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- Title
Properties and prediction accuracy of a sigmoid function of time-determinate growth.
- Authors
Sedmák, Róbert; Scheer, Lubomír
- Abstract
The properties and short-term prediction accuracy of a mathematical model of sigmoid time-determinate growth, denoted as "KM-function", are presented. The model is suitable for representing the asymmetrical sigmoid growth of an organism, starting at zero size and terminating when the final size is reached. 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 allows to model S-shaped growth trajectories with various degree of asymmetry. The suitability of such theoretical model to predict the real growth of trees was empirically assessed. Three and four-parameters forms of the KM-function was compared with three classical (Richards, Korf and Weibull) growth functions using two parametrization methods, i.e., the nonlinear least squares (NLS) and the Bayesian method. The parametrization/validation dataset was made of 67 tree diameter series obtained from stem analyses. Main results may be summarized as follows: (i) the use of the three-parameter KM-function with the Bayes parametrization method is recommended when the minimization of prediction bias is required; (ii) the best short-term prediction results, in terms of minimization of root square error (RMSE), were obtained using the four-parameter Weibull's function and the NLS parametrization method; (iii) three-parameter functions parametrized by Bayesian methods show a considerably smaller RMSE (by 15-25%) and biases (by 40-60%) than four-parameter functions using the NLS method. Overall, our results confirmed the relative usefulness of the KM-function in comparison with classical growth functions, especially when combined with Bayesian parametrization methods.
- Subjects
PLANT growth; PREDICTION theory; GROWTH curves (Statistics); MATHEMATICAL models; LEAST squares
- Publication
iForest - Biogeosciences & Forestry, 2015, Vol 8, Issue 5, pe1
- ISSN
1971-7458
- Publication type
Article
- DOI
10.3832/ifor1243-007