最大密度法则研究进展

doi:10.3773/j.issn.1005-264x.2008.02.030

摘要/Abstract

摘要：

该文从理论推导和研究方法等方面对近几十年来关于最大密度法则的研究进展进行了综述,得出结论:1)关于最大密度法则理论主要有几何关系的3/2法则和空间填充分行支状网运输结构的WBE模型。进一步研究发现它们都是建立在一种静态的统计分析基础之上的,因而近几年研究者们开始尝试用动态的个体植物之间的竞争来建立模型。尽管如此,关于最大密度法则的模型仍然没有逃出固有的模式,如用平均植物大小代替整个植物种群。因此,关于最大密度法则理论需要进一步的研究。2)最大密度法则理论在假设条件、数学推导、用于估计参数的原始数据选择等方面存在争议。任何模型的建立都是基于一些特定的条件和假设建立的,因而得到的关系并不是一个万能的定律。所以在分析数据时,这些模型可结合使用。3)在研究方法上,由于大家对最大密度法则的理解不同,标准不同,造成研究方法多种多样。因而建议在以后的研究中建立一个客观统一的方法。

关键词: 最大密度线, 3/2法则, WBE模型, 林分密度

Abstract:

We summarized the research on theory and method related to maximum size-density rules. There are two main theories, Yoda's 3/2 power law based on Euclidian geometry and West, Brown and Enquist's fractal scaling rules (WBE model). However, both are based on static analysis rather than dynamic competition between plants, which is the direction attempted by recent researchers. In spite of this, some researches have not eliminated the reliance on these untenable assumptions, such as the instead of whole population by the average plant size. Further work is needed. In addition, there is ongoing debate regarding assumptions, mathematical deduction and original data points used for estimating parameters. Each model is formulated based on special situations and assumptions, it is not all-purpose; therefore, these models can be coupled, depending on practical situations. Moreover, various methods are used for estimating parameters because of different perceptions and criteria. Therefore uniform criteria need to be established.

Key words: maximum size-density line, 3/2 power law, WBE's model, stand density

付立华, 张建国, 段爱国, 孙洪刚, 何彩云. 最大密度法则研究进展. 植物生态学报, 2008, 32(2): 501-511. DOI: 10.3773/j.issn.1005-264x.2008.02.030

FU Li-Hua, ZHANG Jian-Guo, DUAN Ai-Guo, SUN Hong-Gang, HE Cai-Yun. REVIEW OF STUDIES ON MAXIMUM SIZE-DENSITY RULES. Chinese Journal of Plant Ecology, 2008, 32(2): 501-511. DOI: 10.3773/j.issn.1005-264x.2008.02.030

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链接本文: https://www.plant-ecology.com/CN/10.3773/j.issn.1005-264x.2008.02.030

https://www.plant-ecology.com/CN/Y2008/V32/I2/501

图/表 3

图1 WBE模型图示(West et al., 1997)

Fig.1 Diagram of WBE's model (West et al., 1997)

表1 林分密度与植物各部位质量的关系

Table 1 Relationships between stand density and mass of plant's part

	植株重量 Pant body mass	地上生物量 Shoot biomass	地下生物量 Root biomass	叶子生物量 Leaf biomass	生长速率 Whole-plant growth rate
林分密度 Stand density	M_T∝N^-4^/³ $M ˙$ ∝N^-1^/³	M_sh∝N^-4^/³ $M ˙ sh$ ∝N^-1^/³	M_R∝N^-4^/³ $M ˙ R$ ∝N^-1^/³	M_L ∝N^-1 $M ˙ L$ ∝N0	G_T∝N-1 $G ˙$ ∝N⁰

表1 林分密度与植物各部位质量的关系

Table 1 Relationships between stand density and mass of plant's part

	植株重量 Pant body mass	地上生物量 Shoot biomass	地下生物量 Root biomass	叶子生物量 Leaf biomass	生长速率 Whole-plant growth rate
林分密度 Stand density	M_T∝N^-4^/³ $M ˙$ ∝N^-1^/³	M_sh∝N^-4^/³ $M ˙ sh$ ∝N^-1^/³	M_R∝N^-4^/³ $M ˙ R$ ∝N^-1^/³	M_L ∝N^-1 $M ˙ L$ ∝N0	G_T∝N-1 $G ˙$ ∝N⁰

表2 不同模型的指数值

Table 2 Values of exponents in different models

指数值 Values	Reinke方程 Reinke's equation	Yoda的3/2法则 3/2 power law	WBE模型 WBE's model	Pretzsch经验值 Pretzsch's experimental values
W~d^a		3	8/3	8/3
N~ $d ? b$	-1.605	-2	-2	-1.605
$w ?$ ~N^c		-3/2	-4/3	-3/2

表2 不同模型的指数值

Table 2 Values of exponents in different models

指数值 Values	Reinke方程 Reinke's equation	Yoda的3/2法则 3/2 power law	WBE模型 WBE's model	Pretzsch经验值 Pretzsch's experimental values
W~d^a		3	8/3	8/3
N~ $d ? b$	-1.605	-2	-2	-1.605
$w ?$ ~N^c		-3/2	-4/3	-3/2

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