中文摘要：

Logistic、Mitscherlich、Gompertz方程是一类三参数饱和增长曲线模型，广泛地应用于许多学科领域．本文基于logistic方程饱和值K估计的三点法、四点法，推导出Mitscherlich、Gompertz方程K值的三点法、四点法估计公式，并以南亚热带季风常绿阔叶林中两种优势乔木厚壳桂、黄果厚壳桂种群为例，先用三点法或四点法估计出K值，再通过线性回归与非线性回归相结合的方法，可获得三个增长模型中三个参数的最优无偏估计．实例研究表明，两个优势种群增长数据均符合三个增长模型，但更符合增长曲线呈S形的logistic、Gompertz方程，且以logistic方程最适合于观察；黄果厚壳桂种群增长快于厚壳桂种群．

英文摘要：

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.