It is often necessary in population biology to compare two sets of distance measures. These measures can be based on genetic markers, morphological traits, geographic separation, ecological divergence, and so on. The distance measures can take various forms and frequently have unknown distributional properties. Many different procedures have been developed to compare the correspondence of one set of distances with another set. Prominent among them are the: (1) matrix correlation techniques of Sokal and Rohlf (1962), and Sneath and Sokal (1973); (2) networkmatching techniques of Spielman (1973); (3) matrix dilation and rotation techniques of Gower (1971) and of Schonemann and Carrol (1970); and (4) smallest-space techniques of Lingoes (1965) and Guttman (1968). Each of these strategies has strong points, but all suffer from a difficulty in assessing the statistical significance of attained correspondence. The problem is that a set of all possible pairwise distances between k units (populations, taxa, habitats, etc.) cannot be independent. More recently, a test of matrix correspondence-originally developed by Mantel (1967) and widely applied in geography (Hubert and Golledge, 1982) and psychometrics (Hubert, 1979a, b)-has caught the attention of population biolo

Spatial autocorrelation analysis tests whether the observed value of a nominal, ordinal, or interval variable at one locality is independent of values of the variable at neighbouring localities. The computation of autocorrelation coefficients for nominal, ordinal, and for interval data is illustrated, together with appropriate significance tests. The method is extended to include the computation of correlograms for spatial autocorrelation. These show the autocorrelation coefficient as a function of distance between pairs of localities being considered, and summarize the patterns of geographic variation exhibited by the response surface of any given variable. Autocorrelation analysis is applied to microgeographic variation of allozyme frequencies in the snail Helix aspersa. Differences in variational patterns in two city blocks are interpreted. The inferences that can be drawn from correlograms are discussed and illustrated with the aid of some artificially generated patterns. Computational formulae, expected values and standard errors are furnished in two appendices.

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Spatial autocorrelation analysis tests whether the observed value of a variable at one locality is significantly dependent on values of the variable at neighbouring localities. The method was extended by us in an earlier paper to include the computation of correlograms for spatial autocorrelation. These show the autocorrelation coefficient as a function of distance between pairs of localities, and summarize the patterns of geographic variation exhibited by the response surface of any given variable. Identical variation patterns lead to identical correlograms, but different patterns may or may not yield different correlograms. Similarity in the correlograms of different variation patterns suggests similarity in the generating mechanism of the pattern.The inferences that can be drawn from correlograms are discussed and illustrated. Examination and analysis of variation patterns of several characters or gene frequencies for one population, or of several populations in different places or at different times, permit some conclusions about the nature of the populational processes generating the observed patterns.Autocorrelation analysis is applied to four biological situations differing in the nature of the data (interval or nominal), in the type of grid connecting the localities (regular or irregular), and the field of application (evolution or ecology). The examples comprise genotypes of individual mice, blood group frequencies in humans, gene frequency variation in a perennial herb, and the distribution of species of trees. The implications of our findings are discussed.

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