Properties and prediction accuracy of a sigmoid function of time-determinate growth

Abstract

The properties and short-term prediction accuracy of mathematical model of sigmoid time-determinate growth, denoted as “KM-function”, are presented. Comparative mathematical analysis of the function revealed that it is a model of asymmetrical sigmoid growth, which starts at zero size of an organism and terminates when it reaches its final size. The function assumes a finite length of the growth period and includes a parameter interpretable as the expected lifespan of the organism. Moreover, the possibility for growth curve inflexion at any age is possible, so the function can be used for modelling of S-shaped growth trajectories with various degree of asymmetry. These good theoretical predispositions for realistic growth predictions were empirically evaluated. The KM-function used in three and four-parameter forms was compared with three classical (Richards, Korf and Weibull) growth functions employing two parameterisation methods - nonlinear least squares (NLS) and Bayesian method. The evaluation was conducted on the basis of the tree diameter series obtained from stem analyses. The main empirical findings are: (i) if the minimisation of the prediction bias is required, the KM-function in three-parameter form in connection with Bayes parameterisation can be recommended; (ii) if the minimisation of root square error (RMSE) is required, the best short-term prediction results for a particular dataset were obtained with four-parameter Weibull function employing NLS parameterisation; (iii) moreover, three-parameter functions parameterised by Bayesian methods show a considerably smaller RMSE by 15-25% as well as smaller biases by 40-60% than four-parameter functions employing NLS. Overall, all analyses confirmed relative usefulness of the KM-function in comparison with classical growth functions, especially in connection with Bayesian parameterisation.