Field Crops Research 299 (2023) 108975 Contents lists available at ScienceDirect Field Crops Research journal homepage: www.elsevier.com/locate/fcr Consistency, variability, and predictability of on-farm nutrient responses in four grain legumes across East and West Africa Joost van Heerwaarden a,*, Esther Ronner a, Frederick Baijukya b, Samuel Adjei-Nsiah c, Peter Ebanyat d, Nkeki Kamai e, Endalkachew Wolde-meskel f, Bernard Vanlauwe g, Ken E. Giller a a Plant Production Systems, Wageningen University, P.O.Box 430, 6700 AK Wageningen, the Netherlands b International Institute of Tropical Agriculture (IITA), P.O. Box 3444, Dar es Salaam, Tanzania c International Institute of Tropical Agriculture, CSIR Campus, Accra, Ghana d Department of Agricultural Production, Makerere University, P.O. Box 7062, Kampala, Uganda e Department of Crop Production, Faculty of Agriculture, University of Maiduguri, Maiduguri, Nigeria f World Agroforestry (ICRAF), C/o International Livestock Research Institute, Box 5689, Addis Ababa, Ethiopia g IITA, Natural Resource Management Research Area, Nairobi, Kenya A R T I C L E I N F O A B S T R A C T Keywords: Grain legumes are key components of sustainable production systems in sub-Saharan Africa, but wide-spread Soil fertility nutrient deficiencies severely restrict yields. Whereas legumes can meet a large part of their nitrogen (N) Sub Saharan Africa requirement through symbiosis with N2-fixing bacteria, elements such as phosphorus (P), potassium (K) and Nutrient response variability secondary and micronutrients may still be limiting and require supplementation. Responses to P are generally Legumes strong but variable, while evidence for other nutrients tends to show weak or highly localised effects. Here we present the results of a joint statistical analysis of a series of on-farm nutrient addition trials, implemented across four legumes in four countries over two years. Linear mixed models were used to quantify both mean nutrient responses and their variability, followed by a random forest analysis to determine the extent to which such variability can be explained or predicted by geographic, environmental or farm survey data. Legume response to P was indeed variable, but consistently positive and we predicted application to be profitable for 67% of farms in any given year, based on prevailing input costs and grain prices. Other nutrients did not show significant mean effects, but considerable response variation was found. This response heterogeneity was mostly associated with local or temporary factors and could not be explained or predicted by spatial, biophysical or management factors. An exception was K response, which displayed appreciable spatial variation that could be partly accounted for by spatial and environmental covariables. While of apparent relevance for targeted recommendations, the minor amplitude of expected response, the large proportion of unexplained variation and the unreliability of the pre- dicted spatial patterns suggests that such data-driven targeting is unlikely to be effective with current data. 1. Introduction income (Franke et al., 2018; Muoni et al., 2019; Snapp et al., 2019). A unique advantage is their ability to obtain between 10% and 90% of Grain legumes are important for sustainable intensification of agri- nitrogen demand through symbiosis with nitrogen fixing rhizobia culture, particularly on small farms in sub-Saharan Africa (SSA) (Franke et al., 2018), reducing the need for nitrogen (N) fertiliser. Un- (Droppelmann et al., 2017; Snapp et al., 2019; Vanlauwe et al., 2019b). fortunately, productivity of legumes in SSA remains constrained by low They fit into a diversity of farming systems as monocrop, in rotation or soil fertility (Kermah et al., 2018; Ojiem et al., 2007; Wortmann et al., as relay- or intercrop (Snapp et al., 2019; Thierfelder et al., 2012; 2019), on top of other problems like biotic stresses, poor seed quality Vanlauwe et al., 2019b) and provide benefits in terms of soil fertility, and drought (Giller, 2001; Waddington et al., 2010). As a result, yields soil cover, pest and disease control and as source of food, feed and in SSA often remain below 25% of their water limited potential (van * Corresponding author. E-mail address: joost.vanheerwaarden@wur.nl (J. van Heerwaarden). https://doi.org/10.1016/j.fcr.2023.108975 Received 2 September 2022; Received in revised form 10 May 2023; Accepted 17 May 2023 Available online 26 May 2023 0378-4290/© 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). J. van Heerwaarden et al. F i e l d C r o p s R e s e a r c h 2 99 (2023) 108975 Loon et al., 2018). In summary, the present study aims to establish the main effects of The application of nutrients such as phosphorus (P), potassium (K), nutrient application in grain legumes and to dissect the different types of secondary (Ca, Mg, S) and micronutrients (B, Zn, Mo) has been proposed systematic response variation that are relevant for understanding pro- as a solution to soil fertility constraints in SSA (Kihara et al., 2017; duction risks and potential for tailored application (i.e. predictable Vanlauwe et al., 2019a; Wortmann et al., 2019), as has the use of variation). We address the following research questions: First, what are rhizobium inoculants (Vanlauwe et al., 2019a). For inoculants, yield the average summative effects of P, K and secondary and micronutrient gains of about 100 kg ha− 1 and cost-effectiveness for over 90% of application in the studied areas? Second, what is the magnitude of farmers was recently found for soybean across SSA (van Heerwaarden systematic response variation and how is this variation distributed in et al., 2018). Evidence for other legumes is less clear-cut but positive space and time? Third, is the economic risk associated with systematic responses have been reported in common bean (Amijee and Giller, 1998; variation in nutrient response small enough to permit general nutrient Ndakidemi et al., 2006), chickpea (Wondwosen et al., 2016) and cowpea recommendations? Finally, can variation in response to nutrients be (Boddey et al., 2017; Kyei-Boahen et al., 2017). Since inoculants tend to predicted from geographical and environmental data, to allow site- be cheap they may be considered a low-risk recommendation, unlike specific recommendations? By answering these questions, we evaluate mineral fertilisers, whose high purchase costs require distinct yield the potential to raise yields and to mitigate production risk using benefits to be offset. available knowledge, which is of general interest to similar systems In that regard, it is worth noting that despite well-documented elsewhere. legume responses to phosphorus (Mucheru-Muna et al., 2010; Vester- ager et al., 2008; Wolde-meskel et al., 2018), particularly in soybean 2. Methods (Kamara et al., 2007; Kolawole, 2012; Zingore et al., 2008), most reports only cover individual regions, with considerable variation among 2.1. Data studies and locations (Ronner et al., 2016; Ulzen et al., 2018). Such inconsistent responses have implications for the cost-effectiveness and The data was taken from a total of 399 on-farm trials performed in risk of nutrient application and deserve further investigation, ideally Ghana, Nigeria, Uganda and Tanzania (Fig. 1) from 2015 to 2017 and across different regions and years. Evidence for benefits of other nutri- covering the crops soybean, groundnut, cowpea and climbing bean, ents such as potassium are scarce by comparison (Kihara et al., 2017), yielding a total of 2523 data points. Rainfall in Uganda and Tanzania is and the few published studies tend to include only a small number of bimodal, which in the case of Uganda translated into a wide range of locations, predominantly in pot trials or on-station (Bado et al., 2006; planting dates within a year. Although trials in different countries Keino et al., 2015). A recent exception describing on-farm and on-station differed in exact treatment structure, varieties, agronomic practices and responses to combined application of Mg, S, Zn and B across SSA nutrient formulations, all were researcher-managed, non-replicated, on- (Wortmann et al., 2019) found that among crop types, legumes had the farm experiments which included a zero-input control and at least three smallest relative increases in yield. Similar small and non-consistent plots with cumulative additions of phosphorus, potassium and second- effects were found across different countries for S and micronutrients ary and micronutrients (of various kinds, Table S1). Phosphorus was in soybean and cowpea (Kaizzi et al., 2012; Kihara et al., 2017) and for K applied at an average rate of 15 kg P ha− 1 across fields (10–30 kg P ha− 1, in common bean (Kaizzi et al., 2018), suggesting limited potential for a 18 kg P ha− 1 averaged across experiments) as either single super profitable return to the investment. Hence, the magnitude and consis- phosphate (SSP) or triple super phosphate (TSP) and potassium was tency of agronomic and/or economic benefits of the addition of P, K and applied at 32 kg K ha− 1 (17–60 kg K ha− 1, 27 kg K ha− 1 averaged across other nutrients in smallholder legume production remains an important experiments) as muriate of potash (MOP). The structure of the treat- topic for research. ments did not allow an assessment of the effects of individual secondary Here, we analyse a recently compiled dataset of on-farm nutrient and micronutrients which is why they are treated as single treatment addition trials that were set up to evaluate the additive effects of (SMN). phosphorus (P), potassium (K), and a variety of secondary and micro- For each on-farm trial, household survey data was available from nutrients (abbreviated as SMN here) in four legume crops: soybean which agronomically relevant variables were obtained to be used as co- (Glycine max), groundnut (Arachis hypogaea), cowpea (Vigna unguicu- variates. Digital maps with weather, climatic and soil variables were also lata), and climbing bean (Phaseolus vulgaris), across four countries in compiled for this purpose. Weather variables consisted of monthly East and West Africa (Tanzania, Uganda, Nigeria and Ghana) with the satellite-based rainfall data (rain) for the relevant growing seasons, purpose of assessing the general response to these nutrients and to climatic variables were so-called bioclimatic variables derived from describe the magnitude and patterns of variation. We thereby distin- long-term temperature (temp) and precipitation (prec) data (Fick and guish different types of variation of contrasting agronomic relevance. Hijmans, 2017). Soil variables (soil) consisted of predicted physical and The first distinction is between systematic and non-systematic variation. chemical properties (see Table S2 for full details on all variables). Non-systematic variation is the component of observed variability due to random effects of sampling and experimental error at the experi- 2.2. Statistical methods mental plot level which is highly localised, non-repeatable and hence of limited relevance (van Heerwaarden et al., 2018; Vanlauwe et al., Using the combined data across countries, crops and years, a statis- 2019a). Systematic variation, on the other hand, reflects differences in tical model was implemented that allowed: 1) the estimation and testing growing conditions at the field level and above. This type of response of mean effects of the different types of nutrients and 2) the quantifi- variation is experienced by farmers across locations and time points and cation and dissection of random response variation into different com- is therefore of direct agronomic importance. A second distinction is ponents of variation. To this aim, linear mixed models were used. This made between explainable and predictable systematic variation. type of model contains fixed effect terms to represent factors for which Explainable variation is associated with known climatic, edaphic, the means of the individual levels are of direct interest, as well as weather, biotic stress or crop management conditions and offers op- random effects to represent the variation around the estimated means. portunities for adapting the amount and composition of inputs to local Random effect terms can be specified to account for different sources of circumstances. Such adaptation is only possible when responses are also variation. Variance components are estimated for each term, quanti- predictable, i.e., calculated before the growing season starts. In practice, fying the associated variance, and random effect estimates for each in- much of the explainable variation is likely to be due to unpredictable dividual factor level. The latter estimates are known as linear unbiased growing conditions and constitutes production risk that may negatively predictors (BLUPs) and their inspection provides insights on which affect farmer’s willingness to invest in inputs. specific factor levels contribute most to the random variation. 2 J. van Heerwaarden et al. F i e l d C r o p s R e s e a r c h 2 99 (2023) 108975 Fig. 1. Map showing trial sites used in this study (black dots). Coloured shading marks different agro-ecological zones (Harvest choice, https://doi.org/10.7910/ DVN/M7XIUB). Specifically, the following model was fitted: within-field variation therefore required some simplifying model assumptions; by assuming a single effect across fields for non- (1) yield~crop* (p + k + smn)+experiment/(p + k + smn)+ crop: standard treatments (om, n, i, g and l), plots with such treat- district/(p + k + smn)+ crop:district:year/(p + k + smn)+ ments could be used as de facto within-field replicates to obtain an field/(p + k + smn)+ om+n + i + g+l+error approximate estimate of residual within-field variation. The terms p, k and smn represent phosphorus, potassium, and To gain insight into the contribution of individual random secondary and micronutrients, respectively, which are the main factor levels (e.g. specific districts, fields) to random variation in treatments of interest. Other, non-standard, treatments applied in yield and nutrient responses, principal component analysis (PCA) subsets of experiments were corrected for by including them as was applied to the BLUPs (i.e. random effect estimates) corre- random effects with om, n, i, g and l indicating the application of sponding to the different components of random variation, and manure, nitrogen, inoculant, gypsum or lime respectively. The “* the first two components were visualised with biplots. Where symbol indicates that both main effects and interactions are relevant, data subsets for specific countries or experiments were considered. further analysed with simplified mixed models with field as Random terms in the model are underlined and represent random effect and year or district as fixed effects, to look more in different components of spatial and temporal variation. The “/” depth into specific interactions associated with patterns observed symbol is a nesting operator which ensures that random variation in the biplots. for control yield and nutrient responses is modelled individually Among the random terms in the mixed model, only districts for each component of random spatial and temporal variation. had replicates in time which means that, in contrast to the other The error term is the plot-level residual, representing non- terms, this component (district:crop) represents variation that systematic variation due to within-field heterogeneity and can be predicted and managed in theory. Variation associated experimental error. The remaining random terms correspond to with the remaining components (experiment, district:crop:year, different sources of systematic variation in control yield and field) are unpredictable without additional knowledge and may nutrient response. The following sources of systematic random therefore be considered representative of the production risk that variation are represented in the model: 1) “experiment”, which is farmers face. One step to reducing such production risk is to use a the combination country, year and crop, and represents groups of statistical model that predicts random nutrient response variation on-farm trials with an identical set-up and treatment structure, 2) as a function of underlying climatic, soil or agronomic conditions. district within crop (district:crop), 3) year within district within We explored such an approach here in an attempt to explain crop (district:crop:year), and 4) field, where individual fields are and predict a maximum amount of the total field-level variation not replicated and are unique to a specific year. in control yield and nutrient responses. As a first step we fitted the This model specification allows year-to-year variation to be following, simplified mixed effects model: separated from spatial differences between districts, some of (2) yield~ p + k + smn + (p + k + smn|crop:country) which were only sampled in a single year. Fields were not repli- + (p + k + smn|field)+om+ n + i + g+l+error cated, so the field random term would normally represent the to allocate all random response variation below the crop: residual error in the statistical model. Estimation of residual country level to a fieldlevel random effects term. The operator “|” 3 J. van Heerwaarden et al. F i e l d C r o p s R e s e a r c h 2 99 (2023) 108975 indicates that for each crop:country and field, specific random available. Costs for transport from the point of sale to the homestead effects and interactions were estimated for the three types of were assumed to be 0.05 USD per kg of fertilizer, the average transport nutrients. The BLUPs extracted from this model, representing the cost found by Bonilla Cedrez et al. (2020). field-level deviations for control yield and P, K and SMN Legume grain prices were derived from national market information response, were saved and merged with the corresponding systems (www.tridge.com for Nigeria, www.esoko.com for Ghana, household survey, weather, climatic and soil data described www.agmis.infotradeuganda.com for Uganda) and Temu et al. (2014) above (Table S2). for Tanzania. These prices represent wholesale market prices found on urban markets. Regional information was often missing, and therefore All variables were categorised as either explanatory or predictive. we considered an average annual price per country, per legume. The Predictive variables are defined as those whose values are known before wholesale market prices were converted to farm gate prices for a better the season in which yield was measured, such as climatic and soil comparison with fertiliser costs. On average, farm gate prices were properties and farm and field characteristics such as farm size, land found to be 40–70% of wholesale market prices for different legumes ownership and perceived soil fertility. Explanatory variables alsoen- assessed in studies in Rwanda, DR Congo, Malawi and Tanzania (Birachi, compass information which is only known after planting and harvest, 2012; Langyintuo et al., 2003; Rusike et al., 2013). An overall average of such as rainfall, agronomic management and pest and disease 60% was applied across countries to convert market prices to farm gate occurrence. prices. Subsequently, a random forest (Breiman, 2001) machine learning Fertiliser costs and legume grain prices were converted from national algorithm was implemented to model the field-level random variation in currency to inflation-adjusted purchasing power parity in US dollars yield and response as a function of these predictive and explanatory (Bonilla Cedrez et al., 2020). National currencies from different years variables, either together or as subsets. Goodness of fit of the random were first divided by the consumer price index (CPI) to adjust for forest models was summarised by out of bag (OOB) R squared, which inflation, with 2017 as a reference year. Values were then multiplied should avoid overfitting. It is becoming common to use machine with the purchasing power parity (PPP) dollar value for 2017 (World learning models such as these to map the spatial distribution of pre- Bank, 2020). Cost benefit analyses were based on crop specific grain dicted yield and response (Bonilla-Cedrez et al., 2021; Cao et al., 2021; price averages and country specific input prices in addition overall Kinane et al., 2021) and we used the same approach here. While averages. attractive as a way of identifying potential recommendation domains, such spatial predictions may be subject to large prediction uncertainty 3. Results and spatial biases, specifically when data is not sampled randomly, as is often the case with on-farm data. 3.1. Nutrient main effects We tackle these limitations in two ways. First, we used a statistical approach to delineate the spatial area for which the on-farm locations The overall mean effect of P was found to be highly significant are considered to be representative (Nziguheba et al., 2021). A random (p < 1e− 6) with an average yield gain of 251 kg ha− 1 at an average rate forest model was trained to distinguish between trial locations and of 15 kg P ha− 1. The average effects of K and SMN were estimated at 15 random map coordinates, based on the set of predictive geospatial and 49 kg ha− 1 respectively, and were not significant (p > 0.1). The variables used for the yield and response predictions. Using this model, estimated means for yield with and without inputs in the four crops are the probability of representing a potential trial location was calculated given in Table 1. Most of the extra yield achieved with inputs was due to for each pixel on the map, with pixels having higher probabilities being the addition of phosphorus. In terms of overall grain yield, it seems that most like the sampled on-farm locations. A representative area was then cowpea lagged the other three crops, while climbing bean produced the defined as the set of pixels for which the probability was larger than the largest yields. The main effect of crop or the interaction with crop and lowest 1% of site probabilities found among the original on-farm trial any of the nutrients was not significant however, possibly due to the locations, which corresponded to a probability of 0.53 in this case. large degree of confounding between crop and country, which is an Second, since explanatory variables tend to be spatially correlated, intrinsic feature of the data. predicted patterns may inadvertently reflect unobserved heterogeneity in local conditions and trial implementation rather than true environ- mental contrasts. We therefore compare spatial predictions based on a 3.2. Yield and nutrient response variation full set of environmental variables to those based on coordinates only. A large part of the variation explained by geographic coordinates alone Considerable variability was observed for yield and nutrient re- suggests that the predictive power of environmental variables may be sponses. Summing over all hierarchical variance components (experi- partially related to the unobserved heterogeneity instead of having ment, district, district/year and farm), the standard deviations actual predictive value. In such cases, evaluating the consistency be- associated with control yield, P, K and SMN response were 683, 190, 115 and 125 kg ha− 1 tween the two spatial models can provide a further indication of the , respectively. reliability of the site-specific predictions. Breakdown into hierarchical components (Fig. 2) shows that in general, only a small amount of variation is associated with the pre- 2.3. Analysis of economic benefit and risk dictable district level, with most variation found at the district/year, farm and to a lesser extent the experiment level. Only 2%, 6%, 13% and The BLUPs representing the field-level deviations in P response 8% of total variance, excluding residual variation, was found at the derived from the second mixed model were combined with input and district level for control yield, P, K and SMN response. In terms of grain price information to perform an analysis of economic benefits and risks. Costs for the different types of phosphorus fertiliser (SSP, DAP or Table 1 TSP) were collected from www.Africafertilizer.org for Nigeria, Tanzania Estimated means for yields (kg ha− 1) of grain legumes in control plots and with and Uganda, based on the availability of data between 1-1–2015 and application of P, K and SMN (i.e. secondary and micro-nutrients). 31–12–2017 (the study period). For Ghana, costs for TSP were derived Crop no inputs P only P þ K P þ KþSMN Max. SE from IFDC (2019). As much as possible, regional retail prices for the Soybean 1446 1746 1748 1800 240 different types of fertilisers were considered and expected to represent Groundnut 1259 1477 1512 1531 255 the spatial variation in fertiliser prices as described by Bonilla Cedrez Cowpea 945 1184 1068 1161 292 et al. (2020). For Ghana, only a national average retail price for TSP was Climbing bean 1657 1905 2045 2076 315 4 J. van Heerwaarden et al. F i e l d C r o p s R e s e a r c h 2 99 (2023) 108975 Table 2 At the district level, a few districts show a strong positive projection Effect of different subsets of variables on OOB R2. on the K and SMN vectors, Kwayakusar (Nigeria, soybean) and Kajuru Type control P K SMN (Nigeria, soybean and groundnut), in particular. For the latter district this corresponds to random effects of more than 20 kg ha− 1 above the All explanatory 0.39 0.06 0.33 0.14 Coordinates only 0.23 0.05 0.20 0.09 means of 15 and 49 kg ha− 1 for K and SMN, respectively. Random effects for district level P responses range from − 17 kg ha− 1 Explanatory survey 0.35 0.11 0.30 0.17 (Apac, Uganda, Explanatory remote sensing 0.25 0.04 0.23 0.13 soybean) to 37 kg ha− 1 (Kajuru, Nigeria soybean), with respect to the All predictive 0.31 0.04 0.28 0.13 overall mean of 251 kg ha− 1. For all three types of nutrients, the abso- Predictive survey 0.23 0.04 0.18 0.08 Predictive remote sensing 0.26 0.04 0.24 0.14 lute deviations from the mean are minor, reflecting the limited level of variation at this level of hierarchy. In contrast, variation in P and K response at the district/year level is much more pronounced, with nutrient responses, 80% of districts are expected to have yield gains random effects for P and K ranging from -117–246 and falling within 193–309, -37–67 and 5–93 kg ha− 1 for P, K and SMN -107–140 kg ha− 1 respectively. This translates into several significant respectively, suggesting that there is little to be gained from district- interactions between P and district, namely in Nigerian groundnut trials specific recommendations. in 2015 and 2016 and Ugandan soybean trials in 2017, and between K Regarding the unpredictable components of variation, the first thing and district in Ugandan bean trials in 2016 and Ugandan soybean trials to notice is that despite substantial variation in control yield between in 2017. Similar variation in P response is found at the farm level, with experiments, there is very little variation at this level for any of the random effects ranging from -237–2011 kg ha− 1 above the mean. It is nutrient responses. This suggests that the effects of P, K and SMN are also at this level that the largest variation for response to SMN is relatively stable across experiments performed with different crops over observed with random effects from -110–81 kg ha− 1 with respect to the different countries and years, at least when similar procedures are fol- mean. lowed as was the case here. Second, whereas the district/year and farm level represent similar amounts of variation in the case of control yield 3.3. Economic benefits and P response, there is no variance associated with the farm level for K response and only a negligible amount of variance at the district/year The considerable response variation for P has direct economic rele- level for SMN response. While theoretically, this could be due to large- vance to farmers: although the application of P-fertiliser increased scale and seasonal differences affecting K response and variation in legume yields consistently, the observed variation at the farm level will secondary and micronutrients reflecting local deficiencies, it could also translate in unpredictable economic benefits. Fig. 4 summarises the total be an artefact of the overall small degree of variation in response for variation in P response at the farm level and its relation to profitability. these two types of nutrients. The left panel shows the variation in absolute agronomic response with Dissecting the observed variability by principal component analysis respect to the minimum response required to be profitable given a mean of the random effects (BLUPs) at different hierarchical levels revealed application of 15 kg ha− 1 of P with average costs and grain prices across that at the level of experiment, the 2016 Nigeria groundnut trial projects countries and legumes. Out of all fields, 96% showed an increase in yield strongly on the K and SMN vectors (Fig. 3). This is confirmed by sig- in response to the application of P and 67% of fields had responses above nificant main effects for K and SMN in these trials, with 88 and the average economic minimum, meaning that a third of fields would 118 kg ha− 1 of additional yield respectively (Ca, Mg, Zn, S, B). At the fail to benefit from P application at the tested rates. Similarly, the actual other extreme, the 2015 Ugandan climbing bean trials saw negative distribution of estimated profits, using country and legume specific responses across all districts, leading to a significant negative main ef- prices, is shown in the right panel. Average profit from P application was fect of the combination of Mg, Zn, Mo. The strong projection of the 2016 137 USD ha− 1, and on only 30% of fields application was unprofitable, Nigeria soybean study on the P response vector corresponds to an esti- with 11% posting losses greater than 100 USD ha− 1 against 48% having mated response of 456 kg ha− 1. gains in excess of 100 USD ha− 1. The lack of significant yield responses field district.year district experiment control P K SMN control P K SMN Fig. 2. Left panel: breakdown of random variation at different strata (expressed as standard deviation) for control yield, P, K and SMN. Right panel: variance components expressed as proportions of total variance (excluding residual variance). 5 standard deviation 0 200 400 600 800 1000 1200 proportion of variance 0.0 0.2 0.4 0.6 0.8 1.0 J. van Heerwaarden et al. F i e l d C r o p s R e s e a r c h 2 99 (2023) 108975 Fig. 3. Biplots showing the principal components (PCs) and loadings corresponding to the first PCs calculated for the matrix of BLUPs for the response to P, K, and SNM. Panel a: experiment level, b: district level, c: district.year level and d: field level. to K and SMN means that their application is unlikely to be profitable, which are costly to collect compared to remote sensing data. which is why we did not include them here. Only a small proportion of variation was accounted for by the total set of variables (Fig. 5, Table 1) but overall, model accuracy was slightly higher for explanatory than for predictive models, indicating that 3.4. Patterns and predictability in yield and effect variation season-specific information holds explanatory value. For both explana- tory and predictive variables, model fits were particularly poor for Random forest was used to model farm-level variation in control response to P and SMN (with values of out-of-bag R squared below 0.15) yields and nutrient responses as a function of explanatory and predictive and were better for control yield and response to K (R-squared above soil, climatic and agronomically relevant survey variables (Table S2). 0.33). It is worth mentioning that models with all variables included We were interested in the capacity of the total set of variables to explain were only moderately better compared with a model with geographic and predict patterns of variation. Apart from the general question of how coordinates only. Particularly in the case of response to P and SMN, much variation could be either predicted or explained, the contribution adding variables other than latitude and longitude did not improve the of different types of variables to predictive and explanatory ability was model substantially. Although this suggests that individual variable also of interest, particularly the contribution of the survey variables, 6 J. van Heerwaarden et al. F i e l d C r o p s R e s e a r c h 2 99 (2023) 108975 Fig. 4. Cumulative densities of absolute response (left) and profitability (right) of P application. Vertical lines mark economical minimum rate (average prices across countries and legumes) and 0 profit (country- and legume-specific prices) respectively. importance should be interpreted with caution, the fact that reported 4. Discussion soil fertility and drought severity were found among the three most important explanatory variables for both control yield and K response 4.1. General response and profitability of P, K and SMN (Fig. 5) could point to water and nutrient availability as potential shared constraints. Survey and remote sensing variables were found to be Consistent and profitable nutrient responses are important if general complementary for control yield and K response, with models contain- recommendations are to be made. Among the three types of nutrients ing both having higher accuracies than those with only a single type of tested, only P was found to have a substantial and significant main ef- variable. This was the case for both explanatory and predictive models fect, with a mean response of 251 kg ha− 1. Neither K nor secondary and but, in case of the former, survey variables seemed to contribute more micronutrients were found to have substantial positive effects on information while in the latter models using remote sensing variables average. At the same time, considerable variation in response was were more accurate than those containing only survey variables. In all observed for all three types of nutrients, which reflects earlier findings in cases, however, their accuracy was only marginally better compared to literature. For P, most published estimates of response in soybean, those with coordinates only. common bean, cowpea and groundnut tend to be between 150 and In theory, predictive models such as those evaluated above could 500 kg ha− 1 (Chekanai et al., 2018; Giller et al., 1998; Kaizzi et al., contribute to the development of context-specific nutrient recommen- 2018, 2012; Maman et al., 2017; Ronner et al., 2016; Serme et al., 2018; dations, in which nutrients are targeted to areas where they are pre- Tarfa et al., 2017; Ulzen et al., 2018; Zingore et al., 2008) and can be dicted to be most effective. While attractive, such an approach has considered consistent with the 250 kg ha− 1 found in our study, although important caveats and requires spatial predictions to be accurate, reli- responses below 100 kg ha− 1 (Ikeogu and Nwofia, 2013; Mabapa et al., able and of sufficient amplitude. We use the predictive model for K 2010; Serme et al., 2018; Smithson et al., 1993) and above 500 kg ha− 1 response, which had relatively good accuracy, as an opportunity to (Kaizzi et al., 2018; Kamara et al., 2007; Moses et al., 2018; Tarfa et al., evaluate the potential and limitations for site-specific predictions. 2017) have also been reported. Fig. 6a shows what a map of predicted K response looks like, based on At the tested application rate of 15 kg ha− 1 on average, and the model with all predictive geospatial variables, within the areas for considering only input costs, P application was profitable in terms of which the trials were considered environmentally representative. The immediate response in almost 70% of cases, at a yield response of about map shows quite distinct areas of stronger and weaker response, but the 200 kg ha− 1 (Fig. 4), an outcome which in the absence of systematic magnitude and amplitude of yield response variation is limited, with the spatial variation can be considered representative for the study area. upper 5% predicted K responses being 63 kg ha− 1 compared to a median While such cost-benefit analyses need to be treated with caution, the value of 22 kg ha− 1 respectively. In addition, the reliability of the spatial present result suggests that the application of P could be generally predictions seems questionable. While the predictive model with co- beneficial but also highlights that economic risks may still be an issue to ordinates alone explains almost as much variation as the full model, the farmers, although losses in excess of 100 USD/ha were estimated to be spatial patterns of predictions differ substantially from those predicted rare. Most of the earlier published studies applied larger rates of 30 or by the full set of variables (Fig. 6b). This demonstrates that prediction 40 kg ha− 1 P in soybean, and 15–20 kg ha− 1 in groundnut, common accuracy cannot be credited to the environmental variables included in bean and cowpea. No effect of larger application rates emerges from the model and suggests that spatial predictions probably vary depending literature (for instance, Tarfa et al. (2017) reported an average response on the available data. of 590 kg ha− 1 to 15 kg P ha− 1 in soybean, while Kaizzi et al. (2012) found a response of 180 kg ha− 1 to 37.5 kg P ha− 1. Moreover, it is likely that P addition beyond 20 kg ha− 1 will be less profitable than what we report here, given that nutrient use efficiencies tend to decrease at higher rates. 7 J. van Heerwaarden et al. F i e l d C r o p s R e s e a r c h 2 99 (2023) 108975 control yield, r2: 0.39/0.23 P response, r2: 0.05/0.05 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 K response, r2: 0.33/0.2 SMN response, r2: 0.15/0.09 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 Fig. 5. Histograms showing the distribution of relative variable importance (top 20 remote sensing and survey variables, Table S2) of random forest predictions of control yield and P, K and SMN response, using the full set of variables. The corresponding out of bag R squared values for the full model / model with coordinates only are shown in the plot titles. For K, the insignificant average response reported here is consistent Similarly, other nutrients affected yields in particular cases, but not with other reports of responses below 100 kg ha− 1, or even negative consistently, in line with the limited response to S and micronutrients responses, in soybean, cowpea and groundnut (Kihara et al., 2017; (Kihara et al., 2017) and to Mg-S-Zn-B (Serme et al., 2018; Wortmann Maman et al., 2017; Moses et al., 2018; Serme et al., 2018; Tarfa et al., et al., 2019). Where responses to K and SMN were larger than average, 2017). Negative responses seem to occur in cases where K is not limiting, the magnitude was still small compared with the response to P. caused by a damage to plant roots (Kihara et al., 2017). Still, recent pot experiments in soybean (Baijukya et al., 2021) identified K as being 4.2. Variability and predictability of nutrient response variation potentially limiting on a number of soils collected in East and West Af- rica and there are several field studies reporting grain yield responses Variability of control yields and nutrient responses represent pro- between 100 and 300 kg ha− 1 for groundnut, common bean and cowpea duction risk that may hamper investment in nutrient inputs, unless this (Moses et al., 2018; Serme et al., 2018; Smithson et al., 1993; Tarfa et al., variability can be predicted. Our results suggest that only a relatively 2017) and even an exceptional 700 kg ha− 1 in common bean (Kaizzi, small part of variation can be explained or predicted by geographic, 2018). Such studies may allude to either localised deficiency of K (cf. environmental or survey variables that are commonly collected. This Smithson et al., 1993), though in our study we did not find consistent confirms earlier results showing the lack of explainable patterns in responses at the location level (see also 4.2), or to weather dependent agronomic outcomes (Ronner et al., 2016). In terms of geography, effects (Martineau et al., 2017), creating exceptional circumstances. variation in nutrient response in our study was predominantly 8 af_SLTPPT_T__M_sd1_250m af_SNDPPT_T__M_sd1_250m gyga_af_agg_30cm_pwp__m_1km wc2.1_30s_bio_3 longitude chirps.v2.0.2017.08 wc2.1_30s_bio_9 wc2.1_30s_bio_18 af250m_nutrient_p_m_agg30cm wc2.1_30s_bio_14 severity_weeds chirps.v2.0.2017.05 af_PHIHOX_T__M_sd1_250m af_ORCDRC_T__M_sd1_250m wc2.1_30s_bio_8 wc2.1_30s_bio_6 chirps.v2.0.2015.09 wc2.1_30s_bio_16 wc2.1_30s_bio_11 af250m_nutrient_cu_m_agg30cm wc2.1_30s_bio_6 af250m_nutrient_mn_m_agg30cm wc2.1_30s_bio_18 af250m_nutrient_p_m_agg30cm af_ORCDRC_T__M_sd1_250m af250m_nutrient_n_m_agg30cm af250m_nutrient_n_m_agg30cm chirps.v2.0.2015.07 day.planting day.planting day.weeding1 af_SLTPPT_T__M_sd1_250m chirps.v2.0.2015.07 chirps.v2.0.2015.09 severity_drought day.weeding1 af_BLD_T__M_sd1_250m severity_drought relative_fertility relative_fertility wc2.1_30s_bio_15 wc2.1_30s_bio_7 chirps.v2.0.2015.09 relative_fertility wc2.1_30s_bio_16 chirps.v2.0.2017.08 severity_drought af_CEC_T__M_sd1_250m gyga_af_agg_erzd_tetas__m_1km af_CLYPPT_T__M_sd1_250m chirps.v2.0.2015.07 wc2.1_30s_bio_15 af250m_nutrient_n_m_agg30cm chirps.v2.0.2017.09 af_ORCDRC_T__M_sd1_250m wc2.1_30s_bio_19 chirps.v2.0.2015.03 gyga_af_agg_erzd_tetas__m_1km wc2.1_30s_bio_19 chirps.v2.0.2015.04 chirps.v2.0.2017.09 day.weeding1 FARMSIZE_ha wc2.1_30s_bio_13 chirps.v2.0.2017.03 chirps.v2.0.2015.09 chirps.v2.0.2016.03 severity_drought af250m_nutrient_p_m_agg30cm chirps.v2.0.2015.07 wc2.1_30s_bio_13 af_BLD_T__M_sd1_250m severity_water_logging gyga_af_agg_erzd_awcpf23__m_1km af_BLD_T__M_sd1_250m farmer_perception_fertility farmer_perception_fertility af250m_nutrient_p_m_agg30cm af_PHIHOX_T__M_sd1_250m FARMSIZE_ha J. van Heerwaarden et al. F i e l d C r o p s R e s e a r c h 2 99 (2023) 108975 Fig. 6. Two maps of the predicted absolute response to K (in kg/ha) showing the different spatial patterns produced by a Random Forest model using all remote sensing variables (a., 24% of variation explained, rmse of 62 kg/ha), and geographic coordinates only (b., 20% of variation explained, rmse of 64 kg/ha). Trial sites are shown in red. Predictions for representative areas (i.e., those with a predicted probability of representing a potential trial site of >0.53) are highlighted in full colour. The grayscale background shows predictions for non-representative areas and is included for appreciation of spatial structure of predictions only. associated with the non-predictable levels of district/year and field, straightforward, however. The relatively large variance component for rather than at the predictable district level. The relatively limited vari- district/year and the strong contribution of precipitation and drought ability in nutrient response at the level of experiment suggests that related variables to variation suggest that seasonal effects play an strong differences between the published studies are not explained by important role. Since seasonal effects are unpredictable, they are of little random trial-to-trial variation but rather reflect systematic differences in relevance for local nutrient adjustments. In this regard the amount of implementation (e.g., addition of manure or other nutrients, differences variation that can be predicted from time independent covariates such between varieties, plant densities, etc.), or could be due to studies as climatic and soil parameters are more important. We found K reporting on a limited number of locations. response to be relatively well predicted by those variables, which in Similarly, we found that relatively little variation in nutrient theory could help in generating regional recommendations on K use. Our response could be explained by our total set of covariables. Only K exploration of the patterns and stability of spatial predictions highlights response could be modelled reasonably well, although the maximum the limitations of such an approach, however. The fact that maps of proportion of variation explained was still limited and considerably spatial predictions based on a full set of variables and on geographic below the 40% observed for control yield. Still, the result is indicative of coordinates alone differ substantially, while explaining similar amounts relatively strong influence of geography and/or environment on of variation, suggested that large-scale spatial patterns predicted from observed response variation. Interpretation of such patterns is not on-farm trials are not necessarily reliable and should not be taken at face 9 J. van Heerwaarden et al. F i e l d C r o p s R e s e a r c h 2 99 (2023) 108975 value. In addition, regardless of the reliability of spatial patterns, only scientists, field personnel and farmers involved in conducting the 5% of sites had predicted yield response of more than 63 kg ha− 1, an experiments. outcome that is unlikely to justify any adjustment from general recom- mendations. Combined with the limited accuracy, i.e. 20% of variance Appendix A. Supporting information explained, it seems that effective tailored recommendations (Abera et al., 2022; Chivenge et al., 2022; Ebanyat et al., 2010; Vanlauwe et al., Supplementary data associated with this article can be found in the 2015; Zingore et al., 2008) are not warranted based on our data and may online version at doi:10.1016/j.fcr.2023.108975. be difficult to achieve in practice (van Heerwaarden, 2022). 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