Analytical growth equations and their Genstat 5 equivalents

Abstract

Two ways of representing some of the existing growth functions, (the exponential, the monomolecular or Mitscherlich, the logistic or autocatalytic, the Gompertz, and the Richards equations) are compared. In the first, growth is expressed in the parameters mass at time zero W0, mass at time infinity Wf, and a measure for the relative growth rate k. In the second, different parameters are used because of robust parameter optimization (e.g., by the statistical software package Genstat). The relationships between these fitted parameters and the parameters W0, Wf and k are demonstrated. The properties of these models, such as physical meaning of the parameters, properties at the point of inflection (if it exists), and the growth rate at a limit W -> 0, are examined. The second order exponential polynomial was rewritten in such a way that use was made of a proportionality constant, equal to the relative growth rate at the point of inflection. Application of the growth models is demonstrated using data for lettuce grown in a nutrient film system. Finally, it is shown that, except for the exponential polynomial, all growth equations originate from one single equation.