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Profitability of climate-smart soil fertility investment varies widely across sub-Saharan Africa

Abstract

Soil fertility investments in sub-Saharan Africa, where budgetary resources are scarce, must be well targeted. Using a causal forest algorithm and an experimental maize trial dataset matched with geocoded rainfall, temperature and soils data, we modelled site-specific, ex ante distributions of yield response and economic returns to fertilizer use. Yield response to fertilizer use was found to vary with growing season temperature and precipitation and soil conditions. Fertilizer use profitability—defined as clearing a 30% internal rate of return in at least 70% of the years—was robust to growing season climate and the fertilizer-to-maize price ratio in several locations but not in roughly a quarter of the analysed area. The resulting profitability-assessment tool can support decision makers when climate conditions at planting are unknown and sheds light on the profitability determinants of different regions, which is key for effective smallholder farm productivity-enhancing strategies.

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Fig. 1: Predicted fertilizer yield response at all African sites modelled and predicted profitability of fertilizer use at randomly selected trial sites.
Fig. 2: Site-level IRR predictions and a confusion matrix classifying each site by altering profitability criteria.
Fig. 3: Sensitivity analysis of predicted yield response to fertilizer use and predicted IRR.

Data availability

Data used in this study are openly available, and we have provided citations that include a either a DOI or URL at the point in the methods section where each dataset is described. Our processed estimation dataset is available on Github (https://github.com/julianneq/Africa_Fertilizer_Profitability).

Code availability

All of the code that we have written, including code to generate our estimation dataset, estimate the fertilizer response function, simulate fertilizer response in trial sites and across sub-Saharan Africa, analyse sensitivity of profitability to the diiferent predictors and generate the manuscript tables and figures, are available on Github (https://github.com/julianneq/Africa_Fertilizer_Profitability).

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Acknowledgements

We are grateful to the International Food Policy Research Institute for partially funding this research. We thank C. Barrett for his leadership and guidance and J. Woodard and L. Verteramo for collaboration on earlier related research focused on Ethiopia. Initial seed funding was provided through the National Science Foundation Integrative Graduate Education and Research Traineeship (IGERT) program. We also thank S. Gameda, J. Warner, T. Benson, J. Koo, B. Minten, A. S. Taffesse and S. Rashid of the International Food Policy Research Institute for their contributions to this effort. We thank C. Wortmann for generously sharing data. We are also grateful to S. Kidanu, J. Reid and K. Bomba of the Ethiopian Agricultural Transformation Agency, M. Sheahan, D. Lobell, L. Xue, A. Perello, D. Flannelly, Z. Zeng, J. Mullen, D. Levine and E. Tjernstrom. Any errors are our own.

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Authors and Affiliations

Authors

Contributions

E.B.M. conceived the initial idea for this manuscript. E.B.M., J.D.Q. and A.M.S. collaborated to create the research design. J.D.Q. prepared the historical and synthetic climate data, and A.M.S. prepared the price data. E.B.M. estimated the fertilizer response model and the profitability assessment. J.D.Q. completed the sensitivity analysis. E.B.M. led the writing of the manuscript. E.B.M., J.D.Q. and A.M.S. contributed to editing the manuscript.

Corresponding authors

Correspondence to Ellen B. McCullough, Julianne D. Quinn or Andrew M. Simons.

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Nature Food thanks David Lobell, Aurelie Harou and Jordan Chamberlin for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Ranking, by importance, of predictors included in the causal forest model used to predict the maize yield response to fertilizer, estimated using the grf package in R 75.

Importance is quantified as a weighted sum of the number of times that variable was used to split the data at each depth in the forest. The climate variables include: total precipitation in the 1st and 2nd months of the growing season (precip p1), during the 3rd month (precip p2), and during the 4th and 5th months (precip p3), average daily temperature during the 1st and 2nd months of the growing season (temp p1), during the 3rd month (temp p2), and during the 4th and 5th months (temp p3). The soil variables include: soil cation exchange capacity in centimol charge per kg soil (soilcec), soil pH as determined in a soil/water mixture (soilph), soil clay content share by volume (claypct), soil silt content share by volume (siltpct), soil bulk density in kg per cubic decimeter (bulkdens) soil exchangeable acidity in centimols charge per kg soil (acidity), soil organic matter in g per kg soil (soilom), soil nitrogen content in g per kg soil (soiln), the site’s elevation (elevm), and a binary variable indicating whether the soil is characterized as having poor drainage (poordrain). The management variables include an indicator for whether a hybrid variety was used (compared with an open populated variety) and an indicator for whether the data come from the OFRA trial (wortmann, 15) rather than the CIMMYT-supervised trials 15,52. All continuous variables are standardized prior to estimation to a mean of zero and standard deviation of 1.

Extended Data Fig. 2 Mean predicted fertilizer yield response conditional on each predictor (solid line), bounded by 95% confidence intervals (shaded area).

The gray line in the lower section of each graph shows that explanatory variable’s density over its range. These responses are plotted over average growing season temperature (a), total growing season precipitation (b), soil cation exchange capacity (c), soil pH (d), soil exchangeable acidity (e), soil organic matter (f), total soil nitrogen (g), soil clay content (h), soil silt content (i), soil bulk density (j), and elevation (k). The fertilizer response is predicted using a simulation dataset matching each trial site with 1000 years of climate data sampled from historical (1979-2018) climate distributions for that site, centered on predicted mean 2019 temperatures estimated from a linear trend between 1979-2018. An error is sampled for each prediction based on the standard error of the out-of-sample yield prediction for each observation. The treatment effects are plotted with a local linear regression over the range of each explanatory variable.

Extended Data Fig. 3 Map depicting locations of fertilizer trial data used to estimate the fertilizer response model and maize and urea price data used to predict fertilizer and maize prices.

Panel (a) maps the fertilizer trial data from the three different sources that we have compiled – CIMMYT-supervised trials that were included in the Lobell et al. study 15 (circles), additional CIMMYT-supervised trials accessed through the International Maize Trial Network 52 (triangles), and the OFRA trial data by Wortmann et al. 49 (squares). Panel (b) depicts the locations from which we observe monthly maize prices (in yellow), monthly urea prices (in orange) or both maize and urea prices (in grey). Maize prices were downloaded from the FAO Global Information and Early Warning System (GIEWS) dataset 68. Urea prices were downloaded from AfricaFertilizer.org 69.

Extended Data Fig. 4 Predicted yield response to fertilizer that is expected at least 70% of the time (a), and the price ratio between fertilizer and maize that would be required to satisfy the “robust” profitability criteria.

Panel (a) yield responses are simulated using the random forest yield response model and the synthetic climate dataset. The color shading indicates the simulated yield response to fertilizer (t/ha) at the P=0.7 probability threshold. Given the modeled yield response in panel (a), panel (b) depicts the price ratio between fertilizer and maize that would be required in order for the IRR to exceed 30% at the P=0.7 probability threshold.

Extended Data Fig. 5 Alternate version of Fig. 2c, where “naive” profitability is based on IRR≥30% instead of IRR≥100%.

This figure offers an alternate version of Fig. 2c that applies the same profitability criteria as the "robust" profitability definition defined in the manuscript.

Extended Data Fig. 6 Sensitivity analysis at different points in the yield distribution (a-c) and IRR distribution (d-f).

Panels (a-c) show the predictor to which predicted yield response is most sensitive at the 5th percentile, 50th percentile, and 95th percentile of the yield distribution, respectively. Panels (d-f) show the input variable to which IRR is most sensitive at the 5th percentile, 50th percentile, and 95th percentile of the IRR distribution, respectively. Sensitivity to each input variable is defined using a local, one-at-a-time sensitivity analysis. The variable to which yield difference is most sensitive does not change significantly across its distribution, while the sensitivity of IRR to prices (specifically urea prices) increases as IRR increases. This, and the similarity in sensitivity of yield difference and IRR at low percentiles, suggest that yields are more limiting when profitability is low.

Extended Data Table 1 Summary statistics of estimation dataset by fertilizer management strategy.

The left three columns show raw means (and standard deviations) of the explanatory variables by fertilizer use, along with the normalized difference between fertilized and non fertilized observations. The right three columns show mean (and standard deviation) of the explanatory variables weighted (wgt) by the site-level probability of including some no-fertilizer observations. Technologies and management practices predictors \(\overline{\theta }\) include use the Fertilized plot dummy, the OFRA trial indicator, and the hybrid variety indicator. Site characteristics predictors (Xi) include cation exchange capacity, soil pH, soil exchangeable acidity, soil organic matter, total soil nitrogen, soil clay share, soil silt share, soil bulk density, elevation, and a poor drainage indicator. The weather realization predictors (ωit) include average temperature over three growing season segments and total precipitation over three growing season segments.

Extended Data Table 2 Datasets used to model and simulate fertilizer yield response and profitability.

This table identifies and describes the datasets used to model and simulate the yield response and profitability of fertilizer.

Extended Data Table 3 Fertilizer response and profitability predictions by country.

The first column shows the number of cells per country for which yield predictions are generated (each cell is approximately 770km2 at the equator). The criteria for generating yield predictions are described in the methods section of the paper. The second column shows the mean yield response for each country at the probability threshold (i.e., the average over the country of the yield response to fertilizer that is expected at least 70% of the time). The third column shows what fertilizer to maize price ratio would be required for fertilizer use to be profitable at the probability threshold, given the predicted yield response at the profitability threshold. A lower fertilizer to maize price ratio indicates fertilizer is more affordable relative to maize. The fourth column shows the share of cells modeled in the country for which price data are also available. The fifth column shows the mean profitability (IRR) across cells within a country, for which price data are available, at the probability threshold. The sixth column shows the share of cells in the country (out of the total cells for which price data are available) in which profitability is robust according to the criteria described in the paper.

Extended Data Table 4 Predicted yield response by estimation approach.

FGLS indicates the standard parametric production function estimated with a feasible generalized least squares regression, with variables selected from the full 18x18 prediction vector interacted with itself (fertilizer treatment plus 17 predictors). We select the subset of interacted predictors to include in the regression using a variable selection technique in order to minimize out of sample prediction error (root mean square error). The random forest model results are most directly comparable to the FGLS results in that the random forest model predicts yields using the fertilizer treatment variable and the additional 17 predictors. In both cases, we generate an average predicted fertilizer response by predicting yields at each data point with and without fertilizer use, then collapsing those predicted differences to the site level then averaging using site level propensity weights. RMSE is based on the difference between actual and predicted yields for the prediction dataset. The causal forest model directly estimates the yield response to the treatment variable (fertilizer use) conditional on the vector of 17 predictors, using an approach that is very similar to the random forest model. It does not generate yield predictions, nor can we calculate RMSE because we do not observe an “actual” fertilizer treatment effect. We collapse the causal forest model yield predictions also by collapsing them to the site level then averaging using site level propensity weights.

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Supplementary Discussion: previous attempts to understand fertilizer use in sub-Saharan Africa.

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McCullough, E.B., Quinn, J.D. & Simons, A.M. Profitability of climate-smart soil fertility investment varies widely across sub-Saharan Africa. Nat Food 3, 275–285 (2022). https://doi.org/10.1038/s43016-022-00493-z

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