Analytical growth equations and their Genstat 5 equivalents

This paper compares two ways of representing some of the existing growth fu nctions, i.e., the exponential, the monomolecular or Mitscherlich, the logi stic or autocatalytic, the Gompertz, and the Richards equations. A second o rder exponential polynomial will be discussed as well. In the first express ion growth is expressed in the parameters mass at time zero W-o, mass at ti me infinity W-f, and a measure for the relative growth rate k. In the secon d expression different parameters are used because of robust parameter opti mization (e.g., by the statistical software package Genstat). This paper sh ows the relationships between these fitted parameters and the parameters W- o,W-f and k. This paper addresses the properties of these models, such as p hysical meaning of the parameters, properties at the point of inflection (i f existing), and the growth rate in the limit W --> 0. The second order exp onential polynomial is rewritten in such way that use is made of a proporti onality constant, being equal to the relative growth rate at point of infle ction. Application of the growth models is demonstrated using data of lettu ce grown on nutrient film. Finally, it is shown that, except for the expone ntial polynomial, all growth equations originate from one single equation.