raw_cg_variance: Spatial variance indicator

In spatialwarnings: Spatial Early Warning Signals of Ecosystem Degradation

Spatial variance indicator

Description

This functions computes the spatial variance of a matrix.

Usage

raw_cg_variance(mat, subsize = 5)

Arguments

mat	A matrix. Its values can be logical, with FALSE (empty) or TRUE (occupied) values. The entries can also be continuous (like NDVI or EVI data).
subsize	Dimension of the submatrix used to coarse-grain the original matrix. This must be an integer less than size of the full matrix. Coarse-graining reduces the size of the matrix by a factor subsize in each dimension of the matrix. Variance is calculated on the coarse-grained matrix.

Details

Spatial variance is a measure of fluctuations in space. Based on the theory of critical slowing down, when systems approach critical points they are expected to show increased fluctuations in space. Thus, increasing spatial variance is proposed as an early warning signal of impending critical transitions.

Many high resolution spatial data are classified as FALSE (empty) or TRUE (occupied). In such cases, spatial variance captures just the variance in data, but not that of spatial structure. To resolve the issue, this function employs a method called coarse-graining, proposed in Kefi et al (2014), and described in detail in Sankaran et al. (2017). One must specify a subsize above one for binary valued data sets to obtain meaningful values.

subsize has to be an integer. It has to be less than or equal to half of matrix size (N). subsize must also be preferably a divisor of N. If it is not a divisor of N, the remainder rows and columns are discarded when computing coarse-graining matrices.

Null model evaluations are also done on coarse-grained matrices.

Value

The variance of the coarse-grained matrix as a named vector

References

Guttal, V., and Jayaprakash, C. (2009). Spatial variance and spatial skewness: leading indicators of regime shifts in spatial ecological systems. Theoretical Ecology, 2(1), 3-12.

Kefi, S., Guttal, V., Brock, W.A., Carpenter, S.R., Ellison, A.M., Livina, V.N., et al. (2014). Early Warning Signals of Ecological Transitions: Methods for Spatial Patterns. PLoS ONE, 9, e92097.

Sankaran, S., Majumder, S., Kefi, S., and Guttal, V. (2017). Implication of being discrete and spatial in detecting early warning signals of regime shifts. Ecological Indicators.

See Also

generic_sews

Examples

data(serengeti)
raw_cg_variance(serengeti[[1]])
compute_indicator(serengeti, fun = raw_cg_variance, subsize = 5)

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