A Computer Program for Fitting the Richards Function

Abstract

where b is associated with the constant of integration, while the upper sign within the brackets is applicable when n is positive and the lower sign when n lies in the range -1 < n < 0. The function is not defined for n < -1, nor for n = 0. Mathematical properties of the function are given by Richards [1959] and Causton [1967]. Although Richards' function is probably, as yet, the most realistic mathematical description of plant and animal growth, the problem of fitting (2) to experimental data is a formidable one. Richards describes an empirical method of fitting which is not only very laborious but, in the present author's experience, can produce misleading results. Nelder [1961] describes a method of fitting the curve by least squares based on a realistic statistical model, and also provides special tables to assist in the fitting of the curve by hand. The least squares equations obtained in this process htave no explicit solution and have to be solved by iteration from given starting values, which themselves must be obtained by a rather time-consuming procedure. The method of solution of the least squares equations is readily programmed for an electronic computer, but starting values have still to be provided. If