extrapolateCoverage: Extrapolate Richness Beyond Observed Coverage

In spacc: Fast Spatial Species Accumulation Curves

Extrapolate Richness Beyond Observed Coverage

Description

Predict species richness at coverage levels beyond the empirical maximum, following the Chao et al. (2014) framework. Provides seamless interpolation and extrapolation as a function of sample coverage.

Usage

extrapolateCoverage(x, target_coverage = c(0.9, 0.95, 0.99), q = 0)

Arguments

x	A spacc_coverage object from spaccCoverage().
target_coverage	Numeric vector of target coverage levels (0 to 1). Can exceed observed coverage for extrapolation. Default c(0.90, 0.95, 0.99).
q	Numeric. Diversity order for extrapolation: 0 (richness, default), 1 (Shannon), or 2 (Simpson).

Details

For targets within observed coverage, linear interpolation is used. For targets beyond observed coverage, asymptotic estimators are applied:

• q = 0: Chao1 estimator: S_est = S_obs + f1^2 / (2 * f2), where f1/f2 are singleton/doubleton counts. Extrapolation via coverage deficit.

• q = 1: Shannon extrapolation based on the Good-Turing frequency formula.

• q = 2: Simpson extrapolation using the unbiased estimator.

Value

An object of class spacc_coverage_ext containing:

richness	Matrix of interpolated/extrapolated richness (n_seeds x n_targets)
target_coverage	Target coverage levels
q	Diversity order used
observed_coverage	Mean observed final coverage
observed_richness	Mean observed final richness

References

Chao, A. & Jost, L. (2012). Coverage-based rarefaction and extrapolation: standardizing samples by completeness rather than size. Ecology, 93, 2533-2547.

Chao, A., Gotelli, N.J., Hsieh, T.C., et al. (2014). Rarefaction and extrapolation with Hill numbers: a framework for sampling and estimation in species diversity studies. Ecological Monographs, 84, 45-67.

See Also

spaccCoverage(), interpolateCoverage()

Examples

coords <- data.frame(x = runif(50), y = runif(50))
species <- matrix(rpois(50 * 30, 2), nrow = 50)
cov <- spaccCoverage(species, coords)
ext <- extrapolateCoverage(cov, target_coverage = c(0.95, 0.99))
print(ext)

spacc documentation built on June 20, 2026, 5:07 p.m.