Plant Ecology

, Volume 187, Issue 1, pp 59–82 | Cite as

A comparison of methods for the statistical analysis of spatial point patterns in plant ecology

  • George L. W. PerryEmail author
  • Ben P. Miller
  • Neal J. Enright
Original Paper


We describe a range of methods for the description and analysis of spatial point patterns in plant ecology. The conceptual basis of the methods is presented, and specific tests are compared, with the goal of providing guidelines concerning their appropriate selection and use. Simulated and real data sets are used to explore the ability of these methods to identify different components of spatial pattern (e.g. departure from randomness, regularity vs. aggregation, scale and strength of pattern). First-order tests suffer from their inability to characterise pattern at distances beyond those at which local interactions (i.e. nearest neighbours) occur. Nevertheless, the tests explored (first-order nearest neighbour, Diggle’s G and F) are useful first steps in analysing spatial point patterns, and all seem capable of accurately describing patterns at these (shorter) distances. Among second-order tests, a density-corrected form of the neighbourhood density function (NDF), a non-cumulative analogue of the commonly used Ripley’s K-function, most informatively characterised spatial patterns at a range of distances for both univariate and bivariate analyses. Although Ripley’s K is more commonly used, it can give very different results to the NDF because of its cumulative nature. A modified form of the K-function suitable for inhomogeneous point patterns is discussed. We also explore the use of local and spatially-explicit methods for point pattern analysis. Local methods are powerful in that they allow variations from global averages to be detected and potentially provide a link to recent spatial ecological theory by taking the ‚plant’s-eye view’. We conclude by discussing the problems of linking spatial pattern with ecological process using three case studies, and consider some ways that this issue might be addressed.


Point pattern Spatial statistics Ripley’s K-function Nearest neighbour Neighbourhood density function Poisson process 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



We thank the three anonymous referees whose thorough reviews helped to improve the paper. The preparation of this paper was assisted by funding via Australian Research Council Discovery grant number 34255 to NJE and GLWP.


  1. Amarasekare P (2003) Competitive coexistence in spatially structured environments: a synthesis. Ecol Lett 6:1109–1122CrossRefGoogle Scholar
  2. Baddeley A, Turner R (2000) Practical maximum pseudolikelihood for spatial point patterns. Aust New Zealand J Stat 42:283–322CrossRefGoogle Scholar
  3. Baddeley A, Turner R (2004) Introduction to ‚Spatstat’ version 1.5–5: an Splus/R library for spatial statistics. Department of Mathematics and Statistics, University of Western Australia, Australia.∼ ∼adrian/spatstat.html
  4. Baddeley AJ, Møller J, Waagespetersen R (2000) Non- and semi-parametric estimation of interaction in inhomogeneous point patterns. Statistica Neerlandica 54:329–350CrossRefGoogle Scholar
  5. Baddeley AJ, Silverman BW (1984) A cautionary example on the use of second-order methods for analyzing point patterns. Biometrics 40:1089–1094CrossRefGoogle Scholar
  6. Barot S, Gignoux J, Menaut JC (1999) Demography of a savanna palmtree: predictions from comprehensive spatial pattern analyses. Ecology 80:1987–2005CrossRefGoogle Scholar
  7. Batista JLF, Maguier DA (1998) Modelling the spatial structure of tropical forests. Forest Ecol Manage 110:293–314CrossRefGoogle Scholar
  8. Besag J, Diggle PJ (1977) Simple Monte Carlo tests for spatial pattern. Appl Stat 26:327–333CrossRefGoogle Scholar
  9. Bolker BM, Pacala SW, Neuhauser C (2003) Spatial dynamics in model plant communities: what do we really know? Am Natural 162:135–148CrossRefGoogle Scholar
  10. Brunsdon C, Fotheringham S, Charlton M (1998) Geographically weighted regression—modelling spatial non-stationarity. The Statistician 47:431–443Google Scholar
  11. Cale WG, Henebry GM, Yeakley JA (1989) Inferring process from pattern in natural communities. BioScience 39:600–605CrossRefGoogle Scholar
  12. Carroll SS, Pearson DL (2000) Detecting and modeling spatial and temporal dependence in conservation biology. Conserv Biol 14:1893–1897CrossRefGoogle Scholar
  13. Clark PJ, Evans FC (1954) Distance to nearest neighbor as a measure of spatial relationships in populations. Ecology 35:445–453CrossRefGoogle Scholar
  14. Condit R, Ashton PS, Baker P, Bunyavejchewin S, Gunatilleke S, Gunatilleke N, Hubbell SP, Foster RB, Itoh A, LaFrankie JV, Seng Lee H, Losos E, Manokaran N, Sukumar R, Yamakura T (2000). Spatial patterns in the distribution of tropical tree species. Science 288:1414–1418PubMedCrossRefGoogle Scholar
  15. Couteron P, Seghieri J, Chadouef J (2003) A test for spatial relationships between neighbouring plants in plots of heterogeneous plant density. J Vegetat Sci 14:163–172CrossRefGoogle Scholar
  16. Cressie NAC (1993). Statistics for spatial data revised edition. John Wiley & Sons, New York NY, USAGoogle Scholar
  17. Dale MRT (1999) Spatial pattern analysis in plant ecology. Cambridge University Press, CambridgeGoogle Scholar
  18. Dale MRT, Dixon P, Fortin M-J, Legendre P, Myers DE, Rosenberg MS (2002) Conceptual and mathematical relationships among methods for spatial analysis. Ecography 25:558–577CrossRefGoogle Scholar
  19. Davis JH, Howe RW, Davis GJ (2000) A multi-scale spatial analysis method for point data. Landscape Ecol 15:99–114CrossRefGoogle Scholar
  20. Diggle PJ (1979) On parameter estimation and goodness-of-fit testing for spatial point patterns. Biometrics 35:87–101CrossRefGoogle Scholar
  21. Diggle PJ (2003) Statistical analysis of spatial point patterns (2nd ed). Arnold, London UKGoogle Scholar
  22. Dixon P. (1994) Testing spatial segregation using a nearest-neighbor contingency table. Ecology 75:1940–1948CrossRefGoogle Scholar
  23. Dixon P (2002a). Ripley’s K-function. In: El-Shaarawi AH, Piergorsch WW (eds) Encyclopedia of environmetrics, vol. 3. John Wiley & Sons, New York, NY, USA, pp. 1976–1803Google Scholar
  24. Dixon PM (2002b) Nearest neighbour methods. In: El-Shaarawi AH, Piegorsch WW (eds) Encyclopedia of environmetrics, vol. 3. John Wiley & Sons, New York, NY, USA, pp. 1370–1383Google Scholar
  25. Dixon PM (2002c) Nearest-neighbor contingency table analysis of spatial segregation for several species. Ecoscience 9:142–151Google Scholar
  26. Eccles NS, Esler KJ, Cowling RM (1999) Spatial pattern analysis in Namaqualand desert plant communities: evidence for general positive interactions. Plant Ecol 142:71–85CrossRefGoogle Scholar
  27. Fotheringham AS (1997) Trends in quantitative methods I: stressing the local. Progr Human Geogr 21:88–96CrossRefGoogle Scholar
  28. Fotheringham AS (1999) Trends in quantitative methods III: stressing the visual. Progr Human Geogr 23:597–606CrossRefGoogle Scholar
  29. Galiano EF (1982) Pattern detection in plant populations through the analysis of plant-to-all-plant distances. Vegetatio 49:39–43CrossRefGoogle Scholar
  30. Gatrell AC, Bailey TC, Diggle PJ, Rowlingson BS (1996) Spatial point pattern analysis and its application in geographical epidemiology. Trans Inst Brit Geograph 21:256–274CrossRefGoogle Scholar
  31. Getis A, Franklin J (1987) Second-order neighbourhood analysis of mapped point data patterns. Ecology 68:473–477CrossRefGoogle Scholar
  32. Goreaud F, Pélissier R (1999) On explicit formulas of edge effect correction for Ripley’s K-function. J Veget Sci 10:433–438CrossRefGoogle Scholar
  33. Goreaud F, Pélissier R (2003) Avoiding misinterpretation of biotic interactions with the intertype K 12-function: population independence vs. random labelling hypotheses. J␣Vegetat Sci 14:681–692CrossRefGoogle Scholar
  34. Greig-Smith P (1952) The use of random and contiguous quadrats in the study of the structure of plant communities. Ann Bot 16:293–316Google Scholar
  35. Guttorp P (1991) Spatial statistics in ecology. In: Panel on Spatial Statistics and Image Processing (eds) Spatial statistics and digital image analysis. National Academy Press, Washington, DC, USA, pp.␣129–146Google Scholar
  36. Haase P (1995) Spatial pattern analysis in ecology based on Ripleys K-function—introduction and methods of edge correction. J Veget Sci 6:575–582CrossRefGoogle Scholar
  37. Haase P (2001) Can isotropy vs. anisotropy in the spatial association of plant species reveal physical vs. biotic facilitation? J Vegetat Sci 12:127–136Google Scholar
  38. Hutchings MJ (1979) Standing crop and pattern in pure stands of Mercurialis perennis and Rubus fruticosus in mixed deciduous woodland. Oikos 31:351–357Google Scholar
  39. Jolles AE, Sullvian P, Alker AP, Harvell CD (2002) Disease transmission of Aspergillosis in Sea Fans: inferring process from spatial pattern. Ecology 83:2373–2378Google Scholar
  40. Lancaster J, Downes BJ (2004) Spatial point pattern analysis of available and exploited resources. Ecography 27:94–102CrossRefGoogle Scholar
  41. Legendre P (1994) Spatial autocorrelation: trouble or new paradigm. Ecology 74:1659–1673CrossRefGoogle Scholar
  42. Legendre P, Dale MRT, Fortin M-J, Gurevitch J, Hohn M, Myers D (2002) The consequences of spatial structure for the design and analysis of ecological field surveys. Ecography 25:601–615CrossRefGoogle Scholar
  43. Lotwick HW, Silverman BW (1982) Methods for analysing spatial processes of several types of points. J Roy Stat Soc, Ser B. 44:406–413Google Scholar
  44. Mark AF, Esler AE (1970) An assessment of the point-centred quarter method of plotless sampling in some New Zealand forests. Proc New Zealand Ecol Soc 17:106–110Google Scholar
  45. Marriott FHC (1979) Barnard’s Monte Carlo tests: how many simulations? Appl Stat 28:75–77CrossRefGoogle Scholar
  46. McArdle BH, Hewitt JE, Thrush SF (1997) Pattern from process: it is not as easy as it looks. J Exp Marine Biol Ecol 216:229–242CrossRefGoogle Scholar
  47. Molofsky J, Bever JD, Antonovics J, Newman TJ (2002) Negative frequency dependence and the importance of spatial scale. Ecology 83:21–27Google Scholar
  48. Moravie M-A, Robert A (2003) A model to assess relationships between forest dynamics and spatial structure. J Veget Sci 14:823–834CrossRefGoogle Scholar
  49. Pélissier R (1998) Tree spatial patterns in three contrasting plots of a southern Indian tropical moist evergreen forest. J Trop Ecol 14:1–16CrossRefGoogle Scholar
  50. Perry JN (1995) Spatial analysis by distance indices. J Anim Ecol 64:303–314CrossRefGoogle Scholar
  51. Perry JN, Liebhold AM, Rosenberg MS, Dungan J, Miriti M, Jakomulska A, Citron-Pousty S (2002) Illustrations and guidelines for selecting statistical methods for quantifying spatial pattern in ecological data. Ecography 25:578–600CrossRefGoogle Scholar
  52. Pielou EC (1961) Segregation and symmetry in two-species populations as studied in nearest-neighbour relationships. J Ecol 49:255–269CrossRefGoogle Scholar
  53. Platt WJ, Evans GW, Rathbun SL (1988) The population dynamics of a long-lived conifer (Pinus palustris). Am Natural 131:491–525CrossRefGoogle Scholar
  54. Plotkin JB, Potts MD, Leslie N, Manokaran N, LaFrankie J, Ashton PS (2000a) Species–area curves, spatial aggregation, and habitat specialization in tropical forests. J Theoret Biol 207:81–99CrossRefGoogle Scholar
  55. Plotkin JB, Potts MD, Yu DW, Bunyavejchewin S, Condit R, Foster R, Hubbell S, LaFrankie J, Manokaran N, Seng Lee H, Sukumar R, Nowak A, Ashton PS (2000b) Predicting species diversity in tropical forests. Proc Natl Acad Sci USA 97:10850–10854CrossRefPubMedGoogle Scholar
  56. Podani J, Czaran T (1997) Individual-centered analysis of mapped point patterns representing multi-species assemblages. J Vegetat Sci 8:259–270CrossRefGoogle Scholar
  57. Podani J, Czaran T, Scheuring I (1998) Individual-centered analysis of community pattern: some case studies. Abstr Bot 22:101–112Google Scholar
  58. Purves DW, Law R (2002) Fine-scale spatial structure in a grassland community: quantifying a plant’s eye view. J␣Ecol 90:121–130CrossRefGoogle Scholar
  59. Rathbun SL, Cressie N (1994) A space–time survival point process for a longleaf pine forest in Southern Georgia. J␣Am Stat Assoc 89:1164–1174CrossRefGoogle Scholar
  60. Real LA, McElhany P (1996) Spatial pattern and process in plant–pathogen interactions. Ecology 77:1011–1025CrossRefGoogle Scholar
  61. Ripley BD (1977) Modelling spatial patterns. J Roy Stat Soc, Ser B. Series B. 39:172–212Google Scholar
  62. Ripley BD (1979) Tests of ‚randomness’ for spatial point patterns. J Roy Stat Soc, Ser B 41:368–374Google Scholar
  63. Ripley BD (1981) Spatial statistics. John Wiley& Sons, New York, NYCrossRefGoogle Scholar
  64. Schurr FM, Bossdorf O, Milton SJ, Schumacher J (2004) Spatial pattern formation in semi-arid shrubland: a priori predicted versus observed pattern characteristics. Plant Ecol 173:271–282CrossRefGoogle Scholar
  65. Shi H, Zhang L (2003) Local analysis of tree competition and growth. Forest Sci 49:938–955Google Scholar
  66. Shimatani K (2001) Multivariate point processes and spatial variation of species diversity. Forest Ecol and Manage 142:215–229CrossRefGoogle Scholar
  67. Shimatani K, Kubota Y (2004) Quantitative assessment of multispecies spatial pattern with high species diversity. Ecol Res 19:149–163CrossRefGoogle Scholar
  68. Silvertown J, Antonovics J (eds) (2001) Integrating ecology and evolution in a spatial context. Blackwell Scientific, Oxford, UKGoogle Scholar
  69. Silvertown J, Holtier S, Johnson J, Dale P (1992) Cellular automaton models of interspecific competition for space—the effect of pattern on process. J Ecol 80:527–534CrossRefGoogle Scholar
  70. Sinclair DF (1985) On tests of spatial randomness using mean nearest neighbour distance. Ecology 66:1084–1085CrossRefGoogle Scholar
  71. Skellam JG (1951) Random dispersal in theoretical populations. Biometrika 38:196–218PubMedCrossRefGoogle Scholar
  72. Stamp NE, Lucas JR (1990) Spatial patterns and dispersal distances of explosively dispersing plants in Florida sandhill vegetation. J Ecol 78:589–600CrossRefGoogle Scholar
  73. Stoyan D, Kendall WS, Mekce J (1995) Stochastic geometry and its applications, 2nd edn. John Wiley & Sons, Chichester, UKGoogle Scholar
  74. Stoyan D, Penttinen A (2000) Recent applications of point process methods in forestry statistics. Stat Sci 15:61–78CrossRefGoogle Scholar
  75. Stoyan D, Stoyan H (1994) Fractals, random shapes and point fields: methods of geometrical statistics. John Wiley & Sons, Chichester, UKGoogle Scholar
  76. Thompson HR (1956) Distribution of distance to n th neighbour in a population of randomly distributed individuals. Ecology 37:391–394CrossRefGoogle Scholar
  77. Thönnes E, van Lieshout M-C (1999) A comparative study on the power of van Lieshout and Baddeley’s J-function. Biomet J 41:721–734CrossRefGoogle Scholar
  78. Unwin DJ (1996) GIS, spatial analysis and spatial statistics. Progr Human Geogr 20:540–551Google Scholar
  79. van Lieshout MNM, Baddeley AJ (1996) A nonparametric measure of spatial interaction in point patterns. Stat Neerland 50:344–361CrossRefGoogle Scholar
  80. Venables WN, Ripley BD (1997) Modern applied statistics with S-Plus, 2nd edn. Springer-Verlag, BerlinGoogle Scholar
  81. Ward JS, Parker GR, Ferrandino FJ (1996) Long-term spatial dynamics in an old-growth deciduous forest. Forest Ecol Manage 83:189–202CrossRefGoogle Scholar
  82. Watt AS (1947) Pattern and process in the plant community. J Ecol 35:1–22CrossRefGoogle Scholar
  83. Wiegand T, Moloney KA (2004) Rings, circles, and null-models for point pattern analysis in ecology. Oikos 104:209–229CrossRefGoogle Scholar
  84. Wilhelm A, Steck R (1998) Exploring spatial data by using interactive graphics and local statistics. The Statistician 47:423–430Google Scholar
  85. Yamada I, Rogerson PA (2003) An empirical comparison of edge effect correction methods applied to K-function analysis. Geograph Anal 37:95–109Google Scholar
  86. Zhang LJ, Shi HJ (2004) Local modeling of tree growth by geographically weighted regression. Forest Sci 50:225–244Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006 2006

Authors and Affiliations

  • George L. W. Perry
    • 1
    Email author
  • Ben P. Miller
    • 2
  • Neal J. Enright
    • 2
  1. 1.School of Geography & Environmental ScienceUniversity of AucklandAucklandNew Zealand
  2. 2.School of Anthropology, Geography and Environmental StudiesUniversity of MelbourneMelbourneAustralia

Personalised recommendations