spatialEigenvectors: Spatial Eigenvectors (PCNM/dbMEM)

In spacc: Fast Spatial Species Accumulation Curves

Spatial Eigenvectors (PCNM/dbMEM)

Description

Compute spatial eigenvectors from site coordinates using Principal Coordinates of Neighbour Matrices (PCNM) or distance-based Moran's Eigenvector Maps (dbMEM).

Usage

spatialEigenvectors(
  coords,
  threshold = NULL,
  method = c("pcnm", "dbmem"),
  distance = c("euclidean", "haversine")
)

Arguments

coords	A data.frame with columns x and y, or a spacc_dist object.
threshold	Numeric. Distance threshold for truncation. Default NULL uses the largest edge in the minimum spanning tree.
method	Character. "pcnm" (default) retains all positive eigenvectors; "dbmem" retains only those with positive Moran's I.
distance	Character. "euclidean" (default) or "haversine".

Details

PCNM (Borcard & Legendre 2002) decomposes spatial structure into orthogonal eigenvectors representing patterns at different spatial scales. Large eigenvalues correspond to broad-scale patterns (positive spatial autocorrelation), while small eigenvalues represent fine-scale patterns.

The algorithm:

1. Compute pairwise distances

2. Truncate distances beyond threshold (set to 4 * threshold)

3. Double-centre the squared truncated distance matrix

4. Extract eigenvectors with positive eigenvalues

5. For "dbmem": additionally filter to Moran's I > 0

Value

An object of class spacc_mem containing:

vectors	Matrix of eigenvectors (sites x n_vectors)
eigenvalues	Positive eigenvalues
moran_i	Moran's I for each eigenvector
threshold	Truncation distance used
coords	Original coordinates
n_sites	Number of sites
method	Method used

References

Borcard, D. & Legendre, P. (2002). All-scale spatial analysis of ecological data by means of principal coordinates of neighbour matrices. Ecological Modelling, 153, 51-68.

Dray, S., Legendre, P. & Peres-Neto, P.R. (2006). Spatial modelling: a comprehensive framework for principal coordinate analysis of neighbour matrices (PCNM). Ecological Modelling, 196, 483-493.

See Also

spatialPartition() for variance partitioning with MEMs

Examples

coords <- data.frame(x = runif(30), y = runif(30))
mem <- spatialEigenvectors(coords)
print(mem)

spacc documentation built on June 20, 2026, 5:07 p.m.