[1] Dale MR. Spatial Pattern Analysis in Plant Ecology. Cambridge, UK: Cambridge University Press, 2000 [2] 周红章, 于晓东, 罗天宏, 等. 物种多样性变化格局与时空尺度. 生物多样性, 2000, 8(3): 325-336 [Zhou H-Z, Yu X-D, Luo T-H, et al. How does species diversity change? Spatio-temporal patterns and scales. Biodiversity Science, 2000, 8(3): 325-336] [3] 郭忠玲, 马元丹, 郑金萍, 等. 长白山落叶阔叶混交林的物种多样性、种群空间分布格局及种间关联性研究. 应用生态学报, 2004, 15(11): 2013-2018 [Guo Z-L, Ma Y-D, Zheng J-P, et al. Biodiversity of tree species,their populations’ spatial distribution pattern and interspecific association in mixed deciduous broadleaved forest in Changbai Mountains. Chinese Journal of Applied Ecology, 2004, 15(11): 2013-2018] [4] 闫海冰, 韩有志, 杨秀清, 等. 华北山地典型天然次生林群落的树种空间分布格局及其关联性. 生态学报, 2010, 30(9): 2311-2321 [Yan H-B, Han Y-Z, Yang X-Q, et al. Spatial distribution patterns and associations of tree species in typical natural secondary mountain forest communities of Northern China. Acta Ecologica Sinica, 2010, 30(9): 2311-2321] [5] Niklas KJ. Plant Allometry: The Scaling of Form and Process. Chicago, IL, USA: University of Chicago Press, 1994 [6] Zhang YX, Ma KM, Anand M, et al. Do generalized scaling laws exist for species abundance distribution in mountains? Oikos, 2006, 115: 81-88 [7] 杨勇, 宋向阳, 刘爱军, 等. 内蒙古典型草原物种多样性的空间尺度效应及其分形分析. 草地学报, 2012, 20(3): 444-449 [Yang Y, Song X-Y, Liu A-J, et al. Scale effects and fractal analysis of species diversity in typical steppe of Inner Mongolia. Acta Agrestia Sinica, 2012, 20(3): 444-449] [8] Ver Hoef JM, Glenn-Lewin DC. Multiscale ordination: A method for detecting pattern at several seales. Vegetatio, 1989, 82: 59-67 [9] Bradshaw GA, Spies TA. Characterizing canopy gap structure in forests using wavelet analysis. Journal of Ecology, 1992, 80: 205-215 [10] Ver Hoef JM, Cressie N, Glenn-Lewin DC. Spatial mo-dels for spatial statistics: Some unification. Journal of Vegetation Science, 1993, 4: 441-452 [11] Ripley BD. Spectral analysis and the analysis of pattern in plant communities. Journal of Ecology, 1978, 66: 965-981 [12] 赵玉新, 常帅, 张振兴. 地磁异常场的多重分形谱分析及构图法. 测绘学报, 2014, 43(5): 529-536 [Zhao Y-X, Chang S, Zhang Z-X. Multifractal spectrum analysis and mapping method of geomagnetic anomaly field. Acta Geodaetica et Cartographica Sinica, 2014, 43(5): 529-536] [13] 李东东, 周文磊, 郑晓霞, 等. 基于多重分形谱和支持向量机的风电机组行星齿轮箱故障诊断与研究. 电力系统保护与控制, 2017, 45(11): 43-48 [Li D-D, Zhou W-L, Zheng X-X, et al. Diagnosis and research of wind turbine planetary gearbox faults based on multifractal spectrum support vector machine (SVM). Power System Protection and Control, 2017, 45(11): 43-48] [14] 颜杜民. 全断面隧道施工围岩变形多重分形特征研究. 铁道建筑, 2020, 60(11): 56-58 [Du Y-M. Study on multifractal characteristics of surrounding rock deformation in tunnel construction with full face method. Railway Engineering, 2020, 60(11): 56-58] [15] Mandelbrot BB. The Fractal Geometry of Nature. New York: WH Freeman, 1982 [16] Tjørve E. Shapes and functions of species-area curves: A review of possible models. Journal of Biogeography, 2003, 30: 827-835 [17] Harte J, Kinzing A, Green JL. Self-similarity in the distribution and abundance of species. Science, 1999, 284: 334-336 [18] Montero E. Renyi dimensions analysis of soil particle-size distributions. Ecological Modelling, 2005, 182: 305-315 [19] Yakimov BN, Gelashvili DB, Zhang YX, et al. Quantification of non-power-law diversity scaling with local multifractal analysis. Ecological Informatics, 2018, 48: 48-59 [20] Harte D. Multifractals: Theory and Applications. Boca Raton, FL, USA: Chapman and Hall/CRC, 2001 [21] Wei SG, Li L, Huang ZL, et al. Multifractal analysis of diversity scaling laws in a subtropical forest. Ecological Complexity, 2013, 13: 1-7 [22] 廖崇惠, 李健雄, 黄海涛. 南亚热带森林土壤动物群落多样性研究. 生态学报, 1997, 17(5): 99-105 [Liao C-H, Li J-X, Huang H-T. Soil animal community diversity in the forest of the southern subtropical region, China. Acta Ecologica Sinica, 1997, 17(5): 99-105] [23] 陈小鸟, 由文辉, 易兰. 浙江天童太白山不同海拔土壤动物的群落结构. 生态学杂志, 2009, 28(2): 270-276 [Chen X-N, You W-H, Yi L. Community structure of soil fauna along an altitudinal gradient in Taibai Mountain of Tiantong Region, Zhejiang Province. Chinese Journal of Ecology, 2009, 28(2): 270-276] [24] 佟富春, 金哲东, 王庆礼, 等. 长白山北坡土壤动物群落物种共有度的海拔梯度变化. 应用生态学报, 2003, 14(10): 1723-1728 [Tong F-C, Jin Z-D, Wang Q-L, et al. Co-occurrence of soil fauna communities with changes in altitude on the northern slope of Changbai Mountain. Chinese Journal of Applied Ecology, 2003, 14(10): 1723-1728] [25] 尹文英等. 中国土壤动物检索图鉴. 北京: 科学出版社, 1998 [Yin W-Y, Ed. Pictorial Keys to Soil Animals of China. Beijing: Science Press, 1998] [26] Peitgen HO, Jurgens H, Saupe D. Chaos and Fractals: New frontiers of science. New York, USA: Springer Science & Business Media, 2006 [27] Borda-de-Água L, Hubbell SP, McAllister M. Species-area curves, diversity indices, and species abundance distributions: A multifractal analysis. The American Na-turalist, 2002, 159: 138-155 [28] 马克明, 祖元刚. 兴安落叶松种群格局的分形特征信息维数. 生态学报, 2000, 20(2): 187-192 [Ma K-M, Zu Y-G. Fractal properties of the spatial pattern of Larix gmelini population information dimension. Acta Ecologica Sinica, 2000, 20(2): 187-192] [29] 张娜. 生态学中的尺度问题——尺度上推. 生态学报, 2007, 27(10): 4252-4266 [Zhang N. Scale issues in ecology: Upscaling. Acta Ecologica Sinica, 2007, 27(10): 4252-4266] [30] Bardgett RD, van der Putten WH. Belowground biodiversity and ecosystem functioning. Nature, 2014, 515: 505-511 [31] Peters MK, Hemp A, Appelhans T, et al. Predictors of elevational biodiversity gradients change from single taxa to the multi-taxa community level. Nature Communications, 2016, 7: 13736, https://doi.org/10.1038/ncomms13736 [32] Paz-Ferreiro J, Marinho MD, de Abreu CA, et al. Soil texture effects on multifractal behaviour of nitrogen adsorption and desorption isotherms. Biosystems Engineering, 2018, 168: 121-132 [33] 周虎, 李保国, 吕贻忠, 等 不同耕作措施下土壤孔隙的多重分形特征. 土壤学报, 2010, 47(6): 1094-1100 [Zhou H, Li B-G, Lv Y-Z, et al. Multifractal characteristics of soil pore structure under different tillage systems. Acta Pedologica Sinica, 2010, 47(6): 1094-1100] [34] 杜华强, 汤孟平, 周国模, 等. 天目山物种多样性尺度依赖及其与空间格局关系的多重分形. 生态学报, 2007, 27(12): 5038-5049 [Du H-Q, Tang M-P, Zhou G-M, et al. Linking species diversity with spatial scale dependence to spatial patterns using multifractal analysis. Acta Ecologica Sinica, 2007, 27(12): 5038-5049] [35] Zhang YX, Ma KM, Anand M, et al. Scale dependence of the beta diversity-scale relationship. Community Eco-logy, 2015, 16: 39-47 |