Chao1

Chao1 is a nonparametric estimator of species richness used in ecology to estimate the total number of species in a community from a sample. It is particularly useful when sampling is incomplete and many rare species remain undetected. The estimator relies on the frequencies of rare species observed in the sample, especially singletons and doubletons.

Let S_obs be the number of observed species, f1 the number of species represented by a single individual (singletons), and f2 the number represented by two individuals (doubletons). The original Chao1 estimate is S_obs + f1^2 / (2 f2) while the bias-corrected version is S_obs + f1*(f1-1) / (2*(f2+1)). When f2 equals zero, the bias-corrected form reduces to S_obs + f1*(f1-1)/2.

Chao1 is widely used in ecological studies and microbiome analyses to assess alpha diversity and to compare richness across samples or habitats. It provides a lower bound for species richness and tends to inflate estimates in communities with many rare taxa if sampling depth is low, but performs well when rare species are observed with some frequency.

Limitations include sensitivity to sampling depth, reliance on accurate counts of singletons and doubletons, and assumptions of random sampling and a closed community. It does not model the full underlying abundance distribution and may misestimate richness when detection probabilities vary among species or when many extremely rare species are present.

Chao1 was introduced by Anne Chao in 1984 and has since become a standard method in biodiversity studies, including ecological and microbiome analyses.

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