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Pooling Experiments Over Time to Quantify the Dynamics of Dryland Winter Wheat Yield Response

Dep. of Agricultural Economics, Univ. of California-Davis, Davis, CA 95616

^* Corresponding author.

This research had a dual purpose: (i) statistical estimation of winter wheat (Triticum aestivum L.) yield response as a function of plant available water and applied N fertilizer from an 8-yr experiment in north-central Montana and (ii) illustration of the modeling methods that are appropriate in this type of research. Summer-fallowed and re-cropped treatments were pooled to obtain an indirect estimate of the extra amount of N made available by summer fallow, as well as to improve the implicit experimental design by providing the necessary variation in plant available water, particularly soil water at seeding. The statistical model was nonlinear regression with an error components disturbance term entering multiplicatively. A new flexible functional form is presented for crop response; it is a polynomial generalization of the Mitscherlich single-factor equation. A major task was to validate the regression model by considering various types of specification errors, such as accounting for all concomitant factors associated with pooling the experiments over time. Mineralized N during summer fallow was found to be a negatively sloped linear function of precipitation during the fallow period; the average amount was 24.5 kg ha^–1. Nitrogen and water have strong interactions in shaping the yield response surface, and at high levels of both factors, more of either depresses yield. The depressing effect of N on yield at very low levels of water was clearly discerned.

Received for publication August 20, 1993.