Reparameterizing, Fitting, and Testing a Simple Growth Model

Abstract

If the von Bertalanffy growth model is used to statistically compare the properties of growth in two spatial regions by examination of the estimates of the growth parameter k and the asymptotic length parameter L∞, a possible compound null hypothesis H0, is H0: K1= k2 and L∞1 = L∞ 2 for regions 1 and 2. Since the results of this two-parameter test may be difficult to interpret, an alternative procedure is suggested. In addition, the interpretation of the test must be based upon the nature of the data as well as upon the parameter estimates. A regression fit of the model to real but “inappropriate” data may yield a very “good” statistical fit but unrealistic estimates. The use of a third parameter (for example, t0, the time when length is zero) is necessary to uniquely specify a solution; its inclusion always enhances the statistical fit. Because of the interdependence between parameters k and L∞, we reparameterize the von Bertalanffy model with a new parameter w = k˙L∞. The parameter corresponds to the growth rate near t0 and is suitable for comparisons because of its statistical robustness. In general, the standard Ford-Walford method of estimating the modelˈs parameters is now obsolete and should be replaced with widely available nonlinear regression programs. Such programs generally estimate a variety of statistical criteria that facilitate a quantitative comparison of the growth parameters in H0 above.