Modeling Diameter Distributions of Mixed-Oak Stands In Northwestern Turkey

Özçelik, Ramazan; Cao, Quang V.; Kurnaz, Emine; Koparan, Burak

doi:10.1590/0104776020222801102991

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Forest Management • CERNE 28 • 2022 • https://doi.org/10.1590/0104776020222801102991 copy

Modeling Diameter Distributions of Mixed-Oak Stands In Northwestern Turkey

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

Background:

Diameter distribution models are one of the most important components of growth and yield models. Diameter distribution models, based on the Weibull function, were developed for even-aged mixed-oak stands (Turkey oak, Sessile oak, and Hungarian oak) in northwestern Turkey. Two modeling methods were considered. Weibull parameters were recovered from either equation predicting Dq and Dvar (method of moments) or equations predicting Dq and D ₉₀ (hybrid method). For each modeling method, three estimation methods were considered: (a) Least Squares method, (b) CDF Regression method in which regression coefficients were estimated separately for each species, and (c) CDF Regression method in which regression coefficients were simultaneously estimated for all species.

Results:

Results indicated that the hybrid method coupled with the CDF Regression estimation method yield best results in this study. Similar results were obtained when the regression coefficients were estimated either separately for each species or simultaneously for all species.

Conclusion:

The proposed models enable one to predict diameter distribution of a given mixed-oak species stand in northwestern Turkey, using limited stand information. These models are useful tools for the inventory and management of mixed-oak stands.

Keywords:
Stand structure; Weibull function; Parameter prediction; CDF Regression; Mixed-stands

HIGHLIGHTS

Diameter distribution models were developed for even-aged mixed-oak stands.

Two modelling and three estimation methods were used for estimation of Weibull parameters.

The hybrid method coupled with the CDF Regression estimation method yielded best results.

The models are useful tools for the inventory and management of mixed-oak stands.

Species Group	Quercus cerris	Quercus petraea	Quercus frainetto	Number of plots	Percent
1	✓			2	1.79
2		✓		1	0.89
3			✓	0	0.00
4	✓	✓		50	44.64
5	✓		✓	15	13.39
6		✓	✓	34	30.36
7	✓	✓	✓	10	8.93

Variable	Quercus cerris		Quercus petraea		Quercus frainetto		All
Number of trees/ha	341.02	(214.39)	289.00	(225.15)	299.83	(200.82)	637.53	(233.51)
Basal area (m ²/ha)	13.21	(11.54)	9.06	(8.97)	6.46	(5.92)	20.17	(14.49)
Quadratic mean dbh (cm)	21.70	(6.74)	19.66	(6.84)	15.98	(3.57)	19.48	(6.56)
Minimum diameter (cm)	15.37	(5.58)	14.44	(5.77)	11.07	(2.94)	12.88	(5.20)
Dominant height (m)							18.59	(7.72)
Plot Size (ha)							0.06	(0.02)

Dependent Variable	Species1/	Regression Equation	R2
Dmin	1	\begin{equation}{\rm Dmin}_1=\frac{{\rm Dq}_1}{1+exp\left[a_{01}+a_{11}\ln(N_1)\right]}\end{equation}	0.8935
	2	\begin{equation}{\rm Dmin}_2=\frac{{\rm Dq}_2}{1+exp\left[a_{02}+a_{12}\ln(N_2)\right]}\end{equation}	0.9385
	3	\begin{equation}{\rm Dmin}_3=\frac{{\rm Dq}_3}{1+exp\left[a_{03}+a_{13}\ln(N_3)\right]}\end{equation}	0.7757
Dvar	1	\begin{equation}{\rm Dvar}_1=exp\left[b_{01}+b_{11}\ln(N)+b_{21}\ln(B)+b_{31}\ln(N_1)\right]\end{equation}	0.3857
	2	\begin{equation}{\rm Dvar}_2=exp\left[b_{02}+b_{12}\ln(N_2)+b_{22}\ln(B_2)\right]\end{equation}	0.5449
	3	\begin{equation}{\rm Dvar}_3=exp\left[b_{03}+b_{13}\ln(N)+b_{23}\ln(B)+b_{33}\ln(N_3)+b_{43}\ln(B_3)\right]\end{equation}	0.4986
D90		\begin{equation}D_{90,1}=exp\left[c_{01}+c_{11}\ln(N_1)+c_{21}\ln(B_1)\right]\end{equation}	0.9487
		\begin{equation}D_{90,2}=exp\left[c_{02}+c_{12}\ln(N_2)+c_{22}\ln(B_2)\right]\end{equation}	0.9537
		\begin{equation}D_{90,3}=exp\left[c_{03}+c_{13}\ln(N_3)+c_{23}\ln(B_3)\right]\end{equation}	0.8669

Statistic	Species	Method
Statistic	Species	1a	1b	1c	2a	2b	2c
AD	Q. cerris	1.4761	0.9158	0.9167	0.8879	0.8651	0.8389
		(6.00)	(1.60)	(1.61)	(1.39)	(1.21)	(1.00)
	Q. petraea	0.9705	0.9256	0.9258	1.0896	0.8916	0.9028
		(2.99)	(1.86)	(1.86)	(6.00)	(1.00)	(1.28)
	Q. frainetto	0.8070	0.7826	0.7697	0.9794	0.8000	0.8148
		(1.89)	(1.31)	(1.00)	(6.00)	(1.72)	(2.07)
-lnL	Q. cerris	58.163	54.862	54.875	54.498	54.400	54.331
		(6.00)	(1.69)	(1.71)	(1.22)	(1.09)	(1.00)
	Q. petraea	45.040	44.837	44.839	45.338	44.759	44.771
		(3.42)	(1.67)	(1.69)	(6.00)	(1.00)	(1.11)
	Q. frainetto	42.180	42.247	42.215	42.633	42.204	42.232
		(1.00)	(1.74)	(1.39)	(6.00)	(1.27)	(1.57)
KS	Q. cerris	0.1890	0.1712	0.1713	0.1749	0.1723	0.1719
		(6.00)	(1.00)	(1.02)	(2.05)	(1.30)	(1.19)
	Q. petraea	0.2039	0.2055	0.2055	0.2123	0.2048	0.2052
		(1.00)	(1.96)	(1.93)	(6.00)	(1.51)	(1.78)
	Q. frainetto	0.2024	0.1996	0.1982	0.2162	0.2030	0.2040
		(2.18)	(1.41)	(1.00)	(6.00)	(2.33)	(2.62)
EI	Q. cerris	478.89	459.83	459.89	459.89	457.77	458.12
		(6.00)	(1.49)	(1.50)	(1.50)	(1.00)	(1.08)
	Q. petraea	391.83	391.04	391.07	394.65	390.03	390.25
		(2.95)	(2.10)	(2.13)	(6.00)	(1.00)	(1.23)
	Q. frainetto	408.82	409.33	409.19	412.14	408.37	408.55
		(1.61)	(2.28)	(2.09)	(6.00)	(1.00)	(1.25)

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[1] ✤Corresponding author e-mail ramazanozcelik@isparta.edu.tr