Effective Mesh Size (Aggregation metric)

## Arguments

- landscape
A categorical raster object: SpatRaster; Raster* Layer, Stack, Brick; stars or a list of SpatRasters.

- directions
The number of directions in which patches should be connected: 4 (rook's case) or 8 (queen's case).

## Details

$$MESH = \frac{\sum \limits_{j = 1}^{n} a_{ij} ^ 2} {A} * \frac{1} {10000}$$ where \(a_{ij}\) is the patch area in square meters and \(A\) is the total landscape area in square meters.

The effective mesh size is an 'Aggregation metric'. Because each patch is squared
before the sums for each group i are calculated and the sum is standardized by the
total landscape area, MESH is a relative measure of patch structure. MESH is
perfectly, negatively correlated to `lsm_c_division`

.

## References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

Jaeger, J. A. 2000. Landscape division, splitting index, and effective mesh size: new measures of landscape fragmentation. Landscape ecology, 15(2), 115-130.