A modified Mitscherlich equation for rainfed crop production in semi-arid areas: 1. Theory

Abstract

The classical Mitscherlich equation is based on Liebig's Law of the Minimum and describes the yield response of a crop to an increase in the main factor that is limiting growth. The maximum, or potential, yield is an important parameter in the Mitscherlich equation and is assumed to be constant, that is, not affected by other factors that limit actual yields under field conditions. The assumption that potential yield is a constant does not apply to rainfed agriculture in semi-arid regions because under such conditions potential yields vary with crop-available moisture. A theoretical framework for the application of the Mitscherlich equation to rainfed crop production is presented. Water-limited potential yield is assumed to be a linearly increasing function of available moisture. Similarly, the quantity of nutrients required by a crop to achieve water-limited potential yield is assumed to be a linearly increasing function of seasonal rainfall. Finally, nutrient availability is also thought to depend on available moisture. The general form of the modified Mitscherlich equation for response to nutrients is simplified, by expressing all moisture dependent parameters as functions of annual rainfall.