aij = area (m2) of patch ij.
A = total landscape area (m2).
Description MESH equals 1 divided by the total landscape area (m2) multiplied by the sum of patch area (m2) squared, summed across all patches in the landscape. Note, total landscape area (A) includes any internal background present.
Units Hectares
Range cell size ≦ MESH ≦ total landscape area (A)
The lower limit of MESH is constrained by the cell size and is achieved when the landscape is maximally subdivided; that is, when every cell is a separate patch. MESH is maximum when the landscape consists of a single patch.
Comments Mesh is based on the cumulative patch area distribution and is interpreted as the size of the patches when the landscape is subdivided into S patches, where S is the value of the splitting index. Note, MESH is redundant with DIVISION above, 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, note the similarity between MESH and Area-weight mean patch size (AREA_AM). Conceptually and computationally, these two metrics are almost identical at the landscape level, and under most circumstances will return identical values. Specifically, AREA_AM gives the area-weight mean patch size, where the proportional area of each patch is based on total landscape area excluding any background (i.e., background is excluded from the total landscape area). MESH also gives the area-weighted mean patch size, but the proportional area of each patch is based on the total landscape area including any background. Background is included in the so-called 'pedestal' of Jaeger (2000). Thus, if there is no internal background, these metrics will return identical values. If there is internal background, these metrics will return different values, and the magnitude of the difference will depend on the proportional extent of background. In the latter case, the choice of metrics depends on how you want to consider background.