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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.


Related in: MedlinePlus

Examples of the observed diameter distributions.The diameter frequency percentage distribution (solid line with dots), the diameter cumulative percentage distribution (histograms). (A: 1667 stems/ha, 6 a, 9.8 cm; B: 1667 stems/ha, 12 a, 15.7 cm; C: 1667 stems/ha, 18a, 18.0cm; D: 5000 stems/ha, 6 a, 7.0 cm; E: 5000 stems/ha, 12 a, 10.6 cm; F: 5000 stems/ha, 18a, 12.0cm).
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pone.0126831.g001: Examples of the observed diameter distributions.The diameter frequency percentage distribution (solid line with dots), the diameter cumulative percentage distribution (histograms). (A: 1667 stems/ha, 6 a, 9.8 cm; B: 1667 stems/ha, 12 a, 15.7 cm; C: 1667 stems/ha, 18a, 18.0cm; D: 5000 stems/ha, 6 a, 7.0 cm; E: 5000 stems/ha, 12 a, 10.6 cm; F: 5000 stems/ha, 18a, 12.0cm).

Mentions: Diameter class, k, is defined in absolute scale (e.g., [1, 3) for k = 2 cm, [3, 5) for k = 4 cm, etc.), namely, diameter class k is the midpoint value of the absolute scale. The relative frequency of stems in diameter class k of stand i at plot j is given by:Fkij=NkijNij(1)where Nkij is the number of trees of diameter class k of stand i (i = 1, 2, …, 10) at plot j (j = 1, 2, …, 15), and Nij is the total number of trees of stand i at plot j. The cumulative frequency of stems in diameter class k of stand i at plot j can be obtained by:Ckij=F2ij+F4ij+⋯+F(k−2)ij+Fkij(2)where F2ij, F4ij⋯F(k−2)ij, Fkij are > 0, and Ckij is ≤ 1. The k values for every stand density are listed in Table 1. Fig 1 shows some examples of the observed diameter frequency percentage distribution (solid line with dots) and the diameter cumulative percentage distribution (histograms) for some stands from different planting densities, stand ages and quadratic mean DBH.


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)

Examples of the observed diameter distributions.The diameter frequency percentage distribution (solid line with dots), the diameter cumulative percentage distribution (histograms). (A: 1667 stems/ha, 6 a, 9.8 cm; B: 1667 stems/ha, 12 a, 15.7 cm; C: 1667 stems/ha, 18a, 18.0cm; D: 5000 stems/ha, 6 a, 7.0 cm; E: 5000 stems/ha, 12 a, 10.6 cm; F: 5000 stems/ha, 18a, 12.0cm).
© Copyright Policy
Related In: Results  -  Collection

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

pone.0126831.g001: Examples of the observed diameter distributions.The diameter frequency percentage distribution (solid line with dots), the diameter cumulative percentage distribution (histograms). (A: 1667 stems/ha, 6 a, 9.8 cm; B: 1667 stems/ha, 12 a, 15.7 cm; C: 1667 stems/ha, 18a, 18.0cm; D: 5000 stems/ha, 6 a, 7.0 cm; E: 5000 stems/ha, 12 a, 10.6 cm; F: 5000 stems/ha, 18a, 12.0cm).
Mentions: Diameter class, k, is defined in absolute scale (e.g., [1, 3) for k = 2 cm, [3, 5) for k = 4 cm, etc.), namely, diameter class k is the midpoint value of the absolute scale. The relative frequency of stems in diameter class k of stand i at plot j is given by:Fkij=NkijNij(1)where Nkij is the number of trees of diameter class k of stand i (i = 1, 2, …, 10) at plot j (j = 1, 2, …, 15), and Nij is the total number of trees of stand i at plot j. The cumulative frequency of stems in diameter class k of stand i at plot j can be obtained by:Ckij=F2ij+F4ij+⋯+F(k−2)ij+Fkij(2)where F2ij, F4ij⋯F(k−2)ij, Fkij are > 0, and Ckij is ≤ 1. The k values for every stand density are listed in Table 1. Fig 1 shows some examples of the observed diameter frequency percentage distribution (solid line with dots) and the diameter cumulative percentage distribution (histograms) for some stands from different planting densities, stand ages and quadratic mean DBH.

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