title: Relationship between Modelling Accuracy and Inflection Point Attributes of Several Equations while Modelling Stand Diameter Distributions.
abstract: In this study, seven popular equations, including 3-parameter Weibull, 2-parameter Weibull, Gompertz, Logistic, Mitscherlich, Korf and R distribution, were used to model stand diameter distributions for exploring the relationship between the equations' inflection point attributes and model accuracy. A database comprised of 146 diameter frequency distributions of Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) plantations was used to demonstrate model fitting and comparison. Results showed that the inflection points of the stand diameter cumulative percentage distribution ranged from 0.4 to 0.6, showing a 1/2 close rule. The equation's inflection point attribute was strongly related to its model accuracy. Equation with an inflection point showed much higher accuracy than that without an inflection point. The larger the effective inflection point interval of the fitting curve of the equation was, and the closer the inflection point was to 0.5 for the equations with fixed inflection points, the higher the equation's accuracy was. It could be found that the equation's inflection point had close relationship with skewness of diameter distribution and stand age, stand density, which provided a scientific basis for model selection of a stand diameter distribution for Chinese fir plantations and other tree species.
authors.affiliation: State Key Laboratory of Tree Genetic and Breeding, Key Laboratory of Tree Breeding and Cultivation of State Forestry Administration, Research Institute of Forestry, Chinese Academy of Forestry, Beijing, China.
authors.forename: Aiguo
authors.initials: A
authors.lastname: Duan
authors.affiliation: State Key Laboratory of Tree Genetic and Breeding, Key Laboratory of Tree Breeding and Cultivation of State Forestry Administration, Research Institute of Forestry, Chinese Academy of Forestry, Beijing, China.
authors.forename: Jianguo
authors.initials: J
authors.lastname: Zhang
authors.affiliation: State Key Laboratory of Tree Genetic and Breeding, Key Laboratory of Tree Breeding and Cultivation of State Forestry Administration, Research Institute of Forestry, Chinese Academy of Forestry, Beijing, China.
authors.forename: Xiongqing
authors.initials: X
authors.lastname: Zhang
authors.affiliation: State Key Laboratory of Tree Genetic and Breeding, Key Laboratory of Tree Breeding and Cultivation of State Forestry Administration, Research Institute of Forestry, Chinese Academy of Forestry, Beijing, China.
authors.forename: Caiyun
authors.initials: C
authors.lastname: He
mesh_terms: D002681:China; D032486:Cunninghamia / Q000033:anatomy & histology; D016208:Databases, Factual; D065928:Forests; D008954:Models, Biological; D008962:Models, Theoretical