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

Abstract

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

CLC Number:

S753

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.

Figures/Tables 7

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References 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

Relative Growth Relations between Height and Diameter of Individual Korean Pine under Competitive Environment

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树种 Tree species	株树分布 Distribution
树种 Tree species	0	1	2	3	4	5	6	>6
红松 P.koraiensis	142	251	336	321	315	291	289	1 231
蒙古栎 Q.mongolica	657	548	538	437	378	267	176	175
阔叶树种 Broad-leaved trees	988	634	460	339	204	148	110	293
针叶树种 Coniferous trees	1 825	439	254	160	116	92	62	228
全部 Total	7	12	31	66	91	125	139	2 705

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