Spatial association and dissociation is illustrated by map a where there are ten red and ten green individuals, and map b where the ten green individuals are in exactly the same positions, and there are ten blue individuals. In fact, when viewed as single populations, the blues have a similar spatial pattern to the reds, their positions being merely a rotation and reflection of the reds. If counts were taken of the individuals in 25 cells using the dashed lines, then all three populations, red, green and blue, would each have identical frequency distributions: one count of 4, one of 3, one of 2, one of 1, and 21 zeroes. Furthermore, for both maps, only in the central cell do any of the non-zero counts coincide. For both the red-green counts and the blue-green counts, there are sixteen (0,0) pairs, one (2,0), one (0,2), one (3,0), one (0,3), one (4,0), one (0,4) and one (1,1) pair. The non-spatial correlation coefficient between the counts of the reds and greens, and between the blues and greens, is the relatively small value of -0.115, indicating no difference between the maps and neither strong similarity or dissimilarity. However, in a the ten red and the ten green individuals occur in similar areas and appear positively spatially associated and, by contrast, in b right-hand map, the ten green individuals occupy different areas and appear negatively spatially dissociated from the ten blue individuals. SADIE analysis gives the following values of Ia (with corresponding probability levels, Pa) for the green individuals: 1.45 (0.0079); for the reds: 1.18 (0.13); for the blues: 1.03 (0.36). Using the correlation between the clustering indices of each individual population, the SADIE index of association X (with corresponding probability level P) was, for the red and green populations in map (a): 0.578 (0.01); for the blue and green populations in map (b): -0.117 (0.66). The SADIE association index is capable of distinguishing the strong positive association in map (a) from the (albeit somewhat weaker) negative dissociation in map (b). In a similar fashion to red-blue plots, which give a visual representation of the degree and location of the clustering indices arranged into patches and gaps, SADIE association analysis allows the construction of plots that show areas of strong association and dissociation. For example the plot in map (c) is constructed from the association analysis of the clustering indices from the blue and red populations of map (b); it shows areas of significant positive association in plum and of dissociation in green.

 
 
  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. https://doi.org/10.3897/rethinkingecology.4.30890