raw_clustering: Clustering of pairs

In spatialwarnings: Spatial Early Warning Signals of Ecosystem Degradation

Clustering of pairs

Description

Compute the number of pairs of neighbor cells in a landscape and derive from it clustering indices

Usage

raw_clustering(mat, wrap = TRUE, use_8_nb = FALSE)

pair_counts(mat, wrap = TRUE, use_8_nb = FALSE, prop = TRUE)

Arguments

mat	A matrix, usually with discrete values (logical, integers, etc.)
wrap	Whether space should be considered to wrap at the edges
use_8_nb	Set to TRUE to use an 8-way neighborhood. The default is set to FALSE, which uses a 4-way neighborhood
prop	Return the counts for all pairs in the matrix (FALSE), or the proportions for each pair (out of all possible pairs)

Details

The clustering of pairs is defined as the density of pairs, i.e. the proportion of all neighboring pairs of cells that share the same state, divided by the null expectation given a random, homogeneous spatial structure.

For example, let's consider a matrix with two states, 'a' and 'b'. raw_clustering will count all pairs of cells 'a-a' or 'b-b', and divide this by the total number of pairs. This proportion is then again divided by the probability of obtaining these proportion of pairs under the assumption of no spatial structure (random mixing of cells in the matrix).

Clustering is equal to one when there is no spatial structure. It is above one when two states are found next to each other (i.e. cluster) more than expected by chance. Values below one means that those two states tend to be neighbors less frequently than expected by chance.

If you are only interested in the proportion of pairs for each combination of states, you can use the function pair_counts, which returns a matrix with as many rows and columns as there are states in the matrix, and contains the counts for all possible pairs of cells found in the matrix (or their relative proportions).

Value

A vector with the requested clutering values for raw_clustering, whose names are equal to each state (unique value) found in the original matrix, preceded by 'clust_' (to make sure names are compatible with other functions).

pair_counts returns the counts of pairs of states in the matrix, or the proportion of each pair, depending on the value of prop

Examples

# The clustering of a random matrix is close to one
ls <- 100 # lattice size
mm <- matrix(sample(c("sp1", "sp2", "sp3", "sp4"), size = ls^2, replace = TRUE),
             nrow = ls, ncol = ls)
clust <- raw_clustering(mm, wrap = TRUE, use_8_nb = TRUE)
print(clust)

# Compute clustering along the gradient for the serengeti dataset


data(forestgap)
clust_indic <- compute_indicator(serengeti, raw_clustering,
                                 wrap = TRUE, use_8_nb = FALSE)
# The interesting one is the clustering of state 0 (FALSE in the original matrix),
# which corresponds to grassland pixels, which get more and more clustered with 
# increasing rainfall (see also ?generic_sews for how that compares with generic 
# indicators)
plot(clust_indic, along = serengeti.rain)

# Add null trend
clust_test <- indictest(clust_indic, nulln = 19)
plot(clust_test, along = serengeti.rain)

# Show the proportion of each pairs of states in the matrix... 
pair_counts(serengeti[[5]])

# ... or the total count
pair_counts(serengeti[[5]], prop = FALSE)

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