作 者 ：杜华强,汤孟平,周国模,徐文兵,刘恩斌,施拥军
期 刊 ：生态学报 2007年 27卷 12期 页码：5038~5049
Keywords:species diversity, scale, spatial pattern, multifractal,
摘 要 ：以浙江省天目山国家级自然保护区为例，采用多尺度分析思想，利用多重分形分析方法，研究了不同尺度下物种多样性的变化、空间分布格局以及多样性与空间格局之间的关系。研究主要得到3方面的结论：（1）物种多样性具有尺度依赖性，随着空间尺度的增大，Shannon-Wiener多样性指数H增大，Margalef多样性指数K和均匀度指数E减小；（2）多重分形参数αmin、多重分形谱的变化范围SR等能够定量反映物种的空间分布特征，空间大尺度越大，物种越聚集，空间分布越不均匀；（3）物种多样性与空间格局存在线性或幂函数关系。研究表明多重分形分析定量描述物种空间格局是有效性的，多重分形参数与生物多样性之间的定量关系为研究物种空间格局、生态属性与尺度之间的关系奠定了基础。因此，分形结合传统方法，在生物多样性方面的研究将有很大的潜在价值。
Abstract:Ecological scholars have shown spatial scale dependence with biodiversity. However, because there is no single scale appropriate for measuring variation in resource distributions, the relationship between spatial distributions of limiting resources and patterns of plant diversity has eluded plant ecologists. Thus, a multiscale method is imperative for understanding spatial distribution patterns. The objectives of this study were: (1) to quantify species diversity with selected species indices at different spatial scales, (2) to analyze the spatial distribution patterns of species diversity for the same spatial scales using multifractal theory (a multiscale, spatial structure analytical tool) and (3) to determine relationships between them. A 100m×100m(1hm2.) plot, located in TianMu Mountain National Natural Preservation Areas, in the western of Zhejiang Province, was investigated by precision measuring instruments. For spatial pattern analysis of species based on multiscale idea, the plot was divided into 10 subsets of 10 different spatial scales, namely 10m×10m, 20m×20m……100m×100m. In each scale, species diversity indices, including the Shannon-Wiener index (H), the Margalef index (K), and the Evenness index (E), were first calculated, and then multifractal parameters, such as the singularity index (Lipshitz-Hlder exponents) α and its fractal dimensions f(α) (multifractal spectrums), were computed. All visual algorithm programs were designed with the MatLab language (version 6.5 and above). Then, variations of species diversity and spatial distribution patterns for different scales were analyzed with linear and nonlinear regression and their relationships developed. Results of nonlinear regression analysis with power functions fit to curves of increasing spatial scale versus diversity indices showed strong relationships with H increasing (R2 = 0.71) but E (R2 = 0.89) and K (R2 = 0.88) decreasing indicating that species diversity existed with scale dependence. From the multifractal method, results indicated that species spatial distribution had multifractal features. For instance, through spatial scale changes the multifractal spectrum of species showed a large difference with f(α) being the subset of species with singularity α. So, an infinite hierarchy of dimensions using multifractal formality can characterize the internal spatial pattern. Also, when the spatial scale increased, αmin decreased while αmax increased meaning that large-scale spatial patterns of species were aggregated compared with small-scale patterns. In addition, the f(α)-α spectrum range (SR) and its symmetrical (Dist) in different scales showed that larger spatial scales had a wider SR and less symmetry meaning the spatial distribution of species for larger scales was nonuniform. Moreover, for the diversity indices H, E, and K, strong linear relationships with αmin (R2 = 0.67-0.94) and clear nonlinear associations with power functions for SR (R2 = 0.58-0.89) and Dist (R2 = 0.62-088) were found. Since interactions of species diversity and spatial characteristics are very complex, the above relationships need further validation along with precise explanations of any correlations among their ecological processes. Overall, the importance of spatial scale in fractal theory, patterns, processes, and scales can be linked to fractals in ecology with some innovative achievements occurring when traditional research methods are combined with fractal theory.
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