.39 for GYGA-RD, HC-AEZ, and OFRA-IT inference domains, respectively. The maximum differences in b values were 3.9, 7.7 and 8.81 times the mean associated SE for GYGA-RD, HC-AEZ, and OFRA-IT inference domains, respectively.

Table 5 Maize P response function results for selected Harvest Choice (HC) AEZs, Global Yield Gap Atlas (GYGA) recommendation domains and OFRA Inference Tool domains in Sub-Saharan Africa
Full size table
Fig. 3
figure 3

Maize response to P by inference domains in Sub-Saharan Africa

Full size image

Response information for K was available for just seven of the query locations (Table 3). The overall potential yield response to applied K (coefficient b) was only 0.22 Mg ha−1 with a range of 0.00–0.36 Mg ha−1 for GYGA6701 and Wenchi, respectively (Table 6). Bougouni, Mlingano, Nyakunguru and Wenchi had b values of 0.15, 0.34, 0.36, and 0.36 Mg ha−1, respectively, although all were in HC313 which had a b value of 0.26 Mg ha−1. Similarly, Nyakunguru and Siaya were in GYGA7501 which had a b value of 0.25 Mg ha−1 while the respective values determined from the OFRA-IT queries were 0.36 and 0.33 Mg ha−1, respectively. The overall coefficient c value for queries with a response was 0.86. GYGA6701 and GYGA10301 had too little response to K to estimate c. HC324 had an exceptionally high c value which is reflected in the near linear effect of K on yield response up to 60 kg ha−1 K (Fig. 4a). With the exceptions of HC324 and GYGA9501, the overall response to K represented the HC-AEZ and GYGA-RD based estimates well. The OFRA-IT query results however split into two groups with yield increases due to K application of <0.16 and >0.33 Mg ha−1 with the overall response function poorly representing all sites (Fig. 4b). Latitude was not a determinant of response to K. The mean R2 values for maize yield response to applied K were just 4.8, 3.1 and 5.6% for GYGA-RD, HC-AEZ, and OFRA-IT inference domains, respectively. The maximum differences in b values were 3.3, 1.3 and 3.3 times the mean associated SE for GYGA-RD, HC-AEZ, and OFRA-IT inference domains, respectively.

Table 6 Maize K response function results for selected Harvest Choice (HC) AEZs, Global Yield Gap Atlas (GYGA) recommendation domains and OFRA Inference Tool domains in Sub-Saharan Africa
Full size table
Fig. 4
figure 4

Maize response to K by inference domains in Sub-Saharan Africa

Full size image

Interpretation of the S and Zn results need caution as trial distribution was narrow with trials often conducted in response to suspected deficiencies. The S trials were conducted primarily in Malawi, Nigeria and southern Tanzania, and most Zn trials were conducted in Nigeria. Maize S response coefficients for b ranged by location from 0.142 to 0.947 Mg ha−1 (Table 7). The lower b values are associated with low c values implying that much of the response is achieved at low S rates. The two locations with low response were in one GYGA-RD and the two locations with high response to S were in another GYGA-RD. Two of the high response and one of the low response locations were in HC313 while the other two locations were in HC 312. Maize Zn response functions were determined for only three locations due to limited data availability. There was too little maize response to Zn for the Wenchi query to estimate the c value. The Zn response functions determined from the Mali and Burkina Faso queries had b values >0.57 Mg ha−1.

Table 7 Maize S and Zn response function results for selected OFRA Inference Tool domains
Full size table

Sensitivity of the OFRA Inference Tool

Mean coefficient b values were similar for OFRA-IT queries with the default criteria and with the criteria ranges expanded by 20–25% for N and P responses but less than for the queries with the narrow criteria ranges (Table 8). This difference however was much affected by the Achefer results, 83% of which were from several locations of research conducted in 2013 by one research team where yields and responses were unusually great. The mean b coefficient value for K response was higher for the default compared with the wide query but similar compared with the narrow query. The mean coefficient c values were similar for the three sets of query criteria for N and P, but relatively high for K with the default compared with other criteria.

Table 8 Comparison of query results with wide, intermediate and narrow ranges of search criteria†
Full size table

The mean b coefficient standard errors for response to N, P, and K was much higher using the narrow compared with the intermediate (default) and wide range of criteria in the OFRA-IT query. The mean coefficient C standard errors were similar for N for the three sets of query criteria but highest and least for P and K response using the wide and narrow ranges of search criteria, respectively.

The mean R2 values were highest for N and least for K. The R2 values for N response were on average similar for the three query criteria. The mean R2 value for P response was greater for the narrow compared with the other queries, but if the unusually high R2 for P at Achefer was omitted, the three query ranges had similar R2. Responses to K were small and R2 values were low for all queries.

The standard error for coefficient b for N and P response, and the R2 value for P response decreased as observations for P response increased. The R2 for N response and the standard errors for the c coefficients did not vary with number of observations.

Discussion

Maize responses to applied nutrient were highly varied across site-seasons as expected given the high variability in maize yield (http://www.yieldgap.org) and the many biotic and abiotic constraints that affect maize growth, yield and response in Sub-Saharan Africa. The findings of this research support the expectation that results from areas of similar conditions can be applied to decision making at a location of interest (Aiken et al. 2001), but with more confidence for maize response to applied N and little confidence for maize response to applied K as indicated by R2 values. The R2 values were lowest for HC-AEZ for which each AEZ represented relatively more area and research findings compared with the GYGA-RD and the locations used for the OFRA-IT queries (Tables 4, 5, 6). The OFRA-IT queries resulted in higher R2 values for N, P, and K compared with HC-AEZ and GYGA-RD which generally had more and fewer response functions per inference domain, respectively, compared with the OFRA-IT queries (Tables 4, 5, 6). The OFRA-IT queries resulted in greater separation of response functions compared with HC-AEZ and GYGA-RD (Figs. 2, 3, 4). While the query methods often did not differ with statistical significance, the differences in response functions imply much difference in yield increase and profit potential due to nutrient application. For example, if the cost of using N is $1 kg−1 and maize value to farmer is $0.2 kg−1, the projected N rate to maximize returns to N use is 64 kg ha−1 with $94 ha−1 net return to N and a yield increase of 0.79 Mg ha−1 for Mlingano. In contrast for Achefer, the projected N rate to maximize returns to N use is 90 kg ha−1 with $330 ha−1 net return to N and a yield increase of 2.10 Mg ha−1. A similar comparison for the constrained farmer whose available finance allows application of just $40 ha−1 of N with a projected mean profit of 269 and 86 $ ha−1 for Achefer and Mlingano, respectively, with mean projected yield increases of 1.55 and 0.63 Mg ha−1.

Results indicate that use of the OFRA-IT is superior to use of the HC-AEZ and GYGA-RD inference domains for finding maize-nutrient response results that are applicable to a point of interest. The HC-AEZ and GYGA-RD are climate based while the OFRA-IT considers soil and climate related variables, including distance from the equator which accounts for variation in rainfall modality and therefore monthly distribution of rainfall.

The OFRA-IT inference domain results were sometimes affected by expanding or decreasing criteria ranges but often not and not greatly. The default values which were determined from agronomic judgement worked similarly well as for wider and narrower query criteria. The results suggest that query criteria should be widen for crop-nutrient responses that are relatively data scarce. A risk of narrowing the query criteria is that the results may be unduly affected by a small set of research results, even for the data abundant maize N and P responses.

Conclusions

Estimates of crop response functions lack exactness globally but especially with SSA smallholder agriculture where crops inconsistently encounter numerous uncontrolled biotic and abiotic constraints. In consideration of crop nutrient response function differentiation, standard errors, standard deviations, and R2 values, selecting relevant maize nutrient response functions for estimating an inference, maize nutrient response function overall appeared to be best estimated using OFRA-IT (http://agronomy.unl.edu/OFRA) and less ecologically specific with HC-AEZ compared with other query options. The OFRA-IT was tolerant of differing query criteria ranges and the default criteria worked well for maize response to applied N, P, and K. Queries for crop-nutrient responses that are relatively data scarce may be improved by widening the criteria ranges.