indicator_sdr: Spectral Density Ratio (SDR) indicator
In spatialwarnings: Spatial Early Warning Signals of Ecosystem Degradation

Description Usage Arguments Details Value References See Also Examples

Compute the ratio of low frequencies over high frequencies of the r-spectrum. It also computes a null value obtained by randomizing the matrix.

1 2	indicator_sdr(input, sdr_low_range = NULL, sdr_high_range = NULL, nreplicates = 999)

`input`	A matrix or a logical matrix (TRUE/FALSE), or a list of these.
`sdr_low_range`	The range of values (in proportion) to use for the computation of the spectral density ratio. For example, for the lowest 20% (default value), set `sdr_low_range` to `c(0, .2)`.
`sdr_high_range`	The range of values (in proportion) to use for the computation of the spectral density ratio. For example, for the highest 20% (default value), set `sdr_high_range` to `c(.8, 1)`.
`nreplicates`	The number of replicates to compute for the null distribution

SDR measures the increase in long-range correlations before a critical point. It is the ratio of the average low frequency value over high frequency values. In this implementation, an increase in SDR implies a "reddening" of the r-spectrum. See also spectral_spews for a more complete description.

Low and high frequencies are averaged in order to compute the SDR. The parameters sdr_low_range and sdr_high_range control which frequencies are selected for averaging. For example sdr_low_range = c(0, .2) (default) uses the lower 20 the average of low frequencies. sdr_high_range = c(.8, 1) uses the higher 20

A list (or a list of lists if input was a list of matrices) with components:

'value': SDR of the matrix

If nreplicates is above 2, then the list has the following additional components :

'null_mean': Mean SDR of the null distribution
'null_sd': SD of SDR 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 SDR in the null distribution. A low p-value means that the indicator value is significantly higher than the null values.

Carpenter, S.R. & Brock, W.A. (2010). Early warnings of regime shifts in spatial dynamics using the discrete Fourier transform. Ecosphere

spectral_spews, rspectrum

## Not run:  
serengeti.sdr <- indicator_sdr(serengeti, nreplicates = 499)
do.call(rbind, serengeti.sdr) # convert results to data.frame

## End(Not run)