indicator_psdtype: Change in patch-size distributions types

In spatialwarnings: Spatial Early Warning Signals of Ecosystem Degradation

Change in patch-size distributions types

Description

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.

Usage

indicator_psdtype(
  x,
  xmin = 1,
  merge = FALSE,
  fit_lnorm = FALSE,
  xmin_bounds = NULL,
  best_by = "AIC",
  wrap = FALSE,
  nbmask = "von_neumann"
)

Arguments

x	A logical (TRUE/FALSE values) matrix or a list of these.
xmin	The xmin to be used to fit the patch size distributions. Use the special values "estimate" to use an estimated xmin for each fit
merge	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_lnorm	Fit also a log-normal distribution
xmin_bounds	Restrict the possible xmins in this range (defaults to the whole range of observed patch sizes)
best_by	The criterion used to select the best distribution type (one of "AIC", "BIC" or "AICc").
wrap	Determines whether patches are considered to wrap around the matrix when reaching the side
nbmask	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.

Details

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.

Value

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.

References

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.

See Also

patchdistr_sews

patchdistr_sews

Examples

data(forestgap)

# One logical matrix only
indicator_psdtype(forestgap[[1]])

# A list of these matrices
 
indicator_psdtype(forestgap)

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