Economic phosphorus fertilization using a linear response and plateau function

The linear response and plateau model is now used extensively to depict the relationship between crop yield and soil test level. This function has not been subjected to economic analysis extensively as the variation in critical level is seldom known. Yield data for corn, soybean, and wheat grown on a sandy Typic Umbraquult, which has a low phosphrous (P) sorption capacity, for 13 years were available from a residual P experiment. The study had six replications with 20 observations each, so critical levels of Mehlich-3-extractable P (M3P) were calculated on each replication. The critical level mean and standard deviation per crop were used to determine the probability of the critical level being within a 2.5 mg/L increment of M3P. Expected profit was calculated by summation of the gross income minus P fertilizer and other production costs for each increment at selected M3P recommendations. The yield critical levels for the three crops were between 25 and 32 mg/L and the standard deviations 23 to 31% of the mean. With current crop prices and fertilizer costs the economic critical levels were between 31 and 35 mg/L, so a mean of 33 mg/L seems applicable for these three crops. This value is about 14% greater than the average yield critical level when using the linear response and plateau model, indicating that for most field crops the soil test level beyond which no fertilization is suggested should be about 1.14 times the average critical level for yield. Certainly, this value should not be greater than 1.5 times the yield critical level. Utilization of this information would result in more economic production of these field crops and less over-fertilization of soils.