Spatial Hill Number Beta Diversity

Compute multisite beta diversity as gamma/alpha decomposition of Hill numbers along the spatial accumulation curve (Jost 2007 framework).

Usage

spaccHillBeta(
  x,
  coords,
  q = c(0, 1, 2),
  n_seeds = 50L,
  distance = c("euclidean", "haversine"),
  parallel = TRUE,
  n_cores = NULL,
  progress = TRUE,
  seed = NULL
)

Arguments

x: A site-by-species matrix (rows = sites, cols = species).
coords: A data.frame with columns x and y, or a spacc_dist object.
q: Numeric vector. Orders of diversity. Default c(0, 1, 2).
n_seeds: Integer. Number of random starting points. Default 50.
distance: Character. "euclidean" or "haversine".
parallel: Logical. Use parallel processing? Default TRUE.
n_cores: Integer. Number of cores. Default NULL.
progress: Logical. Show progress? Default TRUE.
seed: Integer. Random seed.

Value

An object of class spacc_hill_beta containing:

gamma: Named list of n_seeds x n_sites matrices (one per q)
alpha: Named list of n_seeds x n_sites matrices (one per q)
beta: Named list of n_seeds x n_sites matrices (one per q)
q: Vector of q values
coords: Original coordinates
n_seeds, n_sites, n_species: Dimensions

Details

At each accumulation step k, the function computes:

Gamma: Hill number of the pooled community (all k sites combined)
Alpha: Generalized mean of per-site Hill numbers (Jost's power mean)
Beta: gamma / alpha (effective number of distinct communities)

Beta = 1 means all sites are identical; beta = k means all sites are completely different. This provides the Hill-number analogue of the Baselga-based spaccBeta().

References

Jost, L. (2007). Partitioning diversity into independent alpha and beta components. Ecology, 88, 2427-2439.

Examples

# \donttest{
coords <- data.frame(x = runif(40), y = runif(40))
species <- matrix(rpois(40 * 20, 2), nrow = 40)

hb <- spaccHillBeta(species, coords, n_seeds = 10, progress = FALSE)
plot(hb)
# }