Measures of spatial pattern for counts

SADIE (Spatial Analysis by Distance Indices) is a new methodology to detect and measure the degree of nonrandomness in the two-dimensional spatial patterns of populations. It applies the same principles to data in the form of maps as to data in the form of counts at specified locations, but with different techniques. This paper considers data in the form of counts such as occur commonly in ecology. For such data the method has an advantage over traditional approaches that measure only statistical variance heterogeneity, because all the spatial information in the sample is used. Two indices and associated tests are reviewed, one based on the total distance of the sample from a completely regular arrangement, the other from a completely crowded arrangement. A new diagnostic plot is presented to aid interpretation. Results from some artificial data are studied to survey the properties of both indices for defined patterns of clustering. Indices based on the distance to regularity are powerful at detecting aggregation when several clusters are present; those based on the distance to crowding have the power to detect aggregation only when a single cluster is present. Methods are presented to estimate the typical cluster size and intercluster distance, suitable for data from sample units in the form of a contiguous grid. Examples are given for cyst-nematode field data and plant virus disease.