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Interrelationships Among SADIE Indices for Characterizing Spatial Patterns of Organisms

The SADIE (spatial analysis by distance indices) methodology for data analysis is a useful approach for quantifying the patterns of organisms (in terms of patches and gaps) and testing for randomness of the patterns. We investigated the interrelationship among key SADIE indices: index for distance to regularity for a data set (I_a), a global measure of aggregation or clustering; the local clustering indices (v_i and v_j), scaled distances to regularity for each individual sampling unit; and the averages of v_i and v_j across all sampling units, which are additional global measures of aggregation. We demonstrated that v_i and v_j are mathematically related to I_a and showed conditions when I_a and mean local clustering indices give very similar results. Overall differences in average v_i and Iv_j I values, and between I_a and these averages, decreased with increasing size of the sampling grid in a simulation study. This was because one component of v_i and v_j (iY)—a measure of the distance to regularity under randomness for a given location (not a given count)—was found generally to vary little with location, except for locations near corners of the sampling grid. Nevertheless, because distance to regularity for individual observed counts was location-dependent, and this location effect varied with the observed counts value as well, a new-scaled index for each count × location combination may be warranted. The implications of these findings on epidemiological research are discussed.