Adapting the QUEFTS model to predict attainable yields when training data are characterized by imperfect management

Understanding yield responses to nutrient application is a key input for extension advice and strategic agricultural investments in developing countries. A commonly used model for yield responses to nutrient inputs in tropical smallholder farming systems is QUEFTS (QUantitative Evaluation of the Fertility of Tropical Soils). While QUEFTS has a strong conceptual foundation, a key assumption is that nutrients are the only limiting factors. One implication of this is the required assumption of ‘perfect management’. This may be problematic in the application of QUEFTS in smallholder farming systems with a wide variety of yield limiting factors. In a previous study, QUEFTS was calibrated using farm trials in two major maize production zones in Nigeria. To reduce observed variability in correlations between estimated soil nutrient (N, P, K) supply and soil parameters (e.g. soil organic carbon, soil pH; step 1 of QUEFTS) a Mahalanobis distance method was used to remove data points not adhering to expected correlations. In this study, we assessed an alternative approach: can the QUEFTS model be adapted to fit smallholder farming systems and associated variation in management? Using 676 observations from the same nutrient omission trials in two major maize production zones in Nigeria, we compare a standard linear regression approach with a quantile regression approach to calibrate QUEFTS. We find that under the standard linear regression approach, there is a poor relation between predicted and observed yields. Using quantile regression, however, QUEFTS performed better at predicting attainable yields – defined as the 90th percentile of observed yields – under a wide variety of production conditions. Our results indicate that using quantile regression as a way to predict attainable yields, is a useful alternative implementation of QUEFTS in smallholder farming systems with high variability in management and other characteristics.