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Relationship between Modelling Accuracy and Inflection Point Attributes of Several Equations while Modelling Stand Diameter Distributions.

Duan A, Zhang J, Zhang X, He C - PLoS ONE (2015)

Bottom Line: 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.

View Article: PubMed Central - PubMed

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.

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.

No MeSH data available.


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Frequency percentage of different distribution interval of ordinates of stand inflection points.
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pone.0126831.g005: Frequency percentage of different distribution interval of ordinates of stand inflection points.

Mentions: For every 146 stands, there was always an equation among the seven equations that could precisely model the observed diameter distribution. Based on the best model, RSS valuse were all very small, and less than 0.01 (Table 3). The inflection point of every observed diameter distribution could be calculated based on its best equation. In fact, no single equation always had the best model accuracy for all the stands. For the 146 stands, the R distribution was selected as the best equation for 71 times, 3-parameter Weibull, 2-parameter Weibull, Logistic 55, 3, 2 respectively. R distribution and 3-parameter Weibull were simultaneously selected 7 times (Fig 4). The 146 inflection values were then obtained for the 146 stands from different equations. Fig 5 summarizes the distribution of inflection point of the 146 stands. The inflection points of the observed stand diameter cumulative percentage distributions ranged from 0.3787 to 0.6436, mainly between (0.4, 0.6) (Fig 5).


Relationship between Modelling Accuracy and Inflection Point Attributes of Several Equations while Modelling Stand Diameter Distributions.

Duan A, Zhang J, Zhang X, He C - PLoS ONE (2015)

Frequency percentage of different distribution interval of ordinates of stand inflection points.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4446310&req=5

pone.0126831.g005: Frequency percentage of different distribution interval of ordinates of stand inflection points.
Mentions: For every 146 stands, there was always an equation among the seven equations that could precisely model the observed diameter distribution. Based on the best model, RSS valuse were all very small, and less than 0.01 (Table 3). The inflection point of every observed diameter distribution could be calculated based on its best equation. In fact, no single equation always had the best model accuracy for all the stands. For the 146 stands, the R distribution was selected as the best equation for 71 times, 3-parameter Weibull, 2-parameter Weibull, Logistic 55, 3, 2 respectively. R distribution and 3-parameter Weibull were simultaneously selected 7 times (Fig 4). The 146 inflection values were then obtained for the 146 stands from different equations. Fig 5 summarizes the distribution of inflection point of the 146 stands. The inflection points of the observed stand diameter cumulative percentage distributions ranged from 0.3787 to 0.6436, mainly between (0.4, 0.6) (Fig 5).

Bottom Line: 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.

View Article: PubMed Central - PubMed

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.

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.

No MeSH data available.


Related in: MedlinePlus