aij = area (m2) of patch ij.
pij = perimeter (m) of patch ij.
N = total number of patches in the landscape.
Description PAFRAC equals 2 divided by the slope of regression line obtained by regressing the logarithm of patch area (m2) against the logarithm of patch perimeter (m). That is, 2 divided by the coefficient b1 derived from a least squares regression fit to the following equation: ln(area) = b0 + b1ln(perim). Note, PAFRAC excludes any background patches.
Units None
Range 1 ≦ PAFRAC ≦ 2
A fractal dimension greater than 1 for a 2-dimensional landscape mosaic indicates a departure from a Euclidean geometry (i.e., an increase in patch shape complexity). PAFRAC approaches 1 for shapes with very simple perimeters such as squares, and approaches 2 for shapes with highly convoluted, plane-filling perimeters. PAFRAC employs regression techniques and is subject to small sample problems. Specifically, PAFRAC may greatly exceed the theoretical range in values when the number of patches is small (e.g., < 10), and its use should be avoided in such cases. In addition, PAFRAC requires patches to vary in size. Thus, PAFRAC is undefined and reported as "N/A" in the "basename".land file if all patches are the same size or there is only 1 patch.
Comments Perimeter-area fractal dimension at the landscape level is identical to the class level (see previous comments), except here all patches in the landscape are included in the regression of patch area against patch perimeter.