β-多样性的研究:应用多元回归和典范分析研究生态方差的分解

doi:10.17521/cjpe.2007.0124

摘要/Abstract

摘要：

β-多样性刻画了地理区域中不同地点物种组成的变化,是理解生态系统功能、生物多样性保护和生态系统管理的一个重要概念。该文介绍了如何从群落组成,相关环境和空间数据角度去分析β-多样性。β-多样性可以通过计算每个地点的多样性指数,进而对可能解释点之间差异的因子所作的假设进行检验来研究。也可以将涵盖所有点的群落组成数据表看作是一系列环境和空间变量的函数,进行直接分析。这种分析应用统计方法将多样性指数或群落组成数据表的方差进行关于环境和空间变量的分解。该文对方差分解进行阐述。方差分解是利用环境和空间变量来解释β-多样性的一种方法。β-多样性是生态学家用来比较不同地点或同一地点不同生态群落的一种手段。方差分解就是将群落组成数据表的总方差无偏分解成由各个解释变量所决定的子方差。调整的决定系数提供了针对多元回归和典范冗余分析的无偏估计。方差分解后,可以对感兴趣的方差解释部分进行显著性检验,同时绘出基于这部分方差解释的预测图。

关键词: 调整的决定系数, β-多样性, 生物多样性, 典范冗余分析, 群落组成, 方差分解

Abstract:

Aims Beta diversity is the variation in species composition among sites in a geographic region. Beta diversity is a key concept for understanding the functioning of ecosystems, for the conservation of biodiversity, and for ecosystem management. This paper describes how to analyze it from community composition and associated environmental and spatial data tables.

Methods Beta diversity can be studied by computing diversity indices for each site and testing hypotheses about the factors that may explain the variation among sites. Or, one can carry out a direct analysis of the community composition data table over the study sites, as a function of sets of environmental and spatial variables. These analyses are carried out by the statistical method of partitioning the variation of the diversity indices or the community composition data table with respect to environmental and spatial variables. Variation partitioning is briefly described in this paper.

Important findings Variation partitioning is a method of choice for the interpretation of beta diversity using tables of environmental and spatial variables. Beta diversity is an interesting “currency" for ecologists to compare either different sampling areas, or different ecological communities co-occurring in an area. Partitioning must be based upon unbiased estimates of the variation of the community composition data table that is explained by the various tables of explanatory variables. The adjusted coefficient of determination provides such an unbiased estimate in both multiple regression and canonical redundancy analysis. After partitioning, one can test the significance of the fractions of interest and plot maps of the fitted values corresponding to these fractions.

Key words: adjusted coefficient of determination, beta diversity, biodiversity, canonical redundancy analysis, community composition, variation partitioning

Pierre Legendre. β-多样性的研究:应用多元回归和典范分析研究生态方差的分解. 植物生态学报, 2007, 31(5): 976-981. DOI: 10.17521/cjpe.2007.0124

Pierre Legendre. STUDYING BETA DIVERSITY: ECOLOGICAL VARIATION PARTITIONING BY MULTIPLE REGRESSION AND CANONICAL ANALYSIS. Chinese Journal of Plant Ecology, 2007, 31(5): 976-981. DOI: 10.17521/cjpe.2007.0124

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链接本文: https://www.plant-ecology.com/CN/10.17521/cjpe.2007.0124

https://www.plant-ecology.com/CN/Y2007/V31/I5/976

图/表 2

图1 表示将对应变量y或应变量矩阵Y的方差分解成自变量矩阵X和W的Venn图(Legendre, 1993) 长方形代表100% y或Y的方差。[b]是由线性模型X和线性模型W所解释方差的交集(不是交互作用)。改自 Legendre (1993)

Fig.1 Venn diagram representing the partition of the variation of a response variable Y or a response matrix Y between two sets of explanatory variables X and W (Legendre, 1993) The rectangle represents 100% of the variation in y or Y. Fraction [b] is the intersection (not the interaction) of the amounts of variation explained by linear models of X and W

表1 计算图1所示调整的方差组分[a] 到 [d]的方法(需使用3个多元回归或典范分析)

Table 1 Method for calculating the adjusted fractions of variation [a] to [d] depicted inFig. 1 (Three multiple regressions or canonical analyses are required)

典范分析 Canonical analyses	计算R² Compute R² (eq. 5)	计算 $R a 2$ 和各方差组分 Compute $R a 2$ (eq. 6) and fractions of variation	显著性检验可行性 Tested for significance
Y~X	R² of Y~X	[a+b]= $R a 2$ of Y~X	可行Yes
Y~W	R² of Y~W	[b+c]= $R a 2$ of Y~W	可行Yes
Y~(X,W)	R² of Y~(X,W)	[a+b+c]= $R a 2$ of Y~(X,W)	可行Yes
		[a]=[a+b]-[b]	可行Yes
		[b]=[a+b]+[b+c]-[a+b+c]	不可行No
		[c]=[b+c]-[b]	可行Yes
		Residuals=[d]=1-[a+b+c]	不可行No

表1 计算图1所示调整的方差组分[a] 到 [d]的方法(需使用3个多元回归或典范分析)

Table 1 Method for calculating the adjusted fractions of variation [a] to [d] depicted inFig. 1 (Three multiple regressions or canonical analyses are required)

典范分析 Canonical analyses	计算R² Compute R² (eq. 5)	计算 $R a 2$ 和各方差组分 Compute $R a 2$ (eq. 6) and fractions of variation	显著性检验可行性 Tested for significance
Y~X	R² of Y~X	[a+b]= $R a 2$ of Y~X	可行Yes
Y~W	R² of Y~W	[b+c]= $R a 2$ of Y~W	可行Yes
Y~(X,W)	R² of Y~(X,W)	[a+b+c]= $R a 2$ of Y~(X,W)	可行Yes
		[a]=[a+b]-[b]	可行Yes
		[b]=[a+b]+[b+c]-[a+b+c]	不可行No
		[c]=[b+c]-[b]	可行Yes
		Residuals=[d]=1-[a+b+c]	不可行No

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