Abstract
Three functions that analyze point patterns are the L (a transformation of Ripley’s K function), pair correlation, and K2 functions. We tested these functions with Genton’s spatial index, which measures the distance between observed and random theoretical lines for a function over all lag distances. We simulated points from random, moderately regular, extremely regular, and clustered distributions at different density levels and a fixed plot size and for regular distributions at varying plot sizes. The spatial index clearly was able to identify clustered patterns. However, there was overlap in spatial index values between random and moderately regular distributions at lower densities. The spatial index for the L function also became more negative as plot size increased, indicating edge effects, whereas the pair correlation and K2 function values fluctuated with plot size. Using confidence envelopes rather than a spatial index, we also identified distributions other than the known distribution at low densities. These results indicate that ecologists should be cautious about 1) assigning random or regular distribution, particularly for the L function and the K2 function, 2) comparing point patterns of different densities and plot sizes, and 3) interpreting the pair correlation and K2 functions.
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Abbreviations
- CSR:
-
Complete Spatial Randomness
- GSI:
-
Genton’s spatial index.
References
Baddeley, A. and R. Turner. 2005. Spatstat, an R package for analyzing spatial point patterns. J. Stat. Softw. 12:1–42.
Hui, G., L. Li, Z. Zhao and D. Puxing. 2007. Comparison of methods in analysis of the tree spatial distribution pattern. Acta Ecol. Sin. 27:4717–4728.
Clark, P. J. and F. C. Evans. 1954. Distance to the nearest neighbor as a measure of spatial relationships in populations. Ecology 35:445–453.
Genton, M. G., D. T. Butry, M. L. Gumpertz and J. P. Prestemon. 2006. Spatio-temporal analysis of wildfire ignitions in the St Johns River Management District, Florida. Int. J. Wildland Fire 15:87–97.
Loosemore, N. B. and E. D. Ford. 2006. Statistical inference using the G or K point pattern spatial statistics. Ecology 87:1925–1931.
Moravie, M-A. and A. Robert. 2003. A model to assess relationships between forest dynamics and spatial structure. J. Veg. Sci. 14:823–834.
Perry, G. L. W., B. P. Miller and N. J. Enright. 2006. A comparison of methods for the statistical analysis of spatial point patterns in plant ecology. Plant Ecol. 187:59–82.
Pielou, E. C. 1961. Segregation and symmetry in two-species populations as studied by neares-neighbor relationships. J. Ecol. 49:255–269.
Pommerening, A. 2002. Approaches to quantifying forest structures. Forestry 75:305–324.
Ripley, B. D. 1976. The second-order analysis of stationary point processes. J. Appl. Probab. 13:255–266.
Schiffers, K., F. M. Schurr, K. Tielbörger, C. Urbach, K. Moloney and F. Jeltsch. 2008. Dealing with virtual aggregation – a new index for analyzing heterogeneous point patterns. Ecography 31:545–555.
Stoyan, D. and A. Penttinen. 2000. Recent applications of point process methods in forestry statistics. Stat.Sci. 15:61–78.
The R Development Core Team 2010. R. 2.11.1. A language and environment. www.r-project.org.
Yang, J., H. S. Hong, S. R. Shifley and E. J. Gustafson. 2007. Spatial patterns of modern period human-caused fire occurrence in the Missouri Ozark highlands. Forest Sci. 53:1–15.
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Hanberry, B.B., Yang, J. & He, H.S. Evaluating functions to describe point patterns. COMMUNITY ECOLOGY 14, 1–7 (2013). https://doi.org/10.1556/ComEc.14.2013.1.1
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DOI: https://doi.org/10.1556/ComEc.14.2013.1.1