R/indicator_variance.R

In spatialwarnings: Spatial Early Warning Signals of Ecosystem Degradation

#' @title Spatial variance indicator
#'
#' @description This functions computes the spatial variance of spatial data. 
#'   It also computes a null value obtained by randomizing 
#'   the matrix.
#' 
#' @param input A matrix or a list of matrices. The matrix 
#'   values can be logical, with \code{FALSE} (empty) or \code{TRUE} (occupied) 
#'   values. The entries can also be continuous (like NDVI or EVI data). 
#' 
#' @param 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 
#'   \code{subsize} in each dimension of the matrix. Variance is calculated 
#'   on the coarse-grained matrix. 
#' 
#' @param nreplicates Number of replicates to produce to estimate null 
#'   distribution of index.
#' 
#' @return A list (or a list of lists if input was a list of matrices) with 
#'   components:
#'     \itemize{
#'       \item `value`: Spatial variance of the matrix
#'     }
#'   If nreplicates is above 2, then the list has the following additional 
#'   components : 
#'     \itemize{
#'       \item `null_mean`: Mean spatial variance of the null distribution
#'       \item `null_sd`: SD of spatial variance in the null distribution
#'       \item `z_score`: Z-score of the observed value in the null distribution 
#'                          (value minus the null mean and divided by null 
#'                          standard deviation)
#'       \item `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. 
#'     }
#' 
#' @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. 
#' 
#' 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. 
#' 
#' \code{subsize} has to be an integer. It has to be less than or equal to 
#' half of matrix size (N). \code{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. 
#' 
#' @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. 
#' 
#' @examples
#' 
#' data(serengeti)
#' \dontrun{
#' indicator_variance(serengeti, nreplicates = 499)
#' }
#' 
#'@export
indicator_variance <- function(input, 
                               subsize     = 5, 
                               nreplicates = 999) {
  
  check_mat(input) # checks data input
  
  if (is.list(input)) { 
    # Returns a list of lists
    return( lapply(input, indicator_variance, subsize, nreplicates) )
  } else { 
    
    # We alter the raw_variance function so it includes coarse_graining 
    #   in case subsize is above 1. 
    indicf <- raw_variance
    if ( subsize > 1 ) { 
      indicf <- with_coarse_graining(raw_variance, subsize)
    } 
    
    # Compute and return indicator
    return( compute_indicator_with_null(input, nreplicates, indicf) ) 
    
  }
}

raw_variance <- function(mat) { var(as.vector(mat)) }