adj_mat: Function to compute the adjacency matrix of an area.

Creates an adjacency matrix of an area of interest. This could be the accessible area (M) of a species or any geographic region of interest.

Usage

adj_mat(modelsparse, ngbs = 1, eigen_sys = FALSE, which_eigs = 1)

Arguments

modelsparse: A setA object returned by the function model2sparse.
ngbs: Numeric. Number of neighbors (see details).
eigen_sys: Logical. If TRUE the eigen analyses of the adjacency matrix will be returned.
which_eigs: Numeric. Which eigen value and eigen vector will be returned.

Value

Returns an object of class setM with 7 slots. The first contains the adjacency matrix. A n x n sparse matrix (n=number of non-NA cells of the niche model) where connected cells are represented by 1. The second slot has the adjacency list. It is a list of matrices with four columns (FromRasCell -from cell ID of the raster-, -to cell ID of the raster-, -from non-NA cell-, -to non-NA cell-). Other slots contain information about initial coordinates where dispersal occurs (initial_points), number of cells used to define the neighborhood (ngbs), non-NA coordinates (coordinates), and a matrix of eigen vectors (eigen_vec).

Details

The model is a raster object of the area where the dispersal process will occur.

The function creates an adjacency matrix where cells are considered connected based on:

The specified neighborhood size (`ngbs`)
The spatial resolution of the input raster
Only non-NA cells in the original model

When `eigen_sys = TRUE`, the function performs spectral decomposition using eigs, which is particularly useful for:

Analyzing network connectivity properties
Identifying clusters or communities in the landscape
Modeling dispersal processes using spectral graph theory

The number of neighbors depends on the dispersal abilities of the species and the spatial resolution of the niche model; for example, a species's with big dispersal abilities will move throughout more than 1 km^2 per day, so the idea is to give an approximate number of moving neighbors (pixels) per unit of time.

References

Soberón J, Osorio-Olvera L (2023). “A dynamic theory of the area of distribution.” Journal of Biogeography6, 50, 1037-1048. doi:10.1111/jbi.14587 , https://onlinelibrary.wiley.com/doi/abs/10.1111/jbi.14587. .

Author

Luis Osorio-Olvera & Jorge Soberón

Examples

x_coord <- c(-106.5699, -111.3737,-113.9332,
             -110.8913, -106.4262, -106.5699)
y_coord <- c(16.62661, 17.72373, 19.87618,
             22.50763, 21.37728, 16.62661)
xy <- cbind(x_coord, y_coord)
p <- sp::Polygon(xy)
ps <- sp::Polygons(list(p),1)
sps <- sp::SpatialPolygons(list(ps))
mx_grid <- bamm::shape2Grid(sps,resolution = 0.25,ones = TRUE)
mx_sparse <- bamm::model2sparse(model=mx_grid, threshold = 0.1)
adj_mx <- bamm::adj_mat(modelsparse=mx_sparse,
                        ngbs=1,eigen_sys=TRUE,which_eigs=1)
print(adj_mx)
#> Set M of the BAM digram it contains 7 slots 
#> 
#> @coordinates: A matrix with longitude and latitude values of each cell of the raster area
#> 
#>              x        y
#> [1,] -110.8082 22.38263
#> [2,] -110.5582 22.38263
#> [3,] -111.3082 22.13263
#> [4,] -111.0582 22.13263
#> [5,] -110.8082 22.13263
#> [6,] -110.5582 22.13263
#> @eigen_val: Eigen values of the connectivity matrix M
#> 
#> [1] 7.879909
#> @eigen_vec: Eigen vector of the connectivity matrix M
#> 
#>              [,1]
#> [1,] -0.005016999
#> [2,] -0.005372111
#> [3,] -0.006135915
#> [4,] -0.009435098
#> [5,] -0.011856916
#> [6,] -0.012869369
mx_grid_eigen <- mx_grid
mx_grid_eigen[mx_sparse@cellIDs] <- adj_mx@eigen_vec
raster::plot(mx_grid_eigen)