Diversity-Area Relationship (DAR)

Extend the classic species-area relationship (SAR) to a diversity-area relationship using Hill numbers of any order q. Instead of plotting species richness vs. sites, this plots effective diversity vs. cumulative area.

Usage

dar(
  x,
  coords,
  q = c(0, 1, 2),
  n_seeds = 50L,
  method = "knn",
  area_method = c("convex_hull", "voronoi", "count"),
  distance = c("euclidean", "haversine"),
  parallel = TRUE,
  n_cores = NULL,
  progress = TRUE,
  seed = NULL
)

Arguments

x: A site-by-species matrix (abundance data recommended).
coords: A data.frame with columns x and y, or a spacc_dist object.
q: Numeric vector. Diversity orders. Default c(0, 1, 2).
n_seeds: Integer. Number of random starting points. Default 50.
method: Character. Accumulation method. Default "knn".
area_method: Character. How to estimate cumulative area: "voronoi" (Voronoi tessellation, requires sf), "convex_hull" (convex hull of accumulated sites, requires sf), or "count" (use site count as proxy, no dependencies). Default "convex_hull".
distance: Character. Distance method. Default "euclidean".
parallel: Logical. Use parallel processing? Default TRUE.
n_cores: Integer. Number of cores.
progress: Logical. Show progress? Default TRUE.
seed: Integer. Random seed.

Value

An object of class spacc_dar containing:

hill: A spacc_hill object with diversity curves
area: Matrix of cumulative areas (n_seeds x n_sites)
q: Diversity orders used
area_method: Method used for area estimation

Details

The DAR (Ma, 2018) generalizes the SAR by replacing species richness (q=0) with Hill numbers of any order. This reveals how different facets of diversity scale with area:

q=0 (richness) recovers the classic SAR
q=1 (Shannon) shows how common species diversity scales
q=2 (Simpson) shows how dominant species diversity scales

References

Ma, Z.S. (2018). DAR (diversity-area relationship): extending classic SAR for biodiversity and biogeography analyses. Ecology and Evolution, 8, 10023-10038.

Arrhenius, O. (1921). Species and area. Journal of Ecology, 9, 95-99.

Examples

# \donttest{
coords <- data.frame(x = runif(50), y = runif(50))
species <- matrix(rpois(50 * 30, 2), nrow = 50)

dar <- dar(species, coords, q = c(0, 1, 2))
plot(dar)
# }