Skip to main content
Book cover

Landscape Ecological Analysis pp 253–279Cite as

Spatial Statistics in Landscape Ecology

  • Chapter

Abstract

In ecology, especially in plant ecology, it is commonplace to identify and quantify spatial patterns (Greig-Smith 1952, 1964; Kershaw 1964). In fact, most ecological data are inherently composed of several levels of spatial structure: large-scale trends (species responses to climate conditions, to migration process, etc.), small scale patterns, patchiness (weather conditions, physical conditions, dispersal mechanisms, predation, competition, etc.), and local random noise. Therefore, the notion of spatial autocorrelation implies that “Everything is related to everything else, but near things are more related than distant things” (Tobler 1970) and “with spatial data, there is a better than random chance that one can predict attribute values from a given areal unit from those taken on by its juxtaposed areal units …” (Haining 1980). Griffith (1992) provides several other definitions of spatial autocorrelation, which include “a diagnostic tool for spatial model misspecification; a surrogate for unobserved geographical variables; a nuisance in applying conventional statistical methodology to spatial data series; an indicator of the appropriateness of, and possible artifact of, areal unit demarcation.”

Keywords

  • Spatial Pattern
  • Spatial Autocorrelation
  • Landscape Ecology
  • Canonical Correspondence Analysis
  • Spatial Statistic

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-1-4612-0529-6_12
  • Chapter length: 27 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   129.00
Price excludes VAT (USA)
  • ISBN: 978-1-4612-0529-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   169.99
Price excludes VAT (USA)
Hardcover Book
USD   219.99
Price excludes VAT (USA)
Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Anselin, L. 1992. SpaceStat: A Program for the Analysis of Spatial Data. National Center for Geographic Information and Analysis. University of California, Santa Barbara.

    Google Scholar 

  • Bailey, T.C., and A.C. Gatrell. 1995. Interactive Spatial Data Analysis. Longman Scientific & Technical. Essex.

    Google Scholar 

  • Baker, W.L., and Y. Cai. 1992. The r.le programs for multiscale analysis of landscape structure using the GRASS geographical information system. Landscape Ecology 7: 291–302.

    CrossRef  Google Scholar 

  • Beaulieu, P., and K. Lowell. 1994. Spatial autocorrelation among forest stands identified from the interpretation of aerial photographs. Landscape and Urban Planning 29: 161–169.

    CrossRef  Google Scholar 

  • Boots, B.N., and A. Getis. 1988. Point Pattern Analysis. Sage University Scientific Geography Series, Vol. 8. Sage publications, Beverly Hills.

    Google Scholar 

  • Borcard, D., P. Legendre, and P. Drapeau. 1992. Partialling out the spatial component of ecological variation. Ecology 73: 1045–1055.

    CrossRef  Google Scholar 

  • Bourgault, G., and D. Marcotte. 1991. Multivariable variogram and its application to the linear model of coregionalization. Mathematical Geology 23: 899–928.

    CrossRef  Google Scholar 

  • Bradshaw, G.A. 1991. Hierarchical analysis of pattern and processes in Douglasfir forests using the wavelet transform. Ph.D. Dissertation, Oregon State University.

    Google Scholar 

  • Brodie, C., G. Houle, and M.-J. Fortin. 1995. Development of a P. balsamifera clone in subarctic Québec reconstructed from spatial analyses. Journal of Ecology 83: 309–320.

    CrossRef  Google Scholar 

  • Burrough, P.A. 1987. Spatial aspects of ecological data. In: Community and Landscape Ecology, pp. 213–251. R.H.G. Jongman, C.J.F. ter Braak, and O.F.R. van Tongeran (eds.). Pudoc Wegeningen, Nertherlands.

    Google Scholar 

  • Chatfield, C. 1984. The Analysis of Time Series: An Introduction, 3d ed. Chapman and Hall, London.

    Google Scholar 

  • Clark, P.J., and F.C. Evans. 1954. Distance to nearest neighbour as a measure of spatial relationships in populations Ecology 35: 445–453.

    Google Scholar 

  • Cliff, A.D., and J.K. Ord. 1981. Spatial Processes: Models and Applications. Pion, London.

    Google Scholar 

  • Clifford, P., S. Richardson, and D. Hémon. 1989. Assessing the significance of the correlation between two spatial processes. Biometrics 45: 123–134.

    CrossRef  PubMed  CAS  Google Scholar 

  • Clifford, P., S. Richardson, and D. Hémon. 1993. Response: reader reaction. Modifying the t test for assessing the correlation between two spatial processes. Biometrics 49: 305–314.

    CrossRef  Google Scholar 

  • Cohen, W.B., T.A. Spies, and G.A. Bradshaw. 1990. Semivariograms of digital imagery for analysis of conifer canopy structure. Remote Sensing Environment 34: 167–178.

    CrossRef  Google Scholar 

  • Cressie, N.A.C. 1991. Statistics for Spatial Data. Wiley John & Sons, New York.

    Google Scholar 

  • Dale, M.R.T. 1990. Two-dimensional analysis of spatial pattern in vegetation for site comparison. Canadian Journal of Botany 68: 149–158.

    CrossRef  Google Scholar 

  • Dale, M.R.T., and D.J. Blundon. 1990. Quadrat variance analysis and pattern development during primary succession. Journal of Vegetation Science 1: 153–164.

    CrossRef  Google Scholar 

  • Deutsch, C.V., and A.G. Journel. 1992. GSLIB: Geostatistical Software Library and User's Guide. Oxford University Press, New York.

    Google Scholar 

  • Diggle, P.J. 1983. Statistical Analysis of Spatial Point Patterns. Academic Press. London.

    Google Scholar 

  • Duncan, R.P. 1991. Competition and the coexistence of species in a mixed podocarp stand. Journal of Ecology 79: 1073–1084.

    CrossRef  Google Scholar 

  • Duncan, R.P. 1993. Flood disturbance and the coexistence of species in lowland podocarp forest, south Westland, New Zealand. Journal of Ecology 81: 403–416.

    CrossRef  Google Scholar 

  • Duncan, R.P., and G.H. Stewart. 1991. The temporal and spatial analysis of tree age distributions. Canadian Journal of Forostur Research 21: 1703–1710.

    CrossRef  Google Scholar 

  • Dutilleul, P. 1993. Reader Reaction. Modifying the t test for assessing the correlation between two spatial processes. Biometrics 49: 305–314.

    CrossRef  Google Scholar 

  • Englund, E.J. 1990. A variance of geostatisticians. Mathematical Geology 22: 417–455.

    CrossRef  Google Scholar 

  • Ford, E.D., and E. Renshaw. 1984. The interpretation of process from pattern using two-dimensional spectral analysis: modeling single species patterns in vegetation. Vegetatio 56: 113–123.

    Google Scholar 

  • Fortin, M.-J. 1992. Detection of ecotones: definition and scaling factors. Ph.D. Dissertation, State University of New York at Stony Brook.

    Google Scholar 

  • Fortin, M.-J. 1994. Edge detection algorithms for two-dimensional ecological data. Ecology 75: 956–965.

    CrossRef  Google Scholar 

  • Fortin, M.-J., and P. Drapeau. 1995. Delineation of ecological boundaries: comparison of approaches and significance tests. Oikos 72: 323–332.

    CrossRef  Google Scholar 

  • Fortin, M.-J., and J. Gurevitch. 1993. Mantel tests: spatial structure in field experiments. In: Design and analysis of ecological experiments, pp. 342–359. S.M. Scheiner and J. Gurevitch (eds.). Chapman & Hall. New York.

    Google Scholar 

  • Fortin, M.-J., P. Drapeau, and P. Legendre. 1989. Spatial autocorrelation and sampling design in plant ecology. Vegetatio 83: 209–222.

    CrossRef  Google Scholar 

  • Getis, A., and B. Boots. 1978. Models of Spatial Process: An Approach to the Study of Point, Line and Area Patterns. Cambridge Univ. Press, Cambridge.

    Google Scholar 

  • Getis, A., and J. Franklin. 1987. Second-order neighborhood analysis of mapping point patterns. Ecology 68: 473–477.

    CrossRef  Google Scholar 

  • Greig-Smith, P. 1952. The use of random and contiguous quadrats in the study of the structure of plant communities. Annals of Botany. New Series 16: 293–316.

    Google Scholar 

  • Greig-Smith, P. 1964. Quantitative plant ecology, 2nd ed. Butterworth, London.

    Google Scholar 

  • Griffith, D.A. 1992. What is spatial autocorrelation? Reflection on the past 25 years of spatial statistics. L'Espace géographique 3: 265–280.

    CrossRef  Google Scholar 

  • Gustafson, E.J., and G.R. Parker. 1992. Relationships between landcover proportion and indices of landscape spatial pattern. Landscape Ecology 7: 101–110.

    CrossRef  Google Scholar 

  • Haase, P. 1995. Spatial pattern analysis in ecology based on Ripley's k:-function: Introduction and methods of edge correction. Journal of Vegetation Science 6: 575–582.

    CrossRef  Google Scholar 

  • Haining, R. 1980. Spatial autocorrelation problems. In: Geography and the Urban Environment, pp. 1–44. D. Herbert and R. Johnston (eds.). John Wiley & Sons, London.

    Google Scholar 

  • Haining, R. 1990. Spatial Data Analysis in the Social and Environmental Sciences. Cambridge University Press, Cambridge.

    CrossRef  Google Scholar 

  • Haining, R. 1991. Bivariate correlation with spatial data. Geographical Analysis 23: 210–227.

    CrossRef  Google Scholar 

  • Harvey, L.E. 1996. Macroecological studies of species composition, habitat and biodiversity using GIS and canonical correspondence analysis. In: Proceedings, Third International Conference/Workshop on Integrating GIS and Environmental Modeling, Sante Fe, NM, January 21-26, 1996, CD-ROM and WWW (http: / /WWW.ncgia.ucsb.edu/conf/SANTE_FECD_ROM/main.htlm).

    Google Scholar 

  • Hope, A.C.A. 1968. A simplified Monte Carlo significance test procedure. Journal of the Royal Statistical Society Seres B 30: 582–598.

    Google Scholar 

  • Isaaks, E.H., and R.M. Srivastava. 1989. An Introduction to Applied Geostatistics. Oxford University Press, Oxford.

    Google Scholar 

  • Johnston, C.A., J. Pastor, and G. Pinay. 1992. Quantitative methods for studying landscape boundaries. In: Landscape boundaries: Consequences for Biotic Diversity and Ecological Flows, pp. 107–128. A. Hansen and F. di Castri (eds.). Springer-Verlag, New York.

    Google Scholar 

  • Journel, A.G., and C. Huijbregts. 1978. Mining Geostatistics. Academic Press. London.

    Google Scholar 

  • Kenkel, N.C. 1988. Pattern of self-thinning in jack pine: testing the random mortality hypothesis. Ecology 69: 1017–1024.

    CrossRef  Google Scholar 

  • Kershaw, K.A. 1964. Quantitative and Dynamic Ecology. Edward Arnold, London.

    Google Scholar 

  • Kotliar, N.B., and J.A. Wiens. 1990. Multiple scales of patchiness and patch structure: a hierarchical framework for the study of heterogeneity. Oikos 59: 253–260.

    CrossRef  Google Scholar 

  • Leduc, A., P. Drapeau, Y. Bergeron, and P. Legendre. 1992. Study of spatial components of forest cover using partial Mantel tests and path analysis. Journal of Vegetation Science 3: 69–78.

    CrossRef  Google Scholar 

  • Legendre, P. 1993. Spatial autocorrelation: trouble or new paradigm? Ecology 74: 1659–1673.

    CrossRef  Google Scholar 

  • Legendre, P., and M.-J. Fortin, 1989. Spatial pattern and ecological analysis. Vegetatio 80: 107–138.

    CrossRef  Google Scholar 

  • Legendre, P., R.R. Sokal, N.L. Oden, A. Vaudor, and J. Kim. 1990. Analysis of variance with spatial autocorrelation in both the variable and the classification criterion. Journal of Classification 7: 53–75.

    CrossRef  Google Scholar 

  • Legendre, P., and M. Troussellier. 1988. Aquatic heterotrophic bacteria: modeling in the presence of spatial autocorrelation. Limnology and Oceanography 33: 1055–1067.

    CrossRef  Google Scholar 

  • Li, H., and J.F. Reynolds. 1995. On definition and quantification of heterogeneity. Oikos 73: 280–284.

    CrossRef  Google Scholar 

  • Ludwig, J.A., and J.F. Reynolds. 1988. Statistical Ecology. John Wiley & Sons, New York.

    Google Scholar 

  • Manly, B.F.J. 1991. Randomization and Monte Carlo methods in biology. Chapman & Hall, London.

    Google Scholar 

  • Mantel, N. 1967. The detection of disease clustering and a generalized regression approach. Cancer Research 27: 209–220.

    PubMed  CAS  Google Scholar 

  • Matheron, G. 1970. La théorie des variables régionalisées, et ses applications. Les Cahiers du Centre de Morphologie Mathématique de Fontainebleau, Fascicule 5, Fontainebleau.

    Google Scholar 

  • McGarigal, K., and B.J. Marks. 1995. FRAGSTATS: spatial pattern analysis program for quantifying landscape structure. U.S. Forest Service General Technical Report PNW 351.

    Google Scholar 

  • McGarigal, K., and W.C. McComb. 1995. Relationship between landscape structure and breeding birds in the Oregon Coast Range. Ecological Monographs 65: 235–260.

    CrossRef  Google Scholar 

  • Moeur, M. 1993. Characterizing spatial patterns of trees using stem-mapped data. Forest Science 39: 756–775.

    Google Scholar 

  • Oden, N.L. 1984. Assessing the significance of a spatial correlogram. Geographical Analysis 16: 1–16.

    CrossRef  Google Scholar 

  • Oden, N.L., and R.R. Sokal. 1986. Directional autocorrelation: an extension of spatial correlograms to two dimensions. Systematic Zoology 35: 608–617.

    CrossRef  Google Scholar 

  • Palmer, M.W. 1993. Putting things in even better order: the advantages of canonical correspondence analysis. Ecology 74: 2215–2230.

    CrossRef  Google Scholar 

  • Palmer, M.W., and P.M. Dixon. 1990. Small-scale environmental heterogeneity and the analysis of species distributions along gradients. Journal of Vegetation Science 1: 57–65.

    CrossRef  Google Scholar 

  • Qi, Y., and J. Wu. 1996. Effects of changing spatial resolution on the results of landscape pattern analysis using spatial autocorrelation indices. Landscape Ecology 11: 39–49.

    CrossRef  Google Scholar 

  • Renshaw, E., and E.D. Ford. 1984. The description of spatial pattern using two-dimensional spectral analysis. Vegetatio 56: 75–85.

    Google Scholar 

  • Riitters, K.H., R.V. O'Neill, C.T. Hunsaker, J.D. Wickham, D.H. Yankee, S.P. Timmins, K.B. Jones, and B.L. Jackson. 1995. A factor analysis of landscape pattern and structure metrics. Landscape Ecology 10: 23–29.

    CrossRef  Google Scholar 

  • Ripley, B.D. 1976. The second-order analysis of stationarity processes. Journal of Applied Problems 13: 255–266.

    CrossRef  Google Scholar 

  • Ripley, B.D. 1977. Modelling spatial patterns. Journal of the Royal Statistical Society Series B 39: 172–212.

    Google Scholar 

  • Ripley, B.D. 1979. Tests of randomness for spatial point patterns. Journal of the Royal Statistical Society Series B 41: 368–374.

    Google Scholar 

  • Ripley, B.D. 1981. Spatial Statistics. John Wiley & Sons, New York.

    CrossRef  Google Scholar 

  • Ripley, B.D. 1988. Statistical Inference for Spatial Processes. Cambridge University Press, Cambridge.

    CrossRef  Google Scholar 

  • Robertson, G.P. 1987. Geostatistics in ecology: interpolating with known variance. Ecology 68: 744–748.

    CrossRef  Google Scholar 

  • Rossi, R.E., DJ. Mulla, A.G. Journel, and E.H. Franz. 1992. Geostatistical tools for modeling and interpreting ecological spatial dependence. Ecological Monographs 62: 277–314.

    CrossRef  Google Scholar 

  • Sokal, R.R. 1979. Ecological parameters inferred from spatial correlograms. In: Contemporary Quantitative Ecology and Related Ecometrics, pp. 167–196. G.P. Patil and M.L. Rosenzweig (eds.). Statistical Ecology Series 12. International Cooperative Publishing House Fairland, MD.

    Google Scholar 

  • Sokal, R.R., and F.J. Rohlf. 1995. Biometrics, 3rd ed. W.H. Freeman, New York.

    Google Scholar 

  • Sokal, R.R., and D.E. Wartenberg. 1983. A test of spatial autocorrelation using an isolation-by-distance model. Genetics 105: 219–237.

    PubMed  CAS  Google Scholar 

  • Sokal, R.R., N.L. Oden, B.A. Thomson, and J. Kim. 1993. Testing for regional differences in means: distinguishing inherent from spurious spatial autocorrelation by restricted randomization. Geographical Analysis 25: 199–210.

    CrossRef  Google Scholar 

  • Smouse, P.E., J.C. Long, and R.R. Sokal. 1986. Multiple regression and correlation extensions of the Mantel test of matrix correspondence. Systematic Zoology 35: 627–632.

    CrossRef  Google Scholar 

  • ter Braak, C.J.F. 1987. Ordination. In: Community and Landscape Ecology, pp. 91–173. R.H.G. Jongman, C.J.F. ter Braak, and O.F.R. van Tongeran (eds.). Pudoc Wageningen, Nertherlands.

    Google Scholar 

  • ter Braak, C.J.F. 1988. Partial canonical correspondende analysis. In: Classification and Related Methods of Data Analysis, pp. 551–558. H.H. Bock (ed.). Elsevier, North Holland.

    Google Scholar 

  • Tobler, W.R. 1970. A computer movie simulating urban growth in the Detroit region. Economic Geography Supplement 46: 234–240.

    CrossRef  Google Scholar 

  • Turner, S.J., R.V. O'Neill, W. Conley, M.R. Conley, and H.C. Humpries. 1991. Pattern and scale: statistics for landscape ecology. In: Quantitative Methods in Landscape Ecology, pp. 17–49. M.G. Turner and R.H. Gardner (eds.). Springer-Verlag, New York.

    Google Scholar 

  • Upton, G.J.G., and B. Fingleton. 1985. Spatial data analysis by example, Vol. 1: Point pattern and quantitative data. John Wiley & Sons, New York.

    Google Scholar 

  • ver Hoef, J. 1993. Universal kriging for ecological data. In: Environmental modeling with GIS, pp. 447–553. M.F. Goodchild, B.O. Parks, and L.T. Steyaert (eds.). Oxford University Press, New York.

    Google Scholar 

  • ver Hoef, J., N.A.C. Cressie, and D.C. Glenn-Lewin. 1993. Spatial models for spatial statistics: some unification. Journal of Vegetation Science 4: 441–452.

    CrossRef  Google Scholar 

  • Wartenberg, D. 1985. Multivariate spatial autocorrelation: a method for explanatory geographical analysis. Geographical Analysis 17: 263–283.

    CrossRef  Google Scholar 

  • Webster, R. and M.A. Oliver. 1990. Statistical Methods in Soil and Land Resource Survey. Oxford University Press, Oxford.

    Google Scholar 

Download references

Authors
  1. Marie-Josée Fortin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Plant Biology, Arizona State University, Tempe, AZ, 85287-1601, USA

    Jeffrey M. Klopatek

  2. Appalachian Laboratory, University of Maryland, Frostburg, MD, 21532, USA

    Robert H. Gardner

Rights and permissions

Reprints and Permissions

Copyright information

© 1999 Springer Science+Business Media New York

About this chapter

Cite this chapter

Fortin, MJ. (1999). Spatial Statistics in Landscape Ecology. In: Klopatek, J.M., Gardner, R.H. (eds) Landscape Ecological Analysis. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0529-6_12

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-0529-6_12

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-6804-8

  • Online ISBN: 978-1-4612-0529-6

  • eBook Packages: Springer Book Archive