skbio.math.diversity.alpha.chao1

skbio.math.diversity.alpha.chao1(counts, bias_corrected=True)[source]

Calculate chao1 richness estimator.

Uses the bias-corrected version unless bias_corrected is False and there are both singletons and doubletons.

Parameters:

counts : 1-D array_like, int

Vector of counts.

bias_corrected : bool, optional

Indicates whether or not to use the bias-corrected version of the equation. If False and there are both singletons and doubletons, the uncorrected version will be used. The biased-corrected version will be used otherwise.

Returns:

double

Computed chao1 richness estimator.

See also

chao1_ci

Notes

The uncorrected version is based on Equation 6 in [R33]:

\[chao1=S_{obs}+\frac{F_1^2}{2F_2}\]

where \(F_1\) and \(F_2\) are the count of singletons and doubletons, respectively.

The bias-corrected version is defined as

\[chao1=S_{obs}+\frac{F_1(F_1-1)}{2(F_2+1)}\]

References

[R33](1, 2) Chao, A. 1984. Non-parametric estimation of the number of classes in a population. Scandinavian Journal of Statistics 11, 265-270.