The Law of the Minimum as a Thinking Tool

Abstract

The law of the minimum, reputedly originally conceived by Justus von Liebig more than one hundred fifty years ago, is a powerful tool in understanding processes with unknown details. The objective of this study was to provide a rationale and some evidence for such a claim. To do so, I assume that the law of the minimum is to be specified as the linear response and plateau (LRP) model: Y=min {X, U}, where X is the limiting variable when it is smaller than U, and U the limiting variable when it is smaller than X. These variables may be either stocks or flows. The study shows that the law thus specified has nothing to do with empiricism but is purely a form of thinking that can be intuitively or logically understood by anyone. As such, it can be applied not only to biological, chemical, and physical processes of academic interests, but also to various processes in our daily lives. In this article, the following examples were given: (ii) the dry-matter partition associated with crop production, (i) crop growth in an environment of abundant resources, and (ffi) evapotranspiration in relation to precipitation and net radiation. The law of the minimum is also shown to be useful in analyzing the relationship between sink and source variables to identify the limiting factor. © 2006, The Society of Agricultural Meteorology of Japan. All rights reserved.