竞争环境下红松单木树高与胸径的相对生长关系

doi:10.11707/j.1001-7488.20201011

摘要/Abstract

摘要：

目的: 基于博弈论研究蒙古栎阔叶混交林下红松单木树高与胸径相对生长关系，探索红松单木生长受自身遗传和外部环境影响的资源分配规律，为阔叶混交林下红松更新和培育提供技术支撑。方法: 选择11块面积1 hm²蒙古栎阔叶混交林样地，以红松为对象木筛选半径5 m内的红松、蒙古栎、其他阔叶树种以及其他针叶树种4类所有竞争木，统计竞争木断面积加权距离、胸径和树高等，基于博弈论并结合线性联立方程组构建以红松单木为对象的树高与胸径生长竞争模型，采用交叉检验对模型进行评价，研究红松单木树高与胸径生长的相互作用规律。结果: 树高与胸径生长竞争模型拟合效果良好，最小二乘法拟合结果略优于似乎不相关回归法。红松自身斜率项均为正且非常显著，反映红松内部遗传因素是互利共生的，占主导作用；而外部环境影响是次要的，红松、蒙古栎和其他阔叶树种的距离、胸径和树高对红松单木树高和胸径的参数值符号相反且显著，呈现一种寄生关系。其他针叶树种的相关参数不太显著，呈现原始协作关系。结论: 本研究构建的树高与胸径生长竞争模型可客观描述蒙古栎阔叶混交林下红松单木树高与胸径相对生长关系，基于博弈论能有效揭示红松自身遗传和外界环境干扰下树高与胸径生长的资源分配规律，蒙古栎阔叶混交林适合红松生长。

关键词: 博弈论, 线性联立方程组, 相对生长关系, 红松, 阔叶混交林

Abstract:

Objective: Based on the game theory, the study of relative growth relationships between height and diameter of juvenile Korean pine, which was planted in Mongolian oak broad-leaved mixed forest, was carried out to provide a technology support for the regeneration and cultivation of Korean pine from broad-leaved mixed forest. Method: The total competitive trees, including Korean pine, Mongolian oak, broad-leaved trees excepted Mongolian oak and coniferous trees excepted Korean pine around 5 m radius of objective tree Korean pine, were selected through 11 plots with a hectare each of Mongolian oak broad-leaved mixed forest. Then basal area weighting distance, diameter and height corresponding to these competitive trees were calculated for constructing systems of linear simultaneous equations between height and diameter of Korean pine. Furthermore, the model was tested with cross validation and evaluated with several statistical indicators. However, the interactions between height and diameter growth of Korean pine were discussed from the insight of the game theory. Result: Growth competition model between height and diameter were excellent in fitting data. The result from method of ordinary least squares(OLS)was slightly better than that of seemingly unrelated regression(SUR). The slopes from diameter and height of Korean pine were positive and highly significant, which reflected that internal genetic factors of Korean pine had a beneficial relationship of mutualism and predominated in that. Accordingly, the perturbation from external environment was secondary. The coefficients of L, D, and H from Korean pine, Mongolian oak and broad-leaved tree were significant, and however took the opposite values for height and diameter of Korean pine, which indicated a harmful relationship of parasitism. Differently, the coefficients from coniferous tree were non-significant, which led to a relationship of synergism. Conclusion: Growth competition model between height and diameter not only objective ly described relative growth relationships of Korean pine in Mongolian oak broad-leaved mixed forest, but also revealed the resource allocation of height and diameter growth under the conditions of genetic factors or the disturbance from external environments, combining with the game theory. Furthermore, Mongolian oak broad-leaved mixed forest provided a stable environment for Korean pine.

Key words: game theory, systems of linear simultaneous equations, relative growth relationship, Korean pine, broad-leaved mixed forest

中图分类号:

S753

段光爽,王秋燕,宋新宇,张会儒,符利勇. 竞争环境下红松单木树高与胸径的相对生长关系[J]. 林业科学, 2020, 56(10): 105-112.

Guangshuang Duan,Qiuyan Wang,Xinyu Song,Huiru Zhang,Liyong Fu. Relative Growth Relations between Height and Diameter of Individual Korean Pine under Competitive Environment[J]. Scientia Silvae Sinicae, 2020, 56(10): 105-112.

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参考文献 0

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类型 Types		平均值 Mean	最小值 Min.	最大值 Max.	标准差 SD	株数 Number
红松 P.koraiensis	D/cm	5.2	1.0	28.6	3.96	3 927
红松 P.koraiensis	H/cm	4.4	1.4	11.9	2.53	3 927
蒙古栎 Q.mongolica	D/cm	19.5	1.4	70.1	9.84	2 890
蒙古栎 Q.mongolica	H/cm	13.4	1.8	36.6	4.29	2 890
阔叶树种 Broad-leaved tree	D/cm	12.3	1.0	64.0	8.82	4 188
阔叶树种 Broad-leaved tree	H/cm	10.6	1.5	31.1	4.81	4 188
针叶树种 Coniferous tree	D/cm	5.0	1.0	39.1	5.82	1 817
针叶树种 Coniferous tree	H/cm	4.3	1.4	28.8	4.54	1 817

		胸径 DBH
		+(参数 Parameters>0)	0(参数 Parameters=0)	-(参数 Parameters < 0)
树高 Tree height	+(参数 Parameters>0)	+/+(互利共生 Mutualism)	+/0(偏利共生 Commensalism)	+/-(寄生关系 Parasitism)
	0(参数 Parameters=0)	0/+(偏利共生 Commensalism)	0/0(原始协作 Synergism)	0/-(偏害共生 Amensalism)
	-(参数 Parameters < 0)	-/+(寄生关系 Parasitism)	-/0(偏害共生 Amensalism)	-/-(竞争关系 Competition)

参数 Parameters	普通最小二乘法 Ordinary least squares		似乎不相关回归法 Seemingly unrelated regressions
参数 Parameters	H	D	H	D
a_H/λ_D	1.089 3^***	-0.612 9^***	0.797 7^***	-1.199 7^***
b_H/β_D	0.562 9^***	1.417 6^***	0.626 2^***	1.576 9^***
a₁/λ₁	-0.087 9^***	0.046 1	-0.063 3^***	0.095 0^***
a₂/λ₂	-0.018 3	0.050 8	-0.026 1	0.042 7
a₃/λ₃	-0.066 8^***	0.112 5^***	-0.072 3^***	0.115 2^***
a₄/λ₄	-0.025 6	-0.028 4	-0.005 4	0.004 4
b₁/γ₁	-0.142 3^***	0.244 7^***	-0.155 7^***	0.248 3^***
b₂/γ₂	-0.012 1^***	0.018 6^***	-0.012 6^***	0.019 9^***
b₃/γ₃	-0.004 4	0.006 5	-0.004 5	0.007 1
b₄/γ₄	-0.000 2	0.013 3	-0.004 3	0.007 6
c₁/β₁	0.299 8^***	-0.384 3^***	0.287 0^***	-0.450 1^***
c₂/β₂	0.032 6^***	-0.054 1^***	0.035 1^***	-0.055 8^***
c₃/β₃	0.018 2^**	-0.028 8^**	0.019 1^**	-0.030 3^**
c₄/β₄	0.010 6	-0.045 9^*	0.020 3	-0.033 9

估计方法 Method	H					D
估计方法 Method	${\bar e}$	σ²	RMSE	TRE	R²	${\bar e}$	σ²	RMSE	TRE	R²
OLS	0.033 6	1.046 5	1.023 5	4.208 6	0.835 1	-0.144 6	2.719 8	1.655 5	6.574 9	0.826 8
SUR	0.062 4	1.118 5	1.059 4	4.365 5	0.823 3	-0.109 5	2.800 7	1.677 1	6.415 6	0.822 3

估计方法 Method	截距 Intercept	D/H	L₁	L₂	L₃	L₄	D₁	D₂	D₃	D₄	H₁	H₂	H₃	H₄
OLS	+/-	+/+	-/+	0/+	-/+	-/0	-/+	-/+	0/0	0/0	+/-	+/-	+/-	0/-
SUR	+/-	+/+	-/+	0/0	-/+	0/0	-/+	-/+	0/0	0/0	+/-	+/-	+/-	0/0