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PAFRAC (landscape level)

Source: R/lsm_l_pafrac.R
lsm_l_pafrac.Rd

Perimeter-Area Fractal Dimension (Shape metric)

Usage

lsm_l_pafrac(landscape, directions = 8, verbose = TRUE)

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).

verbose

Print warning message if not sufficient patches are present

Value

tibble

Details

$$PAFRAC = \frac{2}{\beta}$$ where \(\beta\) is the slope of the regression of the area against the perimeter (logarithm) \(N \sum \limits_{i = 1}^{m} \sum \limits_{j = 1}^{n} \ln a_{ij} = a + \beta N \sum \limits_{i = 1}^{m} \sum \limits_{j = 1}^{n} \ln p_{ij}\)

PAFRAC is a 'Shape metric'. It describes the patch complexity of the landscape while being scale independent. This means that increasing the patch size while not changing the patch form will not change the metric. However, it is only meaningful if the relationship between the area and perimeter is linear on a logarithmic scale. Furthermore, if there are less than 10 patches in the landscape, the metric returns NA because of the small-sample issue.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

None

Range

1 <= PAFRAC <= 2

Behaviour

Approaches PAFRAC = 1 for patches with simple shapes and approaches PAFRAC = 2 for irregular shapes

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

Burrough, P. A. 1986. Principles of Geographical Information Systems for Land Resources Assessment. Monographs on Soil and Resources Survey No. 12. Clarendon Press, Oxford

See also

lsm_p_area, lsm_p_perim,
lsm_c_pafrac

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_l_pafrac(landscape)
#> # A tibble: 1 × 6
#>   layer level     class    id metric value
#>   <int> <chr>     <int> <int> <chr>  <dbl>
#> 1     1 landscape    NA    NA pafrac  1.27