Compute the spatial skewness of spatial data (a matrix).
A matrix. The matrix
values can be logical, with
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
Should the function return the absolute value or raw value of skewness ?
Spatial skewness is a measure of fluctuations in space; specifically, it measures if fluctuations are getting biased (skewed) in one direction. 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 skewness is proposed as an early warning signal of impending critical transitions.
Computing spatial skewness is straightforward. However, detecting trends of skewness that correspond to critical slowing down can be tricky, especially if data come from discrete classification of state variable.
Many high resolution spatial data are classified as FALSE (empty) or TRUE (occupied by plant). In such cases, spatial skewness captures just the skewness 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.
The spatial skewness of the matrix as a named vector
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.
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