This functions fits different patch size distributions types (power-law, log-normal, exponential and truncated power-law) to the patches contained in a matrix. The distributions are returned with their corresponding AIC, BIC and AICc to select the best fit.
indicator_psdtype(
x,
xmin = 1,
merge = FALSE,
fit_lnorm = FALSE,
xmin_bounds = NULL,
best_by = "AIC",
wrap = FALSE,
nbmask = "von_neumann"
)A data.frame (or a list of these if x is a list) with the following columns:
method the method used for fitting (currently: only
log-likelihood is implemented, "ll")
type the type of distribution
npars the number of parameters of the distribution type
AIC, `AICc` and `BIC` the values for Akaike Information Criterion (or the corrected for small samples equivalent AICc), and Bayesion Information Criterion (BIC)
best A logical vector indicating which distribution is the
best fit
plexpo, cutoff, meanlog, sdlog the estimates
for distribution parameters (see pl_fit)
percolation A logical value indicating whether there is
percolation in the system.
A logical (TRUE/FALSE values) matrix or a list of these.
The xmin to be used to fit the patch size distributions. Use the special values "estimate" to use an estimated xmin for each fit
The default behavior is to produce indicators values for each matrix. If this parameter is set to TRUE then the patch size distributions are pooled together for fitting.
Fit also a log-normal distribution
Restrict the possible xmins in this range (defaults to the whole range of observed patch sizes)
The criterion used to select the best distribution type
(one of "AIC", "BIC" or "AICc").
Determines whether patches are considered to wrap around the matrix when reaching the side
Either "moore" for 8-way neighborhood, "von_neumann" for four-way
neighborhood (default), or a 3x3 matrix describing which neighbors to
consider around a cell. See patchsizes for details on how to specify
such neighborhoods.
Patterned ecosystems can exhibit a change in their spatial structure as they become more and more stressed. It has been suggested that this should be reflected in changes in the observed patch size distributions (PSD). The following sequence is expected to occur (Kefi et al. 2011) as patterned ecosystems become more and more degraded:
- Percolation of vegetation patches occurs (a patch has a width or height equal to the size of the system)
- The patch-size distribution follows a power-law
- The patch-size distribution deviates from a power-law as larger patches break down
- The patch-size distribution is closer to an exponential distribution
This indicator fits the observed patch size distribution based on maximum-likelihood (following Clauset et al. 2009 recommendations), then select the best model using AIC, BIC (default) or AICc.
Kefi, S., Rietkerk, M., Roy, M., Franc, A., de Ruiter, P.C. & Pascual, M. (2011). Robust scaling in ecosystems and the meltdown of patch size distributions before extinction: Patch size distributions towards extinction. Ecology Letters, 14, 29-35.
Kefi, S., Rietkerk, M., Alados, C.L., Pueyo, Y., Papanastasis, V.P., ElAich, A., et al. (2007). Spatial vegetation patterns and imminent desertification in Mediterranean arid ecosystems. Nature, 449, 213-217.
Clauset, A., Shalizi, C. R., & Newman, M. E. (2009). Power-law distributions in empirical data. SIAM review, 51(4), 661-703.
patchdistr_sews
patchdistr_sews
data(forestgap)
# One logical matrix only
indicator_psdtype(forestgap[[1]])
# A list of these matrices
# \donttest{
indicator_psdtype(forestgap)
# }
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