Chao1 Richness Estimator

Estimate total species richness from abundance data using the Chao1 estimator (Chao 1984). Uses the number of singletons and doubletons to estimate undetected species.

Usage

chao1(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 ("chao1")
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 (singletons) and f2 (doubletons)

Details

The Chao1 estimator is: $$S_{Chao1} = S_{obs} + \frac{f_1^2}{2 f_2}$$ where $f_1$ is the number of singletons (species with total abundance 1) and $f_2$ is the number of doubletons (abundance 2).

When $f_2 = 0$, the bias-corrected form is used: $$S_{Chao1} = S_{obs} + \frac{f_1 (f_1 - 1)}{2}$$

References

Chao, A. (1984). Nonparametric estimation of the number of classes in a population. Scandinavian Journal of Statistics, 11, 265-270.

Chao, A. (1987). Estimating the population size for capture-recapture data with unequal catchability. Biometrics, 43, 783-791.

Examples

species <- matrix(rpois(50 * 30, 2), nrow = 50)
chao1(species)