Individual tree crown width prediction models for natural Phoebe bournei in central Jiangxi Province

doi:10.12302/j.issn.1000-2006.202006045

JOURNAL OF NANJING FORESTRY UNIVERSITY ›› 2022, Vol. 46 ›› Issue (1): 88-96.doi: 10.12302/j.issn.1000-2006.202006045

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Individual tree crown width prediction models for natural Phoebe bournei in central Jiangxi Province

SHAN Kaili(), ZANG Hao, PAN Ping, NING Jinkui, OUYANG Xunzhi^*()

Key Laboratory of National Forestry and Grassland Administration for the Protection and Restoration of Forest Ecosystem in Poyang Lake Basin, College of Forestry, Jiangxi Agricultural University, Nanchang 330045, China

Received:2020-06-26 Accepted:2020-09-24 Online:2022-01-30 Published:2022-02-09
Contact: OUYANG Xunzhi E-mail:1321566532@qq.com;oyxz@jxau.edu.cn

Abstract

Abstract:

【Objective】 The influence of competitive indices and modeling methods on the prediction of individual tree crowns of natural Phoebe bournei in Jiangxi Province was discussed to provide a reference for accurately predicting the crown width of natural Phoebe bournei.【Method】An individual crown width model was developed based on a dataset comprising 1 011 Phoebe bournei from 25 typical plots of natural secondary Phoebe bournei forest located in Jiangxi Province. The individual tree crown width model was established using four modeling methods: ordinary least squares (OLS) model, mixed effects model, boosted regression trees, and random forest. Four competitive indices, namely, basal area, basal area of larger trees, stand density, and simple competition, were added to reflect the influence of competition on the crown width model. The model evaluation criteria included determination coefficient (R²), root-mean-square error (RMSE), relative mean absolute error (RMA) and mean absolute error (MAE).【Result】The results demonstrated that when no competition index was added, the order of model accuracy was mixed effects model > OLS model > boosted regression trees > random forest; when the competition index was added, the optimal model was as follows: mixed effects model > OLS model> random forest > boosted regression trees (BRT). The OLS model had the best predictive ability when the basal area of larger trees was added; the BRT had the best predictive ability when a simple competition index with a fixed radius of 7 m was added; the random forest had the best predictive ability when the basal area was added. The mixed effects model had the best predictive ability when no competitive index was added (RMSE is 0.846 0, RMA is 0.211 1, MAE is 0.650 1), and it was superior to the other models. 【Conclusion】The results of this study accurately predicted the growth of Phoebe bournei individual tree crowns, thereby providing a theoretical basis for improving the forest quality of natural secondary Phoebe bournei forest.

Key words: Phoebe bournei, crown width model, competitive index, mixed effect model, Jack knife

CLC Number:

S758.5

SHAN Kaili, ZANG Hao, PAN Ping, NING Jinkui, OUYANG Xunzhi. Individual tree crown width prediction models for natural Phoebe bournei in central Jiangxi Province[J]. JOURNAL OF NANJING FORESTRY UNIVERSITY, 2022, 46(1): 88-96.

Figures/Tables 6

Table 1

Table 2

Alternative basic models"

模型 model	模型表达式 model equation	模型形式 model form	模型 model	模型表达式 model equation	模型形式 model form
M1	C_W=a₀+b₀D_BH	线性 Linear	M7	C_W=exp(a₀+b₀D_BH)	Growth
M2	C_W=a₀+b₀D_BH+c₀ $D BH 2$	二次型 Quadratic	M8	C_W=a₀[1-exp(-b₀D_BH) $] c 0$	Richards
M3	C_W=a₀ $D BH b 0$	幂函数 Power	M9	C_W=a₀/[1+b₀exp(-c₀D_BH)]	Logistic
M4	C_W=a₀[1-exp(-b₀D_BH)]	Monomolecular	M10	C_W=a₀/[1+exp[b₀+β₂ln(D_BH+1)]]	Logistic
M5	C_W=[D_BH/(a₀+b₀D_BH)]²	Hossfeld 1	M11	C_W=a₀[1-exp(-b₀ $D BH c 0$ )]	Weibull
M6	C_W=a₀( $b 0 D BH$ )	Compound

Table 2

Table 3

Table 4

Fig.1

Table 5

Parameters estimates and evaluation indexes for models"

项目 item	参数 parameter	OLS模型 OLS model	混合效应模型 mixed effect model
固定参数 fixed parameter	a₀	1.431 366	1.222 190
	b₀	0.134 100	0.222 282
	b₁	0.022 591	—
	c₀	0.001 121	-0.002 181
方差组成 composition of variance	$σ a 0$	—	0.192 855
	$σ b 0$	—	0.011 628
	$σ c 0$	—	0.000 010
	$σ a 0 b 0$	—	-0.027 466
	$σ a 0 c 0$	—	0.000 925
	$σ b 0 c 0$	—	-0.000 313
评价指标 evaluation indexes	R²	0.727 9	0.851 0
	σ(RMSE)	1.149 1	0.850 3
	σ(RMA)	0.281 3	0.217 5
	σ(MAE)	0.829 9	0.614 5

Table 5

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统计量 statistic quantity	闽楠单木 Phoebe bournei individual			林分 stand
统计量 statistic quantity	胸径/cm DBH	树高/m height	冠幅/m crown width	平均胸径/cm average DBH	平均树高/m average height	平均冠幅/m average crown width	密度/ (株·hm^-2) density
平均值 mean	10.10	8.20	2.60	11.80	9.20	3.30	1 657.70
标准差 SD	8.84	3.92	1.93	3.85	1.92	1.22	733.12
最小值 min.	2.00	1.90	0.50	6.60	6.20	1.70	50.00
最大值 max.	69.60	32.00	22.50	24.10	15.00	7.50	2 800.00

模型 model	建模数据 fitting data												检验数据 validation data
	R²			σ(RMSE)			σ(RMA)			σ(MAE)			σ(RMSE)			σ(RMA)			σ(MAE)
	平均值 mean	标准差 SD	平均值 mean		标准差 SD	平均值 mean		标准差 SD	平均值 mean		标准差 SD	平均值 mean		标准差 SD	平均值 mean		标准差 SD	平均值 mean		标准差 SD
M1	0.718 5	0.011 9	1.167 4		0.020 6	0.281 1		0.003 5	0.833 6		0.016 7	1.258 7		0.499 4	0.279 7		0.093 9	0.950 6		0.359 2
M2	0.722 7	0.012 8	1.158 6		0.020 7	0.280 1		0.003 5	0.832 1		0.016 7	1.255 6		0.518 3	0.279 7		0.093 1	0.944 3		0.353 0
M3	0.692 7	0.010 9	1.220 1		0.025 2	0.303 4		0.004 9	0.855 3		0.019 0	1.338 3		0.582 9	0.301 7		0.127 9	1.006 9		0.421 0
M4	0.627 0	0.015 9	1.343 9		0.028 5	0.462 7		0.018 4	0.973 8		0.025 6	1.494 5		0.666 2	0.435 6		0.245 1	1.145 0		0.476 2
M5	0.562 9	0.010 8	1.455 6		0.040 1	0.460 3		0.026 0	1.001 0		0.030 4	1.547 2		0.815 8	0.442 4		0.269 9	1.181 9		0.546 7
M6	0.664 8	0.016 9	1.273 8		0.022 9	0.310 8		0.003 6	0.959 1		0.015 4	1.309 4		0.548 0	0.294 2		0.097 7	0.980 7		0.381 1
M7	0.664 8	0.016 9	1.273 8		0.022 9	0.310 8		0.003 6	0.959 1		0.015 4	1.309 4		0.548 0	0.294 2		0.097 7	0.980 7		0.381 1
M9	0.708 8	0.013 1	1.187 4		0.020 7	0.291 1		0.003 3	0.866 1		0.015 7	1.277 3		0.540 5	0.284 1		0.092 9	0.957 8		0.344 6

模型类型 model	竞争指标 competitive index	σ(RMSE)		σ(RMA)		σ(MAE)
模型类型 model	竞争指标 competitive index	平均值 mean	标准差 SD	平均值 mean	标准差 SD	平均值 mean	标准差 SD
OLS模型 OLS model	无	1.255 6	0.518 3	0.279 7	0.093 1	0.944 3	0.353 0
	A_B	1.284 3	0.490 6	0.280 6	0.097 0	0.956 9	0.338 2
	A_BL	1.230 1	0.521 3	0.276 6	0.101 5	0.926 8	0.359 5
	I_SD	1.267 4	0.462 3	0.278 9	0.093 8	0.943 2	0.308 4
	H_egyi(N=1)	1.259 0	0.524 8	0.280 6	0.095 0	0.946 3	0.356 7
	H_egyi(R=1)	1.261 1	0.524 6	0.280 9	0.094 7	0.954 4	0.012 9
混合效应模型 mixed effects model	无	0.846 0	0.321 8	0.211 1	0.056 5	0.650 1	0.258 1
	A_B	0.894 8	0.331 0	0.219 0	0.052 8	0.690 9	0.263 6
	A_BL	0.846 4	0.314 9	0.211 7	0.054 4	0.649 2	0.251 4
	I_SD	0.895 7	0.333 7	0.218 9	0.052 5	0.691 8	0.266 8
	H_egyi(N=1)	0.848 6	0.322 2	0.211 4	0.055 5	0.652 1	0.255 6
	H_egyi(R=1)	0.839 1	0.317 6	0.210 8	0.056 6	0.649 0	0.263 8
增强回归树 BRT	无	1.502 0	0.627 8	0.311 5	0.113 2	1.067 6	0.446 5
	A_B	1.555 2	0.595 3	0.349 9	0.115 8	1.133 8	0.429 5
	A_BL	1.526 1	0.621 1	0.323 6	0.114 3	1.084 9	0.430 1
	I_SD	1.539 4	0.553 4	0.351 2	0.112 0	1.131 4	0.403 4
	H_egyi(N=4)	1.476 3	0.574 6	0.306 6	0.112 0	1.057 4	0.420 1
	H_egyi(R=7)	1.459 9	0.536 9	0.305 2	0.113 2	1.051 5	0.416 4
随机森林 RF	无	1.567 6	0.656 8	0.340 2	0.109 3	1.140 9	0.465 9
	A_B	1.400 6	0.468 3	0.320 2	0.074 8	1.058 2	0.281 0
	A_BL	1.488 8	0.606 6	0.319 2	0.099 2	1.090 4	0.387 5
	I_SD	1.529 4	0.645 8	0.335 8	0.101 4	1.111 4	0.361 6
	H_egyi(N=8)	1.455 1	0.650 2	0.330 4	0.109 5	1.094 4	0.518 3
	H_egyi(R=6)	1.460 1	0.687 6	0.331 9	0.108 3	1.110 1	0.547 7

Individual tree crown width prediction models for natural Phoebe bournei in central Jiangxi Province

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