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Conceptual and mathematical relationships among methods for spatial analysis

Authors

  • Mark R. T. Dale,

  • Philip Dixon,

  • Marie-Josée Fortin,

  • Pierre Legendre,

  • Donald E. Myers,

  • Michael S. Rosenberg


M. R. T. Dale (mark.dale@ualberta.ca), Dept of Biological Sciences, Univ. of Alberta, Edmonton, AB, Canada T6G 2E9. – P. Dixon, Dept of Statistics, Iowa State Univ., Ames, IA 50011-1210, USA. – M.-J. Fortin, Dept of Zoology, Univ. of Toronto, Toronto, ON, Canada M5S 3G5. – P. Legendre, Dept de Sciences Biologiques, Univ. de Montréal, C.P. 6128 succ. Centre-Ville, Montreal, QC, Canada H3C 3J7. – D. E. Myers, Dept of Mathematics, Univ. of Arizona, P.O. Box 210089, Tucson, AZ 85721, USA. – M. S. Rosenberg, Dept of Biology, Arizona State Univ., Tempe, AZ 85287, USA.

Abstract

A large number of methods for the analysis of the spatial structure of natural phenomena (for example, the clumping or overdispersion of tree stems, the positions of veins of ore in a rock formation, the arrangement of habitat patches in a landscape, and so on) have been developed in a wide range of scientific fields. This paper reviews many of the methods and describes the relationships among them, both mathematically, using the cross-product as a unifying principle, and conceptually, based on the form of a moving window or template used in calculation. The relationships among these methods suggest that while no single method can reveal all the important characteristics of spatial data, the results of different analyses are not expected to be completely independent of each other.

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