This functions computes the spatial variance of spatial data. It also computes a null value obtained by randomizing the matrix.
indicator_variance(input, subsize = 5, nreplicates = 999)
A matrix or a list of matrices. 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
Number of replicates to produce to estimate null distribution of index.
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.
For example, many high resolution spatial data are classified as FALSE (empty) or TRUE (occupied by plant). 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.
A list (or a list of lists if input was a list of matrices) with components:
'value': Spatial variance of the matrix
If nreplicates is above 2, then the list has the following additional components :
'null_mean': Mean spatial variance of the null distribution
'null_sd': SD of spatial variance in the null distribution
'z_score': Z-score of the observed value in the null distribution (value minus the null mean and divided by null standard deviation)
'pval': p-value based on the rank of the observed spatial variance in the null distribution. A low p-value means that the indicator value is significantly higher than the null values.
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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