Spatial autocorrelation in biology 2. Some biological implications and four applications of evolutionary and ecological interest

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.