In maps a-c, the same 25 counts, with mean, m = 9.08 and variance, s2 = 75.9, are arranged in a 5×5 grid. The variance greatly exceeds the mean, so these counts come from a heterogeneous distribution more highly-skewed than the Poisson distribution. However, the frequency distribution of the counts (07, 33, 53, 6, 8, 9, 209) discards any information regarding the spatial arrangement of the counts. The arrangements clearly differ. In a the counts were deliberately arranged so that the larger counts are relatively far away from other large counts (and the smallest counts are far from other small counts), producing a distribution of the counts that is more regular than random. In b the counts were distributed completely randomly amongst the 25 cells of the grid. In c the larger counts are placed close to one another (as are the smaller counts), to yield a distribution that is highly clustered and spatially aggregated. The SADIE technique exposes these differences in spatial distribution. In a the SADIE index of aggregation Ia was less than unity (Ia = 0.80) indicating regularity, with corresponding probability level P = 0.96 indicating a significantly regular pattern. In b Ia is close to unity (Ia = 0.95, P = 0.57) indicating a randomly allocated pattern. In c Ia greatly exceeds unity (Ia = 1.88, P < 0.0002) indicating a significantly clustered pattern of patches and gaps. In d the value of the local index of clustering is shown for each of the 25 grid units of map c after SADIE analysis. Positive values, shown in red, indicate potential patches and negative values, shown in blue, indicate potential gaps; the larger the value, the greater is the evidence for clustering locally. Significant clustering into a patch in the lower left of the grid, and a gap on its opposite edge is shown where the units lie within the red (patch) or blue (gap) areas. In this example of a red-blue plot both patch (red, Vi=1.9, P<0.001) and gap (blue, Vj=-1.7, P<0.001) clusters are evident (Perry et al. 1999).

  Part of: Winder L, Alexander C, Griffiths G, Holland J, Wooley C, Perry J (2019) Twenty years and counting with SADIE: Spatial Analysis by Distance Indices software and review of its adoption and use. Rethinking Ecology 4: 1-16.