Fitting Three-Parameter Growth Models:A Study Case of Two Dominant Tree Populations in Monsoon Evergreen Broad-leaved Forest,China

Logistic,Mitscherlich,and Gompertz growth models are commonly used in various fields such as economics,demography,and population ecology.These non-linear equations belong to saturation growth curve models with three parameters and can be transformed into linearized forms.Some methods have been developed to estimate these parameters that are biologically meaningful. Previous work has presented three-and four-point methods for estimating the saturation parameter K(i.e.,carrying capacity)of the logistic equation.Here we present the three-and four-point methods to estimate the saturation parameter(or asymptotic parameter)K of the Mitscherlich,and Gompertz equations.Firstly we calculate K by the three-or four-point method, and then perform linear regressions in the linearized forms of the three models to estimate the other two parameters and test the significance of these regression equations by analysis of variance. When the linearized regressions are statistically significant,we use the three parameters estimated above as starting values to perform non-linear regressions on the three non-linear equations(using Levenberg-Marquardt method),and obtain the best unbiased estimators of the three parameters of each model. We employ the population growth data of two dominant tree species,Cryptocarya chinensis and C.concinna in the Cryptocarya community in lower subtropical monsoon evergreen broad- leaved forest of the Dinghushan Biosphere Reserve,Guangdong Province of South China for this study case.Our results show that:(1)the population growth data of both tree species statistically follow all the three growth models well,but ecologically match the sigmoid logistic and Gompertz models better,especially the logistic model,and(2)C.concinna population growth is more rapid than C.chinensis population growth.