The perimeter-area method quantifies the patch degree of complexity of the mean planar shapes.

For example, holding shape constant, an increase in patch size will cause a patch decrease in the fractal perimeter-area ratio.

Thus, this index is probably only useful if sample sizes are large (e.g., n 20; although pafrac is computed in fragstats if n 10).

Specifically, the contiguity value for a pixel in the output image is the sum of the products, of each template value and the corresponding input image pixel value, within the nine cell neighborhood.The MAT skeleton is derived from a depth map of the patch, where each pixel value represents the distance (in pixels) to the nearest edge.Instead of providing a black box solution, all these dimension metrics are developed using Dinamica EGO modeling language, thus they dimension serve as templates to derive a wide variety of metrics.For simple Euclidean shapes (e.g., circles and rectangles P A and D 1 (the dimension of a line).If, for example, small and large patches alike have simple geometric shapes, then pafrac will be relatively low, indicating that patch perimeter increases relatively slowly as patch area increases.In landscapes with only a few patches, it is not unusual to get values that greatly exceed the theoretical limits of this index.Therefore, the application of these metrics consists of a powerful tool to describe the consequences of land-use and land-cover dynamics on mean the conservation of biodiversity.A template value of 2 is assigned to quantify horizontal and vertical pixel relationships within the image and a value of 1 is assigned to quantify diagonal relationships.The value of each pixel in the output image, computed when at the center of the moving template, is a function of the number and location of pixels, of the same class, within the nine cell image neighborhood.As the polygons become more complex, the perimeter becomes increasingly plane-filling and P A with.For example, fractal dimension for a landscape class can be estimated using the perimeter-area relationship, so If sufficient data are available, the slope of the line obtained by regressing log(P patch edge lengths, on log(A patch areas, is equal to 2/D (Burrough, 1986).Fractal mean analysis usually is applied to the entire landscape mosaic using the perimeter-area relationship A k P2/D, where k is a constant (Burrough 1986). Inflated values may also result from patches with even small interior fractal openings since these represent edge, and the MAT skeleton will surround the openings, resulting in lower MAT values than if the openings were not present.

Thus, varying the cell size of the input image will affect the patch fractal dimension.

1987) nor is it equal to 2 times the slope (e.g., windows O'Neill.

Therefore, caution should be exercised when using this fractal dimension index as a measure of patch shape complexity.For example, landscape crack metrics trial can be applied to identify the best landscape configuration for forest species conservation -independently of the perceptions of individual species-, which is hypothetically a landscape with: i) a high windows forest cover; ii) a small number of forest fragments; iii) a high.Although fractal analysis typically dimension has not been used to characterize individual patches in landscape ecological research, we use this relationship to calculate the fractal dimension of each patch separately.We refer to this index as the perimeter-area fractal dimension (pafrac) in fragstats.1987, Milne 1988, Turner and Ruscher 1988, Iverson 1989, Ripple.In contrast to the linearity index, related circumscribing circle provides a measure of overall patch elongation.This index may be particularly useful fractal for distinguishing patches that are both linear (narrow) and elongated.A table is output for each metric.Fractal dimension, landscape metrics (McGarigal and Marks, 1995) can be useful tools to assess the quality of habitats when extensive biodiversity inventories or ecological data are not available or are difficult to obtain, as landscape metrics are strongly related to biodiversity indicators (Metzger, 2006).Another method of assessing shape is based on ratio of patch area to the area of the smallest circumscribing circle.