A named vector containing the power-law range value
Arguments
mat
A logical matrix, or a list of logical matrices
xmin_bounds
A vector of two integer values, defining a range in which
to search for the best xmin (see Details).
Details
Some ecosystems show typical changes in their patch-size
distribution as they become more and more degraded. In particular, an
increase in the truncation of the patch-size distribution (PSD) is expected
to occur. The power-law range (PLR) measures the truncation of the PSD
in a single value (see also patchdistr_sews for more details).
To compute the PLR, power-laws are fitted with a variable
minimum patch size (xmin) and the one with the lowest Kolmogorov-Smirnov
distance to the empirical distribution is retained. PLR is then computed
using this best-fitting xmin:
where \(x_{max}\) is the maximum observed patch size, and
\(x_{smallest}\) is the minimum observed patch size.
References
Clauset, A., Shalizi, C. R., & Newman, M. E. (2009).
Power-law distributions in empirical data. SIAM review, 51(4), 661-703.
Berdugo, M., Kefi, S., Soliveres, S. & Maestre, F.T. (2017). Plant spatial
patterns identify alternative ecosystem multifunctionality states in
global drylands. Nature in Ecology and Evolution.