Directional Autocorrelation: An Extension of Spatial Correlograms to Two Dimensions

The method of spatial autocorrelation analysis has been used increasingly in recent years to characterize geographic variation in biological populations and to make inferences concerning population structure based on geographic variation patterns (Jumars et al., 1977; Sokal and Oden, 1978a, b; Sokal, 1979a; Cliff and Ord, 1981; Sokal and Wartenberg, 1981, 1983; Sokal, 1983; Oden, 1984; Wartenberg, 1985). It has been applied to populations of diverse organisms (Jones et al., 1980; Sokal et al., 1980; Sokal and Riska, 1981; Caugant et al., 1982; Sokal and Friedlaender, 1982; Sokal and Menozzi, 1982; Sokal, 1983; Binkley, 1985; Setzer, 1985; Whitley and Clark, 1985; Epperson and Clegg, 1986; Sokal, 1986; Sokal et al., 1986a, b). In this paper, we develop a two-dimensional extension of spatial autocorrelation analysis so that compass directions for geographic trends in biological (and other) variables can be established. We describe the computations, followed by three examples of the method. The directional-autocorrelation method is applied to multivariate genetic and taxonomic distances, as well as to surfaces of individual variables. Before considering directional spatial autocorrelation, we present a brief review of ordinary spatial autocorrelation, which results in one-dimensional correlograms.

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