How can we estimate optimum fertilizer rates with accuracy and precision?

For decades, agronomists have invested time and resources to identify the optimum nitrogen (N) rates for cereal crops. The most common method for estimating the agronomic optimum N rate (AONR) is to design a field experiment with several N fertilizer rates and fit a regression model to the yield observations. Here, we concentrate on its accuracy and precision given choices of experimental design and statistical analysis. Our first finding is that the choice of functional form has a large agronomic effect on the estimate of the AONR, and this depends on the data-generating model. Our second finding is that improving the precision and accuracy of AONR estimates will demand an increase in the number of N rates and replications. Finally, we propose that using either the best-fitting model or a weighted model is preferable to always choosing either the linear-plateau (negative bias) or quadratic-plateau (positive bias) models.