Disaggregating model bias and variability when calculating economic optimum rates of nitrogen fertilization for corn

Efforts to calculate economic optimum rates (EORs) of N fertilization for corn (Zea mays L.) have been hampered by a lack of methods for disaggregating problems caused by model bias and variability in crop responses to N. We illustrate how the concepts of ex post and ex ante analyses can be used in a multistep procedure to disaggregate these problems when calculating ex post EORs when large amounts of data are available. Five models were used to describe yield responses from a collection of 54 small-plot trials that included seven rates of N. The multistep procedure included steps to reduce model bias and steps to reduce unexplained variability by forming categories based on information available at the time of fertilization. The concepts of ex post and ex ante analyses were used to clarify what information is important at each stage of the procedure and to ensure that information generated in early steps is used effectively in later steps. Analyses illustrate that calculated values for EORs should be expected to vary with the amounts of information available and that the new procedure can be described as a systematic search for the best FOR that can be calculated with existing information. Although this procedure may have little practical use when data are collected in traditional small-plot trials, illustration of this method by using data collected in such trials revealed the problems of model bias and variability in yield response as well as the potential for solving these problems in production systems where advances in technology make it practical to collect unprecedented amounts of data.