Calculating ex post economic optimum rates of nitrogen fertilization for corn

Rates of nitrogen (N) fertilization usually are selected with the intent of maximizing profits for producers. The most commonly used method of estimating N fertilizer needs, however, does not directly relate rates to profits. This problem was addressed by developing methodology for calculating economic optimum rates (EORs) of N fertilization from large amounts of data collected in trials using precision farming technologies. Distinctions were made between ex post and ex ante EORs and between EORs for individual trials and for samples of trials. Emphasis was placed on collecting and identifying appropriate samples of yield responses to N. Because ex post EORs are calculated for the sole purpose of calculating ex ante EORs, an appropriate sample must adequately represent the spatial and temporal variability in yield responses within a specified area of interest. Cumulative distribution functions were used to characterize variability in yield responses. Discrete marginal analysis was used to identify break-even rates of fertilization and rates that gave a desired level of profit on the last increment of fertilizer. The complement of the relative variance method and analysis of profit increases were used to evaluate alternative methods for classifying variability in yield responses. The profitability of classification was estimated by calculating ex post EORs for the whole sample and for subdivisions of this sample. Evidence presented suggests that effective systems for classification may have to consider factors that have received little attention in the past. A new procedure for calculating ex post EORs was defined as four steps; (i) define the range of conditions under consideration, (ii) collect an appropriate sample of yield responses, (iii) perform economic analyses on this sample, and (iv) explore the possibility that profits could be increased by dividing the sample into two or more populations that have different ex post EORs. Steps iii and iv should be repeated many times to evaluate all possible systems of classification. Application of two near-optimal rates of N in alternating strips across large areas of land was identified as a simple, efficient, and effective way to generate data needed for calculating ex post EORs by this method.