A generalization of ordinary yield response functions

In an integrated model study of economics and ecology by Vatn et al. (1996), year specific expressions for crop yield response as a function of N-fertilization constituted an important link between the economic and ecological models. It was recognized, however, that data were too few to uniquely estimate yield response functions in all desired simulation scenarios. In future model studies of this type, however, this problem can be reduced by using a generalization of ordinary yield response functions. An ordinary yield function and a generalized yield function were based on a modified version of the Michaelis–Menten equation, where the generalized type of yield function is taking account of the observed differences between years as to how the yield respond to nitrogen fertilizer. Measurements of dry matter in harvested barley grain from field experiments in south-east Norway (1970–1988) were used for parameter estimation and the predictive power was evaluated by cross validation. Based on the prize of grains and nitrogen fertilizers, both yield functions were used to calculate the expected economic optimum amount of N-fertilizer. The particular advantage of using a physiologically grounded functional relationship like the Michaelis–Menten equation, drawbacks and strengths of the two types of yield functions, and the use of dynamic crop-growth models to generate simulated data points of yield dry weight, for use in situations where real observations are few or completely unavailable, are discussed.