Geostatistics, spatial rate of change analysis and boundary detection in plant ecology and biogeography

Progress in Physical Geography

Volumn 30, Issue 2, 2006, Pages 201-231

  Kent, Martin ^a   Moyeed, Rana A ^a   Reid, Catherine L ^a   Pakeman, Robin ^b   Weaver, Ruth ^a  

^a UNIVERSITY OF PLYMOUTH   (United Kingdom)

^b SCOTTISH CROP RESEARCH INSTITUTE   (United Kingdom)

Author keywords

Dissimograms; Kriging; Plant assemblages and plant communities; Spatial analysis and interpolation; Spatial autocorrelation; Spatially constrained clustering; Wombling

Indexed keywords

GEOSTATISTICS; PHYTOGEOGRAPHY; SPATIAL ANALYSIS;

EID: 33646265047     PISSN: 03091333     EISSN: None     Source Type: Journal    
DOI: 10.1191/0309133306pp477ra     Document Type: Review

References (205)

1. Allen, T.F.H. 1998: The landscape 'level' is dead: persuading the family to take it off the respirator. In Peterson, D.L. and Parker, V.T., editors, Ecological scale, New York: Columbia University Press, 35-54.
2. Anderson, M.J. and Gribble, N.A. 1998: Partitioning the variation among spatial, temporal and environmental components in a multivariate dataset. Australian Journal of Ecology 23, 158-67.
3. Andréfouët, S. and Roux, L. 1998: Characterisation of ecotones using membership degrees computed with a fuzzy classifier. International Journal of Remote Sensing 19, 3205-11.
4. Armitage, R.P., Kent, M. and Weaver, R.E. 2004: Identification of the spectral characteristics of semi-natural upland vegetation using direct ordination: a case study from Dartmoor UK. International Journal of Remote Sensing 25, 3369-88.
5. Armitage, R.P., Weaver, R.E. and Kent, M. 2000: Remote sensing of semi-natural upland vegetation: the relationship between species composition and spectral response. In Alexander, R. and Millington, A., editors, Vegetation mapping: patch to planet, Chichester: Wiley, 83-102.
6. Armstrong, M. 1998: Basic linear geostatistics. Berlin: Springer.
7. Atkinson, P.M. 2001: Geographical information science: geocomputation and nonstationarity. Progress in Physical Geography 25, 111-22.
8. Atkinson, P.M. and Lewis, P. 2000: Geostatistical classification for remote sensing: an introduction. Computers and Geosciences 26, 361-71.
9. Austin, M.P. 1999a: A silent clash of paradigms: some inconsistencies in community ecology. Oikos 86, 170-78.
10. Austin, M.P. 1999b: The potential contribution of vegetation ecology to biodiversity research. Ecography 22, 465-84.
11. Austin M.P. 2002: Spatial prediction of species distribution: an interface between ecological theory and statistical modelling. Ecological Modelling 157,101-18.
12. Bailey, T.C. 1994: A review of statistical spatial analysis in geographical information systems. In Fotheringham, S. and Rogerson, P., editors, Spatial analysis and GIS, London: Taylor and Francis, 13-44.
13. Bailey, T.C. and Gatrell, A.C. 1995: Interactive spatial data analysis. Harlow: Longman.
14. Barbujani, G., Jacquez, G.M. and Ligi, L. 1990: Diversity of some gene frequencies in European and Asian populations. V. Steep multilocus clines. American Journal of Human Genetics 47, 867-75.
15. Barbujani G., Oden, N.L. and Sokal, R.R. 1989: Detecting regions of abrupt change in maps of biological variables. Systematic Zoology 38, 376-89.
16. Bellehumeur C. and Legendre, P. 1998: Multiscale sources of variation in ecological variables: modelling spatial dispersion, elaborating sampling designs. Landscape Ecology 13, 15-25.
17. Borcard, D. and Legendre, P. 1994: Environmental control and spatial structure in ecological communities: an example using orbatid mites (Acari, Oribatei). Environmental and Ecological Statistics 1, 37-53.
18. Borcard, D. and Legendre, P. 2002: All-scale spatial analysis of ecological data by means of principal coordinates of neighbour matrices. Ecological Modelling 153, 51-68.
19. Borcard, D., Legendre, P., Avois-Jacquet, C. and Tuomisto, H. 2004: Dissecting the spatial structure of ecological data at multiple scales. Ecology 85, 1826-32.
20. Borcard, D., Legendre, P. and Drapeau, P. 1992: Partialling out the spatial component of ecological variation. Ecology 73, 1045-55.
21. Bormann, F.H. and Likens, G.E. 1979a: Catastrophic disturbance and the steady state in northern hardwood forests. American Scientist 67, 660-69.
22. Bormann, F.H. and Likens, G.E. 1979b: Pattern and process in a forested ecosystem: disturbance, development and the steady state based on the Hubbard Brook Ecosystem Study. New York: Springer.
23. Brown, D.G. 1998a: Classification and boundary vagueness in mapping presettlement forest types. International Journal of Geographical Information Science 12, 105-29.
24. Brown, D.G. 1998b: Mapping historical forest types in Baraga County, Michigan, USA, as fuzzy sets. Plant Ecology 134, 97-111.
25. Burel, F. and Baudry, J. 2003: Landscape ecology: concepts, methods and applications. Enfield, NH: Science Publishers Inc.
26. Burrough, P.A. 1995: Spatial aspects of ecological data. In Jongman, R.H.G., ter Braak, C.F.J. and van Tongeren, O.F.R., editors, Data analysis in community and landscape ecology (second edition), Cambridge: Cambridge University Press, 213-51.
27. Burrough, P.A. 2001: GIS and geostatistics: essential partners for spatial analysis. Environmental and Ecological Statistics 8, 361-77.
28. Burrough, P.A. and Frank, A.U., editors 1996: Geographical objects with indeterminate boundaries. London: Taylor and Francis.
29. Burrough, P.A. and McDonnell, R.A. 1998: Principles of geographical information systems Oxford: Oxford University Press.
30. Cadenasso, M.L., Pickett, S.T.A., Weathers, K.C., Bell, S.S., Benning, TL., Carreiro, M.M. and Dawson, T.E. 2003a: An interdisciplinary and synthetic approach to ecological boundaries. BioScience 53, 717-22.
31. Cadenasso, M.L., Pickett, S.T.A., Weathers, K.C. and Jones, C.G. 2003b: A framework for a theory of ecological boundaries. BioScience 53, 750-58.
32. Callaway, R.M. 1997: Positive interactions in plant communities and the individualistic-continuum concept. Oecologia 112, 255-79.
33. Camarero, J.J., Gutierrez, E. and Fortin, M.-J. 2000: Boundary detection in altitudinal treeline ecotones in the Spanish Central Pyrenees. Arctic, Antarctic and Alpine Research 32, 117-26.
34. Chilès, J-P. and Delfiner, P. 1999: Geostatistics. NewYork: Wiley.
35. Choesin, D. and Boerner, R.E.J. 2002: Vegetation boundary detection: a comparison of two approaches applied to field data. Plant Ecology 158, 85-96.
36. Clarke, K.R. 1993: Non-parametric multivariate analyses of changes in community structure. Australian Journal of Ecology 18, 117-43.
37. Clements, F.E. 1905: Research methods in ecology. University of Nebraska Publishing Company.
38. Clements, F.E. 1916: Plant succession. An analysis of the development of vegetation. Washington, DC: Carnegie Institute, Publication 242.
39. Cliff, A.D. and Ord, J.K. 1981: Spatial processes: models and applications. London: Pion.
40. Clifford, P., Richardson, S. and Hémon, D. 1989: Assessing the significance of the correlation between two spatial processes. Biometrics 45, 123-34.
41. Collins S.L., Micheli, F. and Hartt, L. 2000: A method to determine rates and patterns of variability in ecological communities. Oikos 91, 285-93.
42. Cornelius, J.M. and Reynolds, J.F. 1991: On determining the statistical significance of discontinuities within ordered ecological data. Ecology 72, 2057-70.
43. Cox, C.B. and Moore, P.D. 2000: Biogeography: an ecological and evolutionary approach. (sixth edition). Oxford: Blackwell Science.
44. Cressie, N.A.C. 1993: Statistics for spatial data (revised edition). New York: Wiley.
45. Csillag, F., Fortin, M.-J. and Dungan, J.L. 2000: On the limits and extensions of the definition of scale. Ecological Society of America Bulletin 81, 230-32.
46. Curran, P. 2001: Remote sensing: using the spatial domain. Environmental and Ecological Statistics 8, 331-44.
47. Curran, P. and Atkinson, P.M. 1998: Geostatistics and remote sensing. Progress in Physical Geography 22, 61-78.
48. Cushman, S.A. and Walin, D.O. 2002: Separating the effects of environmental, spatial and disturbance factors on forest community structure in the Russian Far East. Forest Ecology and Management 168, 201-15.
49. Dale, M.R.T. 1988: The spacing and intermingling of species boundaries on an environmental gradient. Oikos 53, 351-56.
50. Dale, M.R.T. 1999: Spatial pattern analysis in plant ecology. Cambridge: Cambridge University Press.
51. Dale, M.R.T. and Fortin, M.-J. 2002: Spatial autocorrelation and statistical tests in ecology. Ecoscience 9, 162-167.
52. Dale, M.R.T., Dixon, P., Fortin, M.-J., Legendre, P., Myers, D.E. and Rosenberg, M.S. 2002: Conceptual and mathematical relationships among methods for spatial analysis. Ecogrophy 25, 558-77.
53. de Mers, M.N. 2000: Fundamentals of geographic information systems (second edition). New York: Wiley.
54. Deutsch, C.V. and Journel, A.G. 1992: GSLIB: geostatistical software library and user's guide. New York: Oxford University Press.
55. Dietz, E.J. 1983: Permutation tests for association between two distance matrices. Systematic Zoology 32, 21-26.
56. Diggle, P.J. 1983: Statistical analysis of spatial point patterns. London: Academic Press.
57. Diggle, P.J., Tawn, J.A. and Moyeed, R.A. 1998: Model-based geostatistics. Applied Statistics 47, 299-350.
58. Diniz-Filho, J.A.F., Bini, L.M. and Hawkins, B. 2003: Spatial autocorrelation and red herrings in geographical ecology. Global Ecology and Biogeography 12, 53-64.
59. Duffey, E. 2004: Definition of ecological community. Bulletin of the British Ecological Society 35, 21.
60. Dungan, J.L. 1998: Spatial prediction of vegetation quantities using ground and image data. International Journal of Remote Sensing 19, 267-85.
61. Dungan, J.L., Perry, J.N., Dale, M.R.T., Legendre, P., Citron-Pousty, S., Fortin, M.-J., Jakomulshka, A., Miriti, M. and Rosenberg, M.S. 2002: A balanced view of scale in spatial analysis. Ecography 25, 626-40.
62. Dutilleul, P. 1993: Modifying the t test for assessing the correlation between two spatial processes. Biometrics 49, 305-14.
63. Everitt, B.S., Landau, S. and Leese, M. 2001: Cluster analysis (fourth edition). London: Arnold.
64. Fagan, W.F., Fortin, M.-J. and Soykan, C. 2003: Integrating edge detection and dynamic modelling in quantitative analyses of ecological boundaries. BioScience 53, 730-38.
65. Faith, D.P., Minchin, P.R. and Belbin, L. 1987: Compositional dissimilarity as a robust measure of ecological distance. Vegetatio 69, 57-68.
66. Farina, A. 2006: Principles and methods in landscape ecology (second edition). Dordrecht: Kluwer.
67. Forman, R.T.T. 1995: Landscape mosaics. Cambridge: Cambridge University Press.
68. Forman, R.T.T. and Godron, M. 1986: Landscape ecology. Chichester: John Wiley.
69. Fortin, M.-J. 1994: Edge detection algorithms for two-dimensional ecological data. Ecology 75, 956-65.
70. Fortin, M.-J. 1997: Effects of data types on vegetation boundary delineation. Canadian Journal of Forestry Research 27, 1851-58.
71. Fortin, M.-J. 1999a: Spatial statistics in landscape ecology. In Klopatek, J.M. and Gardner, R.H., editors, Landscape ecological analysis: issues and applications, New York: Springer, 253-79.
72. Fortin, M.-J. 1999b: Effects of sampling unit resolution on the estimation of spatial autocorrelation. Ecoscience 6, 636-41.
73. Fortin, M.-J. 1999c: Effect of quadrat size and data measurement on the detection of boundaries. Journal of Vegetation Science 10, 43-50.
74. Fortin, M.-J. 2002: Spatial analysis in ecology: statistical and landscape scale issues. Ecoscience 9, iii-v.
75. Fortin, M.-J. and Dale, M. 2005: Spatial analysis: a guide for ecologists. Cambridge: Cambridge University Press.
76. Fortin, M.-J. and Drapeau, P. 1995: Delineation of ecological boundaries: comparison of approaches and significance tests. Oikos 72, 323-32.
77. Fortin, M.-J. and Edwards, G. 2001: Delineation and analysis of vegetation boundaries. In Hunsaker, C., Goodchild, M., Friedl, M. and Case, T., editors, Spatial uncertainty in ecology: implications for remote sensing and GIS applications, Berlin: Springer, 158-74.
78. Fortin, M.-J. and Gurevitch, J. 2001: Mantel tests: spatial structure in field experiments. In Scheiner, S.M. and Gurevitch, J., editors, Design and analysis of ecological experiments (second edition), Oxford: Oxford University Press, 308-26.
79. Fortin, M.-J. and Jacquez, G.M. 2000: Randomisation tests and spatially autocorrelated data. Bulletin of the Ecological Society of America 81, 201-206.
80. Fortin, M.-J., Drapeau, P. and Jacquez, G.M. 1996: Quantification of the spatial co-occurrences of ecological boundaries. Oikos 77, 51-60.
81. Fortin, M.-J., Drapeau, P. and Legendre, P. 1989: Spatial autocorrelation and sampling design in plant ecology. Vegetatio 83, 209-22.
82. Fortin, M.-J., Olson, R.J., Ferson, S., Iverson, L., Hunsaker, C., Edwards, G., Levine, D., Butera, K. and Klemas, V. 2000: Issues related to the detection of boundaries. Landscape Ecology 15, 453-66.
83. Gaston, K.J. 2003: The structure and dynamics of geographic ranges. Oxford: Oxford University Press.
84. Geary, R.C. 1954: The contiguity ratio and statistical mapping. Incorporating Statistics 5, 115-45.
85. Gosz, J.R. 1991: Fundamental ecological characteristics of landscape boundaries. In Holland, M.M., Risser, P.G. and Naiman, R.J., editors, Ecotones: the role of landscape boundaries in the management and restoration of changing environments, London: Chapman and Hall, 8-51.
86. Graham, M.H. 2003: Confronting multicollinearity in ecological multiple regression. Ecology 84, 2809-15.
87. Griffith, D.A. 1987: Spatial autocorrelation: a primer. Resource Publications in Geography. Washington, DC: Association of American Geographers.
88. Griffith, D.A. 1992: What is spatial autocorrelation? Reflections on the past 25 years of spatial statistics. L'Espace Géographique 3, 265-80.
89. Gustafson, E.J. 1998: Quantifying landscape spatial pattern: what is the state of the art? Ecosystems 1, 143-56.
90. Haining, R. 1991: Bivariate correlation with spatial data. Geographical Analysis 23, 210-27.
91. Haining, R. 2003: Spatial data analysis: theory and practice. Cambridge: Cambridge University Press.
92. Handcock, M.S. and Wallis, J.R. 1994: An approach to statistical spatial-temporal modeling of meteorological fields. Journal of the American Statistical Association 89, 369-78.
93. Hansen, A.J. and di Castri, F., editors 1992: Landscape boundaries: consequences for biotic diversity and ecological flows. New York: Springer.
94. Hill, M.O. 1973: Reciprocal averaging: an eigenvector method of ordination. Journal of Ecology 61, 237-50.
95. Hill, M.O. 1974: Correspondence analysis. A neglected multivariate method. Journal of the Royal Statistical Society - Series C 23, 340-54.
96. Hoagland, B.W. and Collins, S.L. 1997: Gradient models, gradient analysis and structure in plant communities. Oikos 78, 23-30.
97. Holland, M.M., Risser, P.G. and Naiman, R.J., editors 1991: Ecotones: the role of landscape boundaries in the management and restoration of changing environments. London: Chapman and Hall.
98. Hunsaker, C., Goodchild, M., Friedl, M. and Case, T., editors 2001: Spatial uncertainty in ecology: implications for remote sensing and GIS applications Berlin: Springer.
99. Isaaks, E.H. and Srivastava, R.M. 1989: Applied geostatistics. New York: Oxford University Press.
100. Jacquez, G.M. 1995: The map comparison problem: tests for overlap of geographic boundaries. Statistics in Medicine 12, 1931-42.
101. Jacquez, G.M. and Maruca, S. 1998: Geographic boundary detection. In Poiker, T.K. and Chrisman, N., editors, Proceedings of the 8th International Symposium on Spatial Data Handling, International Geographical Union.
102. Jacquez, G.M. and Maruca, S. 2001: BoundarySeer_TM 1.0 - software for geographic boundary analysis - user guide. TerraSeer_TM Inc., USA.
103. Jacquez, G.M., Maruca, S. and Fortin, M.-J. 2000: From fields to objects: a review of geographic boundary analysis. Journal of Geographical Systems 2, 221-41.
104. Jetz, W., Rahbek, C. and Lichstein, J.W. 2005: Local and global approaches to spatial data analysis in ecology. Global Ecology and Biogeography 14, 97-98.
105. Johnston, C.A. 1998: Geographic information systems in ecology. Oxford: Blackwell.
106. Johnston, C.A. and Bonde, J. 1989: Quantitative analysis of ecotones using a geographic information system. Photogrammetry and Remote Sensing 55, 1643-47.
107. Johnston, C.A., Pastor, J. and Pinay, G. 1992: Quantitative methods for studying landscape boundaries. In Hansen, H.J. and di Castri, F., editors, Landscape boundaries: consequences for biotic diversity and ecological flows, SCOPE series, New York: Springer 107-28.
108. Jongman, R.H.G., ter Braak, C.J.G. and van Tongeren, O.F.R. 1995: Data analysis in community and landscape ecology, (second edition). Cambridge: Cambridge University Press.
109. Jonsson, B.G. and Moen, J. 1998: Patterns in species associations in plant communities: the importance of scale. Journal of Vegetation Science 9, 327-32.
110. Journel, A.G. and Huijbregts, C. 1978: Mining geostatistics. London: Academic Press.
111. Keitt, T.H., Bjornstad, O.N., Dixon, P.M. and Citron-Pousty, S. 2002: Accounting for spatial pattern when modeling organism-environment interactions. Ecography 25, 616-25.
112. Kent, M. 2003: Making room for space in physical geography. In Holloway, S., Rice S. and Valentine G., editors, Key concepts in geography, London: Sage Publications, 109-30.
113. Kent, M. 2006: Numerical classification and ordination methods in biogeography. Progress in Physical Geography 30, in press.
114. Kent, M. and Coker, P. 1992: Vegetation description and analysis a practical approach. Chichester: Wiley.
115. Kent, M., Gill, W.J., Weaver, R.E. and Armitage, R.P. 1997: Landscape and plant community boundaries in biogeography. Progress in Physical Geography 21, 315-53.
116. Koenig, W.D. 1999: Spatial autocorrelation of ecological phenomena. Trends in Ecology and Evolution 14, 22-26.
117. Koenig, W.D. and Knops, J.M.H. 1998: Testing for spatial autocorrelation in ecological studies. Ecography 21, 423-29.
118. Krige, D.G. 1976: Two-dimensional weighted moving average trend surfaces for ore-evaluation. Journal of the South African Institute of Mining and Metallurgy 66, 13-38.
119. Krige, D.G. and Magri, E.J. 1982: Geostatistical case studies of the advantages of lognormal-dewijsian kriging with mean for a base metal mine and a gold mine. Journal of Mathematical Geology 14, 547-55.
120. Leduc, A., Drapeau, P., Bergeron, Y. and Legendre, P. 1992: Study of spatial components of forest cover using partial Mantel tests and path analysis. Journal of Vegetation Science 3, 69-78.
121. Legendre, P. 1987: Constrained clustering. In Legendre, P. and Legendre, L., editors, Developments in numerical ecology, NATO ASI Series, Berlin: Springer, 289-307.
122. Legendre, P. 1993: Spatial autocorrelation: trouble or new paradigm? Ecology 74, 1659-73.
123. Legendre, P. and Fortin, M.-J. 1989: Spatial pattern and ecological analysis. Vegetatio 80, 107-38.
124. Legendre, P. and Legendre, L. 1998: Numerical ecology. Amsterdam: Elsevier.
125. Legendre, P., Dale, M.R.T., Fortin, M.-J., Gurevitch, J., Hohn, M. and Myers, D. 2002: The consequences of spatial structure for the design and analysis of ecological field surveys. Ecography 25, 601-15.
126. Legendre, P., Sokal, R.R., Oden, N.L., Vaudor, A. and Kim, J. 1990: Analysis of variance with spatial autocorrelation in both the variable and the classification criterion. Journal of Classification 7, 53-75.
127. Lennon, J.J. 2000: Red-shifts and red herrings in geographical ecology. Ecography 23, 101-13.
128. Lepš J. and Šmilauer, P. 2003: Multivariate analysis of ecological data using CANOCO. Cambridge: Cambridge University Press.
129. Leung, Y. 1987: On the imprecision of boundaries. Geographical Analysis 19, 125-51.
130. Levin, S.A. 1992: The problem of pattern and scale in ecology. Ecology 73, 1943-67.
131. Liebhold, A.M. and Gurevitch, J. 2002: Integrating the statistical analysis of spatial data in ecology. Ecography 25, 553-57.
132. Lortie, C.J., Brokker, R.W. Choler, P., Kikvidze, Z., Michalet, R., Pugnaire, F.I. and Callaway, R.M. 2004: Rethinking plant community theory. Oikos 107, 433-38.
133. Longley, P.A., Goodchild, M.F., Maguire, D.J. and Rhind, D.W. 2001: Geographic information systems and science. Chichester: Wiley.
134. Ludwig, J.A. and Cornelius, J.M. 1987: Locating discontinuities along ecological gradients. Ecology 68, 448-50.
135. Mantel, N. 1967: The detection of disease clustering and a generalised regression approach. Cancer Research 27, 209-20.
136. Matérn, B. 1986: Spatial variation. (second edition). Lecture Notes in Statistics, vol. 36. Berlin: Springer.
137. McArdle, B.H. and Anderson, M.J. 2001: Fitting multivariate models to community data: a comment on distance-based redundancy analysis. Ecology 82, 290-97.
138. McBratney, A.B. and deGruijter, J.J. 1992: A continuum approach to soil classification by modified fuzzy k-means with extragrades. Journal of Soil Science 43, 159-75.
139. McCune, B. 2004: Nonparametric multiplicative regression for habitat modelling. Retrieved 23 January 2006 from http://www.pcord.com/ NPMRintro.pdf
140. McCune, B. and Grace, J.B. 2002: Analysis of ecological communities. Gleneden Beach, OR: MjM Software.
141. McCune, B. and Mefford, M.J. 1999: PC-ORD, Multivariate analysis of ecological data, Version 4. Glenden Beach, OR: MjM Software.
142. McCune, B. and Mefford, M.J. 2004: HyperNiche: nonparametric multiplicative habitat modelling, version 1. Gleneden Beach, OR: MjM Software.
143. Meisel, J.E. and Turner, M.G. 1998: Scale detection in real and artificial landscapes using semivariance analysis. Landscape Ecology 13, 347-62.
144. Méot, A., Legendre, P. and Borcard, D. 1998: Partialling out the spatial component of ecological variations: questions and propositions in the linear modelling framework. Environmental and Ecological Statistics 5, 1-27.
145. Mistral, M.O., Buck, D., Meier-Behrmann, D.A., Burnett, T.E., Barnfield, A.J., Scott, A.J., Anderson, B.J. and Wilson, J.B. 2000: Direct measurement of spatial autocorrelation at the community level in four plant communities. Journal of Vegetation Science 11, 911-16.
146. Moran, P.A.P. 1950: Notes on continuous stochastic phenomena. Biometrika 37, 17-37.
147. Moyeed, R.A. and Papritz, A. 2002: An empirical comparison of kriging methods for non-linear spatial point prediction. Mathematical Geology 34, 365-86.
148. Nekola, J.C. and White, P.S. 1999: The distance decay of similarity in biogeography and ecology. Journal of Biogeography 26, 867-78.
149. Nielsen, D.R. and Wendroth, O. 2003: Spatial and temporal statistics - sampling field soils and their vegetation. GeoEcology textbook. Reiskirchen: Catena.
150. Oden, N.L. 1984: Assessing the significance of a spatial correlogram. Geographical Analysis 16, 1-16.
151. Oden, N.L. and Sokal, R.R. 1986: Directional autocorrelation: an extension of spatial correlograms in two dimensions. Systematic Zoology 35, 608-17.
152. Oden, N.L., Sokal, R.R., Fortin, M.-J. and Goebl, H. 1993: Categorical wombling: detecting regions of significant change in spatially located categorical variables. Geographical Analysis 25, 315-36.
153. Økland, R.H. 2003: Partitioning the variation in a plot-by-species data matrix that is related to n sets of exploratory variables. Journal of Vegetation Science 14, 693-700.
154. Økland, R.H. and Eilertsen, O. 1994: Canonical correspondence analysis with variance partitioning: some comments and an application. Journal of Vegetation Science 5, 117-26.
155. Openshaw, S. 1984: The modifable areal unit problem. Concepts and techniques in modern geography 38. Norwich: GeoBooks.
156. Palmer, M.W. 1988: Fractal geometry: a tool for describing spatial patterns of plant communities. Vegetatio 75, 91-102.
157. Palmer, M.W. 1993: Putting things in even better order: the advantages of canonical correspondence analysis. Ecology 74, 2215-30.
158. Pebesma, E.J. 2004: Multivariable geostatistics in S: the gstat package. Computers and Geosciences 30, 683-91.
159. Perry, G.L.W. 2002: Landscapes, space and equilibrium: shifting viewpoints. Progress in Physical Geography 26, 339-59.
160. Perry, J.N., Liebhold, A.M., Rosenberg, M.S., Dungan, J., Miriti, M, Jakomulska, A. and Citron-Pousty, S. 2002: Illustrations and guidelines for selecting statistical methods for quantifying spatial pattern in ecological data. Ecography 25, 578-600.
161. Pinel-Alloul, B., Niyonsenga, T. and Legendre, P. 1995: Spatial and environmental components of freshwater zooplankton structure. Ecoscience 2, 1-19.
162. Pisces Conservation Ltd 2004: Fuzzy grouping for clustering objects while accounting for uncertainty. Software program available from www. pisces-conservation.com. (last accessed 23 January-2006).
163. Qi, Y and Wu, J. 1996: Effects of changing spatial resolution on the results of landscape pattern analysis using spatial autocorrelation indices. Landscape Ecology 11, 39-49.
164. Qinghong, L. and Bråkenhielm, S. 1995: A statistical approach to decompose ecological variation. Water, Air and Soil Pollution 85, 1587-92.
165. Robertson, G.P. 1987: Geostatistics in ecology: interpolating with known variance. Ecology 68, 744-48.
166. Rossi, R.E., Mulla, D.J., Journel, A.G. and Franz, E.H. 1992: Geostatistical tools for modelling and interpreting ecological spatial dependence. Ecological Monographs 62, 277-314.
167. Smouse, P.E., Long, J.C. and Sokal, R.R. 1986: Multiple regression and correlation extensions of the Mantel test of matrix correspondence. Systematic Zoology 35, 627-32.
168. Sokal, R.R. and Oden, N.L. 1978a: Spatial autocorrelation in biology. 1. Methodology. Biological Journal of the Linnean Society 10, 199-228.
169. Sokal, R.R. and Oden, N.L. 1978b: Spatial autocorrelation in biology. 2. Some biological implications and four applications of ecological and evolutionary interest. Biological Journal of the Linnean Society 10, 229-49.
170. Sokal, R.R., Oden, N.L. and Thomson, B.A. 1998a: Local spatial autocorrelation in biological variables. Biological Journal of the Linnean Society 65, 41-62.
171. Sokal, R.R., Oden, N.L. and Thomson, B.A. 1998b: Local spatial autocorrelation in a biological model. Geografiska Annaler 65, 41-62.
172. Sokal, R.R., Oden, N.L., Thompson, B.A. and Kim, J. 1993: Testing for regional differences in means: distinguishing inherent from spurious spatial autocorrelation using and isolation-by-distance model. Geographical Analysis 25, 199-210.
173. Stine, P.A. and Hunsaker, C.T. 2001: An introduction to uncertainty issues for spatial data used in ecological applications. In Hunsaker, C., Goodchild, M., Friedl, M. and Case, T., editors, Spatial uncertainty in ecology: implications for remote sensing and GIS applications, Berlin: Springer, 91-107.
174. Strayer, D.L., Power, M.E., Fagan, W.F., Pickett, S.T.A. and Belnap, J. 2003: A classification of ecological boundaries. BioScience 53, 723-29.
175. Student (Gosset, W.S.) 1914: The elimination of spurious correlation due to position in time or space. Biometrika 10, 179-81.
176. ter Braak, C.J.F. 1986: Canonical correspondence analysis: a new eigenvector technique for multivariate direct gradient analysis. Ecology 67, 1167-79.
177. ter Braak, C.J.F. 1987: The analysis of vegetation-environment relationships by canonical correspondence analysis. Vegetatio 69, 69-77.
178. ter Braak, C.J.F. 1988a: CANOCO - an extension of DECORANA to analyse species-environmental relationships. Vegetatio 75, 150-60.
179. ter Braak, C.J.F. 1988b: Partial canonical correspondence analysis. In Block, H.H., editor, Classification and related methods of data analysis, Amsterdam: North Holland Press, 551-58.
180. ter Braak, C.J.F. and Šmilauer, P. 2003: CANOCO reference manual and user's guide to Conoco for Windows: software for canonical community ordination (version 4.5). Ithaca, NY: Microcomputer Power.
181. ter Braak, C.J.F and Verdonschot, P.F.M. 1995: Canonical correspondence analysis and related multivariate methods in aquatic ecology. Aquatic Ecology 57, 255-89.
182. Thompson, J.D., Weiblen, G., Thompson, B.A., Alfaro, S. and Legendre, P. 1996: Untangling multiple factors in spatial distributions: lilies, gophers and rocks. Ecology 77, 1698-715.
183. Tobler, W. 1970: A computer movie simulating urban growth in the Detroit regions. Economic Geography 46, 234-40.
184. Turner, M.G., Gardner, R.H. and O'Neill, R.V. 2001: Landscape ecology in theory and practice. New York: Springer.
185. Turner, S.J., O'Neill, R.V., Conley, W, Conley, M.R. and Humphries, H.C. 1991: Pattern and scale: statistics for landscape ecology. In Turner, M.G. and Gardner, R.H., editors, Quantitative methods in landscape ecology: the analysis and interpretation of landscape heterogeneity, New York: Springer, 17-49.
186. Upton, G.J.G. and Fingleton, B. 1985: Spatial data analysis by example, volume 1: point pattern and quantitative data. Chichester: Wiley.
187. Upton, G.J.G. and Fingleton, B. 1989: Spatial data analysis by example, Volume 2: categorical and directional data. Chichester: Wiley.
188. Usery, E.L. 1993: Category theory and structure of features in geographic information systems. Cartography and Geographic Information Systems 20, 5-12.
189. Usery, E.L. 1996: A conceptual framework and fuzzy set implementation for geographical features. In Burrough, P.A. and Frank, A.U., editors, 1996: Geographical objects with indeterminate boundaries, London: Taylor and Francis, 71-86.
190. Van der Maarel, E. 1976: On the establishment of plant community boundaries. Berichte Deutche Botanische Gesellschaft 89, 415-43.
191. Ver Hoef, J.M. 1993: Universal kriging for ecological data. In: Goodchild, M.F., Parks, B.O. and Steyaert, L.T., editors, Environmental modelling with GIS, New York: Oxford University Press, 447-553.
192. Ver Hoef, J.M. and Cressie, N. 2001: Spatial statistics: analysis of field experiments. In Scheiner, S.M. and Gurevitch, J., editors, Design and analysis of ecological experiments (second edition), Oxford: Oxford University Press, 289-307.
193. Ver Hoef, J.M., Cressie, N., Fisher, R.N. and Case, T.J. 2001: Uncertainty and spatial linear models for ecological data. In Hunsaker, C.T., Goodchild, M.F., Friedl, M.A. and case T.J., editors, Spatial uncertainty for ecology: implications for remote sensing and GIS applications, New York: Springer, 214-37.
194. Ver Hoef, J.M., Cressie, N.A.C. and Glenn-Lewin, D.C. 1993: Spatial models for spatial statistics: some unification. Journal of Vegetation Science 4, 441-52.
195. Wadsworth, R. and Treweek, J. 1999: Geographical information systems for ecology. Harlow: Longman.
196. Wagner, H.H. 2003: Spatial covariance in plant communities: integrating ordination, geostatistics and variance testing. Ecology 84, 1045-57.
197. Wallace, C.S.A., Watts, J.M. and Yool, S.R. 2000: Characterising the spatial structure of vegetation communities in the Mojave Desert using geostatistical techniques. Computers and Geosciences 26, 397-410.
198. Wang, F. and Hall, G.B. 1996: Fuzzy representation of geographical boundaries in GIST International Journal of Geographical Information Systems 8, 143-62.
199. Webster, R. 1973: Automatic soil-boundary location from transect data. Mathematical Geology 5, 27-37.
200. Webster, R. and Oliver, M.A. 2001: Geostatistics for environmental scientists. Chichester: Wiley.
201. Whittaker, R.H. 1953: A consideration of climax theory: the climax as a population and pattern. Ecological Monographs 23, 41-78.
202. Whittaker, R.H. 1960: Vegetation of the Siskiyou Mountains, Oregon and California. Ecological Monographs 30, 279-338.
203. Whittaker, R.J., Willis, K.J. and Field, R. 2001: Scale and species richness: towards a general hierarchical theory of species diversity. Journal of Biogeography 28, 453-70.
204. Willis, K.J. and Whittaker, R.J. 2002: Species diversity - scale matters. Science 295, 1245-48.
205. Womble, W.H. 1951: Differential systematics. Science 114, 315-22.