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(j) and v(j) are mathematically related to I, and showed conditions when I-a and mean local clustering indices give very similar results. Overall differences in average v(i) and vertical bar v(j)vertical bar 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) (Y-i)-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 x location combination may be warranted. The implications of these findings on epidemiological research are discussed.