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_coverageobject fromspaccCoverage().- 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).
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
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.
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.
Examples
# \donttest{
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)
# }