| 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. |
