浙江省马尾松天然林枯损与进界模型构建及影响因素分析

doi:10.11707/j.1001-7488.LYKX20260068

林业科学 ›› 2026, Vol. 62 ›› Issue (10): 82-92.doi: 10.11707/j.1001-7488.LYKX20260068

浙江省马尾松天然林枯损与进界模型构建及影响因素分析

毛阳骏^1,²,马立帮^1,²,郭昊天^2,³,李同欣^1,²,王懿祥^1,^2,*()

1. 浙江农林大学环境与资源学院/碳中和学院　杭州 311300
2. 浙江农林大学浙江省农林生态系统固碳减排重点实验室　杭州 311300
3. 浙江农林大学林业与生物技术学院　杭州 311300

收稿日期:2026-01-29 修回日期:2026-06-30 出版日期:2026-10-10 发布日期:2026-10-17
通讯作者: 王懿祥 E-mail:wangyixiang@zafu.edu.cn
基金资助:
“十四五”国家重点研发计划项目“南方典型次生林全周期多功能经营技术研究”（2022YFD2200504）。

Model Construction and Influencing Factors Analysis of Mortality and Ingrowth for Natural Pinus massoniana Forests in Zhejiang Province

Yangjun Mao^1,²,Libang Ma^1,²,Haotian Guo^2,³,Tongxin Li^1,²,Yixiang Wang^1,^2,*()

1. College of Carbon Neutrality/College of Environmental and Resource Sciences, Zhejiang Agriculture and Forestry University　Hangzhou 311300
2. Key Laboratory of Carbon Sequestration and Emission Reduction in Agricultural and Forest Ecosystems of Zhejiang Province, Zhejiang Agriculture and Forestry University　Hangzhou 311300
3. College of Forestry and Biotechnology, Zhejiang Agriculture and Forestry University　Hangzhou 311300

Received:2026-01-29 Revised:2026-06-30 Online:2026-10-10 Published:2026-10-17
Contact: Yixiang Wang E-mail:wangyixiang@zafu.edu.cn

摘要/Abstract

摘要：

目的: 构建浙江省马尾松天然林枯损与进界模型，分析影响林分动态的关键因素，为该地区马尾松林的可持续经营提供理论依据。方法: 基于浙江省第五次（1994 年）、第六次（1999 年）、第七次（2004 年）和第八次（2009 年）森林资源连续清查固定样地数据，筛选出马尾松天然林样地389 块，其中311 块作为模拟样本、78 块作为检验样本。采用Kendall’s tau-b相关系数筛选林分与立地因子，分别构建泊松模型（Poisson）、负二项模型（NB）、零膨胀泊松模型（ZIP）、零膨胀负二项模型（ZINB）、Hurdle-泊松模型（HP）和Hurdle-负二项模型（HNB）共6类广义线性模型，对林分枯损与进界过程进行拟合与比较。利用赤池信息准则（AIC）、贝叶斯信息准则（BIC）、–2倍对数似然函数值（–2logL）和Vuong检验比较各模型间的拟合效果，选取平均绝对误差（MAE）和均方根误差（RMSE）评价其预测效果。结果: 1） ZINB模型在枯损与进界模拟中表现最优；2）负二项系列模型（NB、ZINB、HNB）在拟合效果上显著优于相应的泊松系列模型（Poisson、ZIP、HP），ZIP与HP模型拟合效果相当，ZINB模型拟合效果略优于HNB模型；3）林分枯损主要受林分密度、林分胸高断面积、阔叶树胸高断面积和海拔的影响；4）林分进界主要受林分密度、林分胸高断面积和阔叶树胸高断面积的影响，立地因子对进界无显著影响。结论: 林分密度是调控枯损与进界过程的核心变量，但其作用方向相反；阔叶树组成增加有助于降低马尾松林枯损风险并促进更新。建议在马尾松林实际经营中合理控制林分密度并适当补植阔叶树种，从而维持马尾松林的长期健康与生产力。

关键词: 马尾松, 枯损模型, 进界模型, 广义线性模型, 零膨胀模型

Abstract:

Objective: This study aims to develop stand-level mortality and ingrowth models for natural Pinus massoniana forests in Zhejiang Province, and identify the key factors influencing stand dynamics, so as to provide a theoretical basis for the sustainable management of P. massoniana forests in this region. Method: Based on the data from the 5th (1994), 6th (1999), 7th (2004), and 8th (2009) Continuous Forest Inventories in permanent sample plots of Zhejiang Province, a total of 389 sample plots of natural P. massoniana forests were selected, with 311 used for model simulation and 78 for validation. The Kendall’s tau-b correlation coefficient was used to screen stand and site factors. Six types of generalized linear models, including the Poisson model (Poisson), the negative binomial model (NB), the zero-inflated Poisson model (ZIP), the zero-inflated negative binomial model (ZINB), the Hurdle-Poisson model (HP), and the Hurdle-negative binomial model (HNB), were constructed to fit and compare the stand mortality and ingrowth processes. The fitting performance of each model was compared using Akaike information criterion (AIC), Bayesian information criterion (BIC), –2 times the log-likelihood (–2logL), and the Vuong test. The prediction performance was evaluated using mean absolute error (MAE) and root mean square error (RMSE). Result: 1) The ZINB model demonstrated the best overall performance for both mortality and ingrowth simulations. 2) The negative binomial series models (NB, ZINB, HNB) showed significantly better fit than their corresponding Poisson series counterparts (Poisson, ZIP, HP), with comparable performance observed between the ZIP and HP models, and a slight advantage of the ZINB model over the HNB model. 3) Stand mortality was primarily influenced by stand density, stand basal area at breast height, broad-leaved tree basal area at breast height, and elevation. 4) Stand ingrowth was mainly affected by stand density, stand basal area at breast height, and broad-leaved tree basal area at breast height. The site factors showed no significant influence on ingrowth. Conclusion: Stand density is a core variable that simultaneously regulate both mortality and ingrowth processes, but with opposite effects. The increase in the proportion of broad-leaved trees helps reduce mortality risk in P. massoniana stands and promotes its regeneration. It is recommended that practical forest management for P. massoniana should involve in rational control of stand density and appropriate enrichment planting with broad-leaved species, thereby maintaining the long-term health and productivity of P. massoniana forests.

Key words: Pinus massoniana, mortality model, ingrowth model, generalized linear model, zero-inflated model

中图分类号:

S758.5

毛阳骏,马立帮,郭昊天,李同欣,王懿祥. 浙江省马尾松天然林枯损与进界模型构建及影响因素分析[J]. 林业科学, 2026, 62(10): 82-92.

Yangjun Mao,Libang Ma,Haotian Guo,Tongxin Li,Yixiang Wang. Model Construction and Influencing Factors Analysis of Mortality and Ingrowth for Natural Pinus massoniana Forests in Zhejiang Province[J]. Scientia Silvae Sinicae, 2026, 62(10): 82-92.

图/表 9

表1

表2

表3

表4

表5

零膨胀模型和Hurdle模型参数估计及评价统计量①"

类别Class	参数Parameter	ZIP模型ZIP model	ZINB模型ZINB model	HP模型HP model	HNB模型HNB model
林分枯损模型 Stand mortality model	计数部分Count component
	截距Intercept	3.637 3 (0.022 3)^***	3.525 4 (0.224 6)^***	3.637 3 (0.022 3)^***	3.532 8 (0.222 8)^***
	N	0.000 5 (0.000 1)^***	0.000 6 (0.000 1)^***	0.000 5 (0.000 1)^***	0.000 6 (0.000 1)^***
	G	0.043 7 (0.001 0)^***	0.044 6 (0.011 9)^***	0.043 7 (0.001 0)^***	0.044 4 (0.011 8)^***
	G_b	?0.112 6 (0.004 2)^***	?0.092 1 (0.038 7)^*	?0.112 6 (0.004 2)^***	?0.091 8 (0.038 3)^*
	EL	?0.000 8 (0.000 1)^***	?0.000 8 (0.000 3)^*	?0.000 8 (0.000 1)^***	?0.000 8 (0.000 3)^*
	θ	—	0.738 1 (0.078 1)^***	—	0.738 1 (0.078 1)^***
	零部分Zero component
	截距Intercept	6.663 8 (0.676 1)^***	6.654 7 (0.677 3)^***	?6.663 7 (0.676 1)^***	?6.663 7 (0.676 1)^***
	N	?0.003 1 (0.000 4)^***	?0.003 1 (0.000 4)^***	0.003 1 (0.000 4)^***	0.003 1 (0.000 4)^***
	G	?0.326 0 (0.048 4)^***	?0.326 1 (0.048 6)^***	0.326 0 (0.048 4)^***	0.326 0 (0.048 4)^***
	G_b	0.645 8 (0.156 5)^***	0.645 3 (0.157 4)^***	?0.645 8 (0.156 5)^***	?0.645 8 (0.156 5)^***
	AIC	14 745.58	2 118.74	14 745.58	2 118.77
	BIC	14 779.24	2 156.14	14 779.24	2 156.17
	–2logL	14 727.58	2 098.74	14 727.58	2 098.77
林分进界模型 Stand ingrowth model	计数部分Count component
	截距Intercept	5.748 6 (0.013 0)^***	5.703 0 (0.121 6)^***	5.748 6 (0.0130)^***	5.702 0 (0.120 7)^***
	N	–0.001 1 (0.000 1)^***	–0.001 1 (0.000 2)^***	–0.001 1 (0.000 1)^***	–0.001 1 (0.000 2)^***
	G_b	0.048 7 (0.006 6)^***	0.109 9 (0.045 8)^*	0.048 7 (0.006 6)^***	0.108 5 (0.045 2)^*
	θ	—	0.780 7 (0.070 7)^***	—	0.780 7 (0.070 7)^***
	零部分Zero component
	截距Intercept	–6.249 9 (0.652 8)^***	–6.262 2 (0.657 6)^***	6.249 8 (0.652 8)^***	6.249 8 (0.652 8)^***
	N	0.002 0 (0.000 4)^***	0.002 0 (0.000 4)^***	–0.002 0 (0.000 4)^***	–0.002 0 (0.000 4)^***
	G	0.485 3 (0.059 7)^***	0.485 9 (0.059 9)^***	–0.485 3 (0.059 7)^***	–0.485 3 (0.059 7)^***
	G_b	–1.303 4 (0.180 3)^***	–1.304 3 (0.181 3)^***	1.303 4 (0.180 3)^***	1.303 4 (0.180 3)^***
	AIC	23 719.56	2 817.24	23 719.56	2 817.29
	BIC	23 745.74	2 847.16	23 745.74	2 847.21
	–2logL	23 705.56	2 801.24	23 705.56	2 801.29

表5

表6

图1

图2

表7

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调查期次 Inventory round	样地数 Number of plots	枯损发生样地数 Plots with mortality	进界发生样地数 Plots with ingrowth	总样木数 Number of trees	总枯损株数 Mortality stem count	总进界株数 Ingrowth stem count	年均枯损率 Annual mortality rate (%)	年均进界率 Annual ingrowth rate (%)
第六次6th (1999)	93	6	32	7 670	111	333	0.29	0.87
第七次7th (2004)	104	44	59	8 880	421	618	0.95	1.39
第八次8th (2009)	192	113	130	18 740	1 135	1 597	1.21	1.70
总计/平均 Total/mean	389	163	221	35 290	1 667	2 548	0.94	1.44

变量 Variable	变量符号 Variable symbol	平均值 Mean	标准差 Std.	最小值 Min.	最大值 Max.
林分平均年龄Stand mean age/a	A	22.39	6.42	6	42
林分密度Stand density/(trees·hm^–2)	N	1162	666	250	4 650
林分平均高Stand mean height/m	H_d	7.56	2.38	3.5	15.8
林分平方平均胸径Stand quadratic mean diameter at breast height/cm	D_g	10.49	2.79	6.19	23.1
林分算术平均胸径Stand arithmetic mean diameter at breast height/cm	D_m	9.92	2.54	6.13	21.47
林分胸高断面积Stand basal area/(m²·hm^–2)	G	10.04	6.79	0.86	47.65
阔叶树胸高断面积 Broadleaved basal area/(m²·hm^–2)	G_b	0.81	1.44	0	10.5
阔叶树胸高断面积占比Proportion of broadleaved basal area (%)	P_b	7.17	8.83	0	41.1
海拔Elevation/ m	EL	318.55	190.54	40	830
坡度Slope/(°)	SL	28.76	9.57	0	75
土层厚度Soil depth/cm	SD	41.43	13.45	2	100
林分枯损株数Stand mortality stem count/(trees·hm^–2)	MC	53.57	105.70	0	613
林分进界株数Stand ingrowth stem count/(trees·hm^–2)	IC	81.88	133.94	0	738

变量 Variable	变量符号 Variable symbol	相关系数（林分枯损株数） Correlation with stand mortality stem count	相关系数（林分进界株数） Correlation with stand ingrowth stem count
林分平均年龄Stand mean age/a	A	0.10	–0.04
林分密度Stand density/(trees·hm^–2)	N	0.27	–0.17
林分平均高Stand mean height/m	H_d	0.07	–0.07
林分平方平均胸径Stand quadratic mean diameter at breast height/cm	D_g	0.10	–0.09
林分算术平均胸径Stand arithmetic mean diameter at breast height/cm	D_m	0.09	–0.10
林分胸高断面积Stand basal area/(m²·hm^–2)	G	0.28	–0.12
阔叶树胸高断面积 Broadleaved basal area/(m²·hm^–2)	G_b	0.13	–0.12
阔叶树胸高断面积占比Proportion of broadleaved basal area (%)	P_b	0.05	–0.06
海拔Elevation/ m	EL	–0.07	–0.02
坡度Slope/(°)	SL	–0.05	0.01
土层厚度Soil depth/cm	SD	0.06	0.03

类别 Class	参数 Parameter	Poisson模型 Poisson model	NB模型 NB model
林分枯损模型 Stand mortality model	截距 Intercept	2.100 5 (0.018 4)^***	–0.387 6 (0.338 8)
	N	0.001 0 (0.000 1)^***	0.002 0 (0.000 3)^***
	G	0.080 5 (0.000 9)^***	0.157 5 (0.031 9)^***
	G_b	–0.186 9 (0.004 0)^***	–0.224 8 (0.113 4)^*
	EL	–0.001 3 (0.000 1)^***	–0.001 2 (0.000 6)^*
	θ	—	6.900 2 (0.650 8)^***
	AIC	29 126.97	2 467.22
	BIC	29 145.67	2 489.66
	–2logL	29 116.97	2 455.22

林分进界模型 Stand ingrowth model	截距 Intercept	6.210 9 (0.0119)^***	7.399 0 (0.284 9)^***
	N	–0.001 3 (0.000 1)^***	–0.002 0 (0.000 2)^***
	G	–0.124 3 (0.002 1)^***	–0.253 2 (0.026 1)^***
	G_b	0.272 5 (0.006 9)^***	0.922 8 (0.120 8)^***
	θ	—	3.731 9 (0.314 0)^***
	AIC	35 023.81	3 128.70
	BIC	35 038.77	3 147.40
	–2logL	35 015.81	3 118.70

类别 Class	模型 Model	指标Index
类别 Class	模型 Model	均方根误差 RMSE/(trees·hm^–2)	平均绝对误差 MAE/(trees·hm^–2)
林分枯损模型 Stand mortality model	Poisson	79.111 2	42.385 9
	NB	78.319 9	39.829 5
	ZIP	73.133 3	37.051 3
	ZINB	70.703 9	36.996 2
	HP	73.133 3	37.051 3
	HNB	70.784 4	37.006 4

林分进界模型 Stand ingrowth model	Poisson	91.501 9	59.324 4
	NB	129.937 8	70.585 9
	ZIP	90.840 2	57.537 2
	ZINB	89.934 2	56.620 5
	HP	90.840 2	57.537 2
	HNB	89.936 0	56.659 0

浙江省马尾松天然林枯损与进界模型构建及影响因素分析

Model Construction and Influencing Factors Analysis of Mortality and Ingrowth for Natural Pinus massoniana Forests in Zhejiang Province

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类别 Class	模型A Model A	模型B Model B	Vuong检验值 Vuong test statistic	P	较优模型 Preferred model
林分枯损模型 Stand mortality model	Poisson	NB	–7.87	<0.01	NB
	ZIP	ZINB	–5.86	<0.01	ZINB
	HP	HNB	–5.86	<0.01	HNB
	HNB	ZINB	–0.07	>0.05	ZINB

林分进界模型 Stand ingrowth model	Poisson	NB	–12.24	<0.01	NB
	ZIP	ZINB	–9.72	<0.01	ZINB
	HP	HNB	–9.72	<0.01	HNB
	HNB	ZINB	–0.09	>0.05	ZINB

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