aij = area (m2) of patch ij.
A = total landscape area (m2).
Description DIVISION equals 1 minus the sum of patch area (m2) divided by total landscape area (m2), quantity squared, summed across all patches in the landscape. Note, total landscape area (A) includes any internal background present.
Units Proportion
Range 0 ≦ DIVISION ≦ 1
DIVISION = 0 when the landscape consists of single patch. DIVISION is achieves its maximum value when the landscape is maximally subdivided; that is, when every cell is a separate patch.
Comments Division is based on the cumulative patch area distribution and is interpreted as the probability that two randomly chosen pixels in the landscape are not situated in the same patch. Note, the similarity with Simpson's diversity index, only here the sum is across the proportional area of each patch, rather than the proportional area of each patch type in the landscape. Note, DIVISION is redundant with Effective mesh size (MESH) below, i.e., they are perfectly, but inversely, correlated, but both metrics are included because of differences in units and interpretation. DIVISION is interpreted as a probability, whereas MESH is given as an area. In addition, as described below (see MESH), DIVISION is perfectly redundant with Area-weighted mean patch size (AREA_AM) when there is no background.