Spatial Eigenvectors (PCNM/dbMEM)

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".

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

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:

Compute pairwise distances
Truncate distances beyond threshold (set to 4 * threshold)
Double-centre the squared truncated distance matrix
Extract eigenvectors with positive eigenvalues
For "dbmem": additionally filter to Moran's I > 0

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.

Examples