群落物种多度格局的分形解析

doi:10.11867/j.issn. 1001-8166. 2015.10.1144.

生物群落物种多度格局(Species Abundance Distribution, SAD)研究是理解物种多样性决定机制的关键。这个问题不仅关系到物种多样性的保护与恢复,更重要的是,它有助于理清生物群落中各个物种之间错综复杂的相互关系,以及物质与能量在群落中的分配方式。群落物种多度格局研究的核心内容是如何构建SAD生态模型。该类研究始于20世纪30年代,相对已有的SAD模型而言,分形模型对生物群落样本的要求简单,适用性较高,便于不同群落间的比较。鉴于此,从分形模型的起源、假设条件、构建方法、分形参数的生态意义以及存在的问题等几个方面进行总结,以期促进此项工作的开展,为物种多度格局和多样性决定机制研究提供帮助。

关键词: 分形理论, 生物多样性, Zipf-Mandelbrot模型, 蝴蝶群落, 甲虫群落

The study of Apecies Abundance Distribution (SAD) is the key of understanding what determines species diversity. The theoretical exploration of SAD relates to the maintenance and conservation of biodiversity, and more importantly, it is conducive to clarifying complicated relationship among species and the distribution of matter and energy in a community. The research on SAD began in the 1930s, and there are so many kinds of theoretical models of SAD that can fit actual data, such as geometric-series model, log-series model, log-normal model, broken-stick model and so on. However, despite this, these models are often restrictive in their hypotheses and difficult to fit by natural communities. Especially, there is not always a good fit to the community that only has a few species. Thus, Frontier firstly introduced a family of models termed the Zipf-Mandelbrot model. This model is unrestrictive and easily fit by different natural community. Accordingly, this paper reviewed its origin, hypothesis, construction, problems and ecological signification of parameters to promote the research of SAD and the determination of species diversity.

Key words: Fractal theory, Community diversity, Zipf-Mandelbrot model, Butterfly community, Beetles community.

中图分类号:

P935.1

图1 生物群落物种多度随排序位数的递减方式按物种多度由大到小排序,每个物种由横坐标的排序位数(r)和纵坐标的多度(N_r)进行标记。该散点图的递减方式：可能是线性的(如群落A),下弧形的(如群落B)或上弧形等

Fig.1 The monotonically decreasing pattern of a community ordered in species abundance Ranking species abundance from largest to smallest, the decreasing pattern with the rank on the abscissa and relative abundance on the ordinate have three theoretical possibilities: Linear(A),convex(B),or concave

图2 理论分形树 ^{[

30
]} 在分形树的3个等级内(1,2,3),分支数量每增加3倍(K),分支大小缩小2倍(k),总计13个自相似单元,分形维数d=1.585

Fig.2 Theoretical fractal tree ^{[

30
]} During three steps of the succession in theoretical fractal tree(1,2,3), 3 times (K) branch number appear which are 2 times (k) less -size. There are totally 13 auto similar elements, and the fractal dimension is 1.585

表1 在第 i个分形等级上,新增物种数量 R_i以及该等级上物种的多度 N_i如表所示 ^{[

30
]}

Table 1 At the i-th fractal step, numbers of new species ( Ri) and its relative abundance ( Ni) during ecological succession is shown in the following table ^{[

30
]}

分型等级（i）	新增物种数量（R_i）	新增物种的多度（N_i）
-	-	A
1	1	A^.k^-1
2	K	A^.k^-2
3	K²	A^.k^-3
.	.	.
i	Kⁱ^-1	A^.k^-ⁱ
.	.	.

表1 在第 i个分形等级上,新增物种数量 R_i以及该等级上物种的多度 N_i如表所示 ^{[

30
]}

Table 1 At the i-th fractal step, numbers of new species ( Ri) and its relative abundance ( Ni) during ecological succession is shown in the following table ^{[

30
]}

分型等级（i）	新增物种数量（R_i）	新增物种的多度（N_i）
-	-	A
1	1	A^.k^-1
2	K	A^.k^-2
3	K²	A^.k^-3
.	.	.
i	Kⁱ^-1	A^.k^-ⁱ
.	.	.

图3 Zipf-Mandelbrot模型对蝴蝶和甲虫群落的拟合结果以群落物种多度为序,排序位数(r)作为横坐标,相对多度(F_r=N_r/N_T)作为纵坐标,并进行双对数变换,Zipf-Mandelbrot模型的拟合结果如下：（a）树冠层蝴蝶群落样本,β=0.88,γ=1.77;（b）灌木层蝴蝶群落样本,β=2.42,γ=1.41^{[

31
]};甲虫群落1(c)和2(d)的分形参数(β和γ)分别为0.57和1.84,以及2.01和1.33^{[

32
]}

Fig. 3 The fit results of Zipf-Mandelbrot model to SADs of butterflies and beetles communities Ranking species by their abundance in descending order, the SAD is presented with the rank (r) on the abscissa and relative abundance (F_r=N_r/N_T) on the ordinate using log-log axes. Results of Zipf-Mandelbrot model to the actual data are as follows: β=0.88 and γ=1.77 in the canopy butterfly community (a); β=2.42 and γ=1.41in the understory butterfly community (b) ^{[

31
]}; Fractal parameters (β and γ) in beetles communities (1 and 2) are 0.57/1.84 and 2.01/1.33, respectively^{[

32
]}

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摘要

Analyzing Fractal Property of Species Abundance Distribution in A Community