variogram_sews {spatialwarnings}

Early-Warning signals based on variograms (EXPERIMENTAL)

Description

Compute Early-warning signals based on metrics derived form semi-variograms.

Usage

variogram_sews(mat, model = "sph", nmax = 1e+05, nbins = 32, cutoff = NULL)

Arguments

mat

A matrix (TRUE/FALSE values) or a list of matrices

model

The variogram model to use, either "sph" (for a spherical model) or "exp" (for an exponential model)

nmax

The maximum number of pairs of cells to use when computing the variogram

nbins

Number of distance bins to use to compute the variogram

cutoff

Maximum distance to consider in the variogram. If NULL, then a distance equal to one third of the diagonal of the matrix is used

Details

During ecosystem degradation and especially before a regime shift occurs in some ecosystems, spatial autocorrelation is expected to increase in a landscape. This increase can be measured based on variograms, which represent how the difference (variance) between two points in a landscape varies as a function of distance.

The approach used to derive variogram-based EWS is to compute the empirical variogram of a landscape (represented passed as a matrix of values), then fit a variogram model to it. Three parameters are then extracted from the variogram model (see Nijp et al. 2019 for a visual description of these parameters):

1. The nugget (intercept)

2. The partial sill, i.e. the reduction in semivariance at distance zero

3. The correlation range, i.e. the distance at which the relationship between semivariance and distance flattens

Additionally, the structural variance is computed as (partial sill)/(nugget + partial sill), wich quantifies whether the data are spatially structured (structural variance of one), or completely unstructured (value of zero). Theoretical work suggests that partial sill, correlation range and structural variance should increase before a regime shift occurs in an ecosystem (Nijp et al. 2019).

This function offers to fit a spherical model or an exponential model. The best-fitting model depends on your data, you should try different options and review the fits using plot_variogram.

Please note that this part of the package is still experimental and deserves more testing.

Value

A list object of class "variogram_sews", that can be displayed using summary(), plot(), etc. Significance of values can be tested using indictest.

References

Nijp, Jelmer J., Arnaud J.A.M. Temme, George A.K. Voorn, Lammert Kooistra, Geerten M. Hengeveld, Merel B. Soons, Adriaan J. Teuling, and Jakob Wallinga. (2019) Spatial Early Warning Signals for Impending Regime Shifts: A Practical Framework for Application in Real-world Landscapes. Global Change Biology 25 (6): 1905-21. doi: 10.1111/gcb.14591

See Also

raw_structvar, plot_variogram, extract_variogram, predict

indictest, to test the significance of indicator values.

Examples

## Not run: 
serengeti_ews <- variogram_sews(serengeti, 
                                model ="exp")
plot(serengeti_ews, along = serengeti.rain)
summary(serengeti_ews)

plot_variogram(serengeti_ews)

# nulln should be set to a higher values for meaningful results
serengeti_test <- indictest(serengeti_ews, nulln = 9)
plot(serengeti_test) # gray ribbons indicate the null indicator values 
summary(serengeti_test)

## End(Not run)