Tests for Patterns in Geographic Variation

Authors

  • H. H. Royaltey,

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      H. H. Royaltey and E. Astrachan are graduate students, and R. R. Sokal professor in the Department of Ecology and Evolution, State University of New York at Stony Brook

  • E. Astrachan,

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      H. H. Royaltey and E. Astrachan are graduate students, and R. R. Sokal professor in the Department of Ecology and Evolution, State University of New York at Stony Brook

  • R. R. Sokal

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      H. H. Royaltey and E. Astrachan are graduate students, and R. R. Sokal professor in the Department of Ecology and Evolution, State University of New York at Stony Brook

    • *

      Contribution No. 79 from the Program in Ecology and Evolution at the State University of New York at Stony Brook. This study was supported by Grant B035233 from the National Science Foundation. Various members of the Numerical Taxonomy Luncheon Group made useful suggestions. Professor Waldo Tobler of the University of Michigan kindly read and commented upon an earlier draft of this paper. The illustrations were prepared by Joyce Roe, and the manuscript was typed by Barbara Scanlon.


Abstract

We develop tests of whether a pattern of geographic variation departs significantly from random variation over an area. Localities are vertices in a graph whose edges are connections based on criteria of geographic contiguity. Ranked variables are assigned to each locality. Distributions of absolute differences in rank along edges between vertices yield various statistics of edge length that are compared with expectations developed in the paper. Several typical patterns such as a cline, depression, or a crazy-quilt are generated and their behavior characterized by this method. Computational and graphical methods allocate observed patterns to one of several types. The methods are general; three illustrative examples from biology and one from regional studies are furnished.

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