Cumulative effects of K-function in the research of point patterns

doi:10.13287/j.1001-9332.202205.005

Abstract

Abstract: The spatial pattern of plant population is one of primary issues in ecological research. Point pattern analy-sis is considered as an important method to study the spatial pattern of plant population. Ripley's K function has been commonly used for point pattern analysis. However, the cumulative effect of Ripley's K function may lead to specific spatial pattern charcteristics. To explore how the cumulative effect of Ripley's K function affects population pattern, the data of clumped distribution, random distribution and regular distribution of Stipa grandis were simulated by R software. All data generated by R software were analyzed by Ripley's K function and the non-cumulative pairwise correlation function g(r). The results showed that for clumped distribution (or regular distribution), the cumulative effect of Ripley's K function was manifested in two aspects. On the one hand, the scale of clumped distribution (or regular distribution) was increased due to Ripley's K function. On the other hand, Ripley's K function could detect the difference of the distribution of cluster (or negative interaction range) in the sampling space, exhibiting different pattern characteristics. For random distribution, Ripley's K function had no cumulative effect. In conclusion, the combination of Ripley's K function and pairwise correlation function by collecting replicate samples could better reveal the essential characteristics of the pattern in the study of population pattern.

Key words: K-function, pair correlation function, spatial point pattern, cumulative effect

WANG Xin-ting, WANG Dian-jie, LI Hai-bing, TAI Yang, JIANG Chao, LIU Fang, LI Su-ying, MIAO Bai-ling. Cumulative effects of K-function in the research of point patterns[J]. Chinese Journal of Applied Ecology, 2022, 33(5): 1275-1282.

References

[1] Legendre P, Fortin MJ. Spatial pattern and ecological analysis. Vegetatio, 1989, 80: 107-138
[2] Kareiva P. Space: The ﬁnal frontier for ecological theory. Ecology, 1994, 75: 1
[3] Tilman D. Competition and biodiversity in spatially structured habitats. Ecology, 1994, 75: 2-16
[4] Tilman D, Kareiva P. Spatial Ecology: The Role of Space in Population Dynamics and Interspeciﬁc Interactions. Princeton: Princeton University Press, 1997
[5] Condit R. Spatial patterns in the distribution of tropical tree species. Science, 2000, 288: 1414-1418
[6] Dungan JL, Perry JN, Dale MRT, et al. A balanced view of scale in spatial statistical analysis. Ecography, 2002, 25: 626-640
[7] Turner MG. Landscape ecology: What is the state of the science? Annual Review of Ecology, Evolution and Systematics, 2005, 36: 319-344
[8] Law R, Illian J, Burslem DFRP, et al. Ecological information from spatial patterns of plants: Insights from point process theory. Journal of Ecology, 2009, 97: 616-628
[9] Wang X, Wiegand T, Hao Z, et al. Species associations in an old-growth temperate forest in north-eastern China. Journal of Ecology, 2010, 98: 674-686
[10] Jia X, Dai XF, Shen ZX, et al. Facilitation can maintain clustered spatial pattern of plant populations during density-dependent mortality: Insights from a zone-of-influence model. Oikos, 2011, 120: 472-480
[11] 张兰, 张华, 赵传燕. 黑河下游胡杨种群的点格局分析. 应用生态学报, 2014, 25(12): 3407-3412
[12] 王鑫厅, 姜超. 典型草原放牧干扰下的点格局研究. 北京: 科学出版社, 2018
[13] 闫秀, 窦建德, 黄维, 等. 宁夏珍稀濒危植物半日花种群结构和点格局分析. 应用生态学报, 2020, 31(11): 3614-3620
[14] Wang X, Jiang C, Chi Y, et al. Facilitation in plants shifts along a recovery gradient induced by long-term overgrazing in a temperate steppe community. Journal of Vegetation Science, 2021, 32: e13019
[15] Watt AS. Pattern and process in the plant community. Journal of Ecology, 1947, 35: 1-22
[16] Greig-Smith P. Pattern in vegetation. Journal of Eco-logy, 1979, 67: 755-779
[17] Leps J. Can underlying mechanisms be deduced from observed patterns// Krahulec F, Agnew ADQ, Agnew S, eds. Spatial Processes in Plant Communities. The Hague: SPB Academic Publishing, 1990: 1-11
[18] Wiegand T, Gunatilleke S, Gunatilleke N, et al. Analyzing the spatial structure of a Sri Lankan tree species with multiple scales of clustering. Ecology, 2007, 88: 3088-3102
[19] Wiegand T, Moloney KA. A Handbook of Spatial Point Pattern Analysis in Ecology. Boca Raton: Chapman and Hall/CRC Press, 2014
[20] Ripley BD. Spatial Statistics. New York: Wiley, 1981
[21] Stoyan D, Stoyan H. Fractals, Random Shapes and Point Fields: Methods of Geometrical Statistics. New York: John Wiley and Sons, 1994
[22] Dale MRT. Spatial Pattern Analysis in Plant Ecology. Cambridge: Cambridge University Press, 1999
[23] Diggle PJ. Statistical Analysis of Point Patterns. 2nd Ed. London: Arnold, 2003
[24] Diggle PJ. Statistical Analysis of Spatial and Spatio-temporal Point Patterns. 3rd Ed. Boca Raton: CRC Press, 2013
[25] Velázquez E, Martínez I, Getzin S, et al. An evaluation of the state of spatial point pattern analysis in ecology. Ecography, 2016, 39: 1042-1055
[26] Wiegand T, Moloney KA. Rings, circles, and null-models for point pattern analysis in ecology. Oikos, 2004, 104: 209-229
[27] Stoyan D, Penttinen A. Recent application of point process methods in forest statistics. Statistical Science, 2000, 15: 61-78
[28] Ripley BD. The second-order analysis of stationary point processes. Journal of Applied Probability, 1976, 13: 255-266
[29] Ripley BD. Modelling spatial pattern. Journal of the Royal Statistical Society Series B, 1977, 39: 172-212
[30] Wiegand T, Grabarnik P, Stoyan D. Envelope tests for spatial point patterns with and without simulation. Ecosphere, 2016, 7: e01365
[31] Shen G, Yu M, Hu XS, et al. Species-area relationships explained by the joint effects of dispersal limitation and habitat heterogeneity. Ecology, 2009, 90: 3033-3041
[32] 王鑫厅, 柴静, 姜超, 等. 典型草原大针茅种群空间格局及对长期过度放牧的响应. 生物多样性, 2020, 28(2): 128-134