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

Area of Science:

• Forestry
• Quantitative Ecology
• Statistical Modeling

Background:

• Stand diameter distribution is crucial for forest management and yield prediction.
• Various mathematical equations are used to model these distributions, but their accuracy varies.
• Understanding the relationship between equation attributes and accuracy is essential for selecting appropriate models.

Purpose of the Study:

• To evaluate the accuracy of seven common equations for modeling Chinese fir stand diameter distributions.
• To explore the relationship between the inflection point attributes of these equations and their predictive accuracy.
• To provide a basis for selecting accurate distribution models for Chinese fir plantations.

Main Methods:

• Utilized a database of 146 Chinese fir diameter frequency distributions.
• Fitted seven equations: 3-parameter Weibull, 2-parameter Weibull, Gompertz, Logistic, Mitscherlich, Korf, and R distribution.
• Analyzed the inflection point characteristics and their correlation with model accuracy.

Main Results:

• Inflection points of cumulative percentage distributions ranged from 0.4 to 0.6, following a 1/2 rule.
• Equations with inflection points demonstrated significantly higher accuracy than those without.
• Accuracy increased with a larger effective inflection point interval and proximity to 0.5 for fixed inflection points.

Conclusions:

• The inflection point is a critical attribute influencing the accuracy of stand diameter distribution models.
• Model accuracy is related to the inflection point's position, interval, and factors like stand age and density.
• Findings offer a scientific foundation for selecting appropriate distribution models for Chinese fir and potentially other tree species.