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):
The nugget (intercept)
The partial sill, i.e. the reduction in semivariance at
distance zero
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.