raw_plrange: Power-law range indicator

In spatialwarnings: Spatial Early Warning Signals of Ecosystem Degradation

Power-law range indicator

Description

Compute the power-law range of a matrix

Usage

raw_plrange(mat, xmin_bounds = NULL)

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:

\frac{log(x_{max}) - log(x_{min})}{log(x_{max}) - log(x_{smallest})}

where x_{max} is the maximum observed patch size, and x_{smallest} is the minimum observed patch size.

Value

A named vector containing the power-law range value

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.

See Also

patchdistr_sews

Examples

forestgap.plr <- raw_plrange(forestgap[[2]]) 

# Restrict to small xmins 
forestgap.plr2 <- indicator_plrange(forestgap[[2]], xmin_bounds = c(1, 10)) 

spatialwarnings documentation built on Sept. 11, 2024, 8:55 p.m.