Extrapolate Richness to a Larger Area (Ugland T-S Curve)

Estimate species richness for a spatial extent larger than the one sampled, using the total-species (T-S) curve of Ugland, Gray & Ellingsen (2003). Sites are partitioned into spatial subareas; the T-S curve is the expected total richness of random combinations of subareas plotted against their (convex-hull) area; an asymptotic model is fitted to that curve and extrapolated to a target area, with a site-bootstrap confidence interval.

Usage

extrapolateArea(
  x,
  coords,
  target_area = NULL,
  n_subareas = 10L,
  model = c("michaelis-menten", "asymptotic", "weibull", "lomolino", "logistic"),
  n_combos = 30L,
  R = 200L,
  level = 0.95,
  seed = NULL,
  progress = TRUE
)

Arguments

x: A site-by-species matrix (presence/absence or abundance; binarized).
coords: A two-column matrix or data frame of site coordinates (x, y).
target_area: Numeric. Area to extrapolate to, in the squared units of coords. Defaults to twice the observed (convex-hull) area.
n_subareas: Integer. Number of spatial subareas to partition sites into (k-means on coordinates). Default 10; must be between 4 and the number of sites.
model: Character. Area model to fit: "michaelis-menten" (default), "asymptotic", "weibull", "lomolino", or "logistic".
n_combos: Integer. Number of random subarea combinations averaged per T-S point (all combinations are used when there are fewer). Default 30.
R: Integer. Number of site-bootstrap replicates for the confidence interval. Default 200.
level: Numeric. Confidence level. Default 0.95.
seed: Optional integer for reproducibility.
progress: Logical. Show a progress message. Default TRUE.

Value

An object of class spacc_area with components:

ts_curve: Data frame of the T-S curve (n_sub, area, richness, richness_sd)
fit: The fitted nls area model
observed_area, observed_richness: Convex-hull area and richness of the full sample
target_area: Area extrapolated to
predicted_richness, predicted_ci: Extrapolated richness and its bootstrap interval
asymptote, asymptote_ci: Model asymptote and its bootstrap interval

Details

Unlike extrapolate(), which extends the curve in sample count, this answers "how many species in a region of a given area", including areas beyond the sampled extent.

References

Ugland, K.I., Gray, J.S. & Ellingsen, K.E. (2003). The species-accumulation curve and estimation of species richness. Journal of Animal Ecology, 72, 888-897. doi:10.1046/j.1365-2656.2003.00748.x

Examples

# \donttest{
coords <- data.frame(x = runif(150), y = runif(150))
species <- matrix(rbinom(150 * 60, 1, 0.15), nrow = 150)
area_fit <- extrapolateArea(species, coords, n_subareas = 8, progress = FALSE)
print(area_fit)
# }