Improved Chao1 (iChao1) Richness Estimator

Estimate total species richness using the improved Chao1 estimator (Chiu et al. 2014). Uses singletons through quadrupletons (f1–f4) to reduce bias for small samples.

Usage

iChao1(x)

Arguments

x: A site-by-species matrix (abundance data). Columns are pooled across sites.

Value

An object of class spacc_estimate with components:

estimator: Name of the estimator ("iChao1")
estimate: Estimated total richness
se: Standard error of the estimate
lower: Lower 95 percent confidence bound
upper: Upper 95 percent confidence bound
S_obs: Observed species richness
details: List with f1, f2, f3, f4

Details

The improved Chao1 estimator adds a correction term using f3 and f4: $$S_{iChao1} = S_{Chao1} + \frac{f_3}{4 f_4} \max\left(f_1 - \frac{f_2 f_3}{2 f_4}, 0\right)$$

When $f_4 = 0$, the estimator collapses to Chao1.

References

Chiu, C.H., Wang, Y.T., Walther, B.A. & Chao, A. (2014). An improved nonparametric lower bound of species richness via a modified Good-Turing frequency formula. Biometrics, 70, 671-682.

Examples

species <- matrix(rpois(50 * 30, 2), nrow = 50)
iChao1(species)