Improved Chao2 (iChao2) Richness Estimator

Estimate total species richness from incidence data using the improved Chao2 estimator (Chiu et al. 2014). Uses uniques through quadruplicates (Q1–Q4) to reduce bias for small samples.

Usage

iChao2(x)

Arguments

x: A site-by-species matrix (presence/absence or abundance). Automatically binarized.

Value

An object of class spacc_estimate with components:

estimator: Name of the estimator ("iChao2")
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 Q1, Q2, Q3, Q4, n_sites

Details

The improved Chao2 estimator is the incidence-based analogue of iChao1: $$S_{iChao2} = S_{Chao2} + \frac{Q_3}{4 Q_4} \max\left(Q_1 - \frac{Q_2 Q_3}{2 Q_4}, 0\right)$$

When $Q_4 = 0$, the estimator collapses to Chao2.

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(rbinom(50 * 30, 1, 0.3), nrow = 50)
iChao2(species)