Beta Distance-Decay

Compute the distance-decay of community similarity by fitting models to pairwise beta dissimilarity as a function of geographic distance.

Usage

betaDecay(
  x,
  coords,
  index = c("sorensen", "jaccard"),
  model = c("all", "exponential", "power", "linear"),
  distance = c("euclidean", "haversine"),
  n_bins = 50L,
  progress = TRUE
)

Arguments

x: A site-by-species matrix (presence/absence or abundance), or a spacc object (will use its stored coordinates).
coords: A data.frame with columns x and y, or a spacc_dist object.
index: Character. Dissimilarity index: "sorensen" (default) or "jaccard".
model: Character. Decay model to fit: "exponential", "power", "linear", or "all" (default). When "all", fits all three and selects the best by AIC.
distance: Character. Distance method: "euclidean" (default) or "haversine".
n_bins: Integer. Number of distance bins for binned means in plots. Default 50.
progress: Logical. Show progress messages? Default TRUE.

Value

An object of class spacc_beta_decay containing:

pairs: Data.frame with columns distance, dissimilarity, site_i, site_j
fits: Named list of fitted model objects
best_model: Name of best model by AIC
half_life: Distance at which similarity halves (exponential model only)
coefficients: Data.frame of model coefficients and AIC
index: Dissimilarity index used
n_sites: Number of sites
n_pairs: Number of pairwise comparisons

Details

Three decay models are available:

Exponential: \(\beta = 1 - a \cdot e^{-b \cdot d}\)
Power: \(\beta = a \cdot d^b\)
Linear: \(\beta = a + b \cdot d\)

The half-life (exponential model) is the distance at which similarity decays to half its initial value: \(d_{1/2} = \ln(2) / b\).

References

Nekola, J.C. & White, P.S. (1999). The distance decay of similarity in biogeography and ecology. Journal of Biogeography, 26, 867-878.

Morlon, H., Chuyong, G., Condit, R., et al. (2008). A general framework for the distance-decay of similarity in ecological communities. Ecology Letters, 11, 904-917.

Examples

# \donttest{
coords <- data.frame(x = runif(30), y = runif(30))
species <- matrix(rbinom(30 * 20, 1, 0.3), nrow = 30)

bd <- betaDecay(species, coords)
print(bd)
plot(bd)
# }