Chao2

Chao2 is a nonparametric estimator of species richness that uses incidence-based data, that is, presence-absence information collected across multiple sampling units such as sites, plots, or sampling occasions. It serves as the incidence-based counterpart to Chao1, which is based on abundance data. Chao2 aims to estimate the total number of species in a community, including those not detected in all sampling units, by accounting for rare species that occur in only a few units.

The estimator requires three quantities from a study design with S_obs observed species, across a set of sampling units. Q1 denotes the number of species that occur in only one sampling unit (singletons), and Q2 denotes the number of species that occur in exactly two sampling units (doubletons). A bias-corrected form commonly used is S_Chao2 = S_obs + (Q1 × (Q1 − 1)) / (2 × (Q2 + 1)). An alternative, less conservative form is S_Chao2 = S_obs + (Q1^2) / (2 × Q2) when Q2 > 0. If Q2 is zero, the bias-corrected version provides a conservative adjustment to avoid division by zero.

Applications and limitations: Chao2 is widely applied in ecological and biodiversity studies to compare inventories, assess sampling adequacy, and inform conservation decisions. It performs best with a reasonable number of sampling units and reliable detection probabilities. Like other nonparametric estimators, its accuracy depends on the sampling design and the degree to which rare species are detectable across units.

Relation to other methods: It complements abundance-based estimators like Chao1 and is related to nonparametric approaches such as jackknife and rarefaction, each with different data requirements and assumptions.