Construction of the Site Index Model of Secondary Populus Davidiana×Betula Platyphylla Mingled Forest in Northern Hebei Mountains

doi:10.13466/j.cnki.lczyyj.2024.03.009

Abstract

Abstract:

In broad-leaved mingled forest with multiple tree species and complex structures,constructing a high-precision site index model based on the diameter at breast height of dominant trees is a key scientific challenge in evaluating the site quality of these forests.The Populus davidiana and Betula platyphylla broad-leaved mingled forest in Mulan Weichang,Hebei Province is selected as the research object.Based on the survey data from 70 standard plots(each standard land area is 0.06 hm²),using the nonlinear least squares method,BP neural network,and nonlinear mixed-effects model,three parameter estimation methods are used to construct the site index models of P.davidiana and B.platyphylla broad-leaved mingled forest.Using Mean Square Error(MSE),Root Mean Square Error(RMSE),Mean Percentage Bias(MPB),Coefficient of Determination(R²),Adjusted Coefficient of Determination($R_{\mathrm{adj}}^{2}$),Akaike Information Criterion(AIC),Bayesian Information Criterion(BIC),and Negative Twice the Log-Likelihood(-2LL),the impact of different parameter estimation methods on model prediction accuracy is compared.The results show that:1)Among the five candidate equations,the logistic equation with the diameter at breast height of dominant trees as the independent variable is the optimal site index base model for the mingled P.davidiana and B.platyphylla broad-leaved forest,and the MSE,RMSE,MPB,R²,$R_{\mathrm{adj}}^{2}$ of its model are 9.071 7,2.269 6,11.972 9,0.583 8,0.569 9,respectively.2)Compared with the nonlinear least squares method and BP neural network,the site index model of P.davidiana and B.platyphylla broad-leaved mingled forest based on the nonlinear mixed-effects has higher prediction accuracy.The MSE,RMSE,MPB,R²,$R_{\mathrm{adj}}^{2}$ of the model are,5.477 4,1.779 4,9.161 4,0.782 8,0.761 7,respectively.The site index model constructed with the diameter at breast height of dominant trees as the independent variable can be used to evaluate the site quality of mingled forests.

Key words: site index, BP neural network, nonlinear mixed-effects model, broad-leaved mingled forest

CLC Number:

S758.1

DONG Zihua, LI Dayong, LIANG Yu, LIANG Yuanna, WANG Dongzhi, LIU Qiang. Construction of the Site Index Model of Secondary Populus Davidiana×Betula Platyphylla Mingled Forest in Northern Hebei Mountains[J]. Forest and Grassland Resources Research, 2024, (3): 70-78.

Figures/Tables 10

Tab.1

Tab.2

Nonlinear site index candidate models

模型	方程名称	表达式
M₁	舒马赫方程 Schumacher	H_D=a× $e x p - b / D D$
M₂	双曲线方程 Hyperbolic curve	H_D=a+b/D_D
M₃	抛物线方程 Parabola	H_D=a+b×D_D+c× $D D 2$
M₄	逻辑斯蒂方程 Logistic	H_D= $a (1 + b × e x p - c × D D)$
M₅	坎派兹方程 Gompertz	H_D=a×exp[-c×exp(-b×D_D)]

Tab.2

Fig.1

Tab.3

Fitting and evaluation of candidate models

模型	a	b	c	MSE	RMSE	MPB	R²	$R a d j 2$
M₁	29.135 3^***	12.056 7^***		9.388 5	2.450 5	12.228 8	0.578 2	0.571 3
M₂	23.620 9^***	-150.710 0^***		9.955 2	2.417 5	12.470 3	0.513 6	0.505 6
M₃	-0.151 3^*	1.008 6^*	-0.014 4^*	9.786 3	2.325 4	12.064 2	0.577 3	0.563 3
M₄	21.533 0^***	4.932 3^*	0.131 7^**	9.071 7	2.269 6	11.972 9	0.583 8	0.569 9
M₅	23.398 6^***	0.084 6^*	2.124 8^**	9.506 0	2.335 9	11.977 6	0.578 0	0.563 9

Tab.3

Tab.4

Tab.5

Tab.6

Tab.7

Comparison of accuracy among different parameter estimation methods

参数估计方法	MSE	RMSE	MPB	R²	$R a d j 2$
非线性最小二乘法	9.071 7	2.269 6	11.972 9	0.583 8	0.569 9
BP神经网络	6.364 0	1.997 2	10.820 6	0.620 8	0.609 5
非线性混合效应	5.477 4	1.779 4	9.161 4	0.782 8	0.761 7

Tab.7

Fig.2

Fig.3

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变量	最大值	最小值	标准差	平均值
海拔/m	1 530.00	1 233.00	79.98	1 359.86
坡度/(°)	23.70	5.00	3.88	13.36
平均胸径/cm	24.24	6.96	3.90	15.10
平均树高/m	18.88	7.87	2.76	13.15
密度/(株/hm²)	2 817.00	233.00	577.95	1 158.33
郁闭度/%	0.80	0.55	0.71	0.09
胸径/cm	32.31	7.15	4.84	16.73
树高/m	22.72	7.14	3.84	14.53
冠幅/m	6.54	1.45	4.15	3.63
枝下高/m	5.26	1.25	4.97	3.41

类别	传递函数
输入层到隐含层	H₁=tansig(-4.1D_D+4.2)
	H₂=tansig(-3.9D_D)
	H₃=tansig(4D_D+4.5)
隐含层到输出层	H_D=purelin(-0.618 3H₁+0.904 2H₂+ 0.540 5H₃+0.633 1)

随机效应参数位置	AIC	BIC	-2LL
a	1 038.7	1 057.4	1 028.7
b	1 030.4	1 049.2	1 020.4
a、b	1 033.0	1 051.7	1 022.9
b、a	1 037.9	1 056.6	1 027.8

参数	估计值	标准差	95%置信区间		P值
a	21.947 8	3.472 4	18.439 7	32.052 3	<0.000 1
b	3.338 1	0.252 0	3.066 9	3.694 6	<0.000 1
c	0.108 3	0.007 3	0.129 3	0.137 8	0.001 3
μ_i	0.001 4	0.002 1	0.000 1	0.002 8	0.000 5
σ²	0.106 8	0.011 8	0.031 0	0.109 7	0.001 0