Compute the power-law range of a matrix
A logical matrix, or a list of logical matrices
Controls whether the patch-size distributions of the input
matrices are merged together before computing the power-law range. Setting
this value to
A vector of two integer values, defining a range in which to search for the best xmin (see 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:
(log(xmax) - log(xmin))/(log(xmax) - log(xsmallest))
where x_max is the maximum observed patch size, and x_smallest is the minimum observed patch size.
A data.frame with columns minsize, maxsize which are the observed minimum and maximum patch sizes. The estimated x_min and the value of the power-law range. If multiple matrices were provided, then a list of data.frames is returned
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.
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