Singleton-free estimator (FE)

See also
Alpha diversity
Alpha diversity metrics
Novel alpha diversity metrics
Log-normal abundance distribution

The singleton-free estimator (FE) (R.C. Edgar and H. Flyvbjerg, manuscript in preparation) estimates total richness using a non-parametric theory similar to Chao1, except that singletons are not considered. Let

N = number of observed OTUs,
n _k = number of observed OTUs with abundance k .

Then FE is calculated as

FE = N - n ₁ + 2n ₂ ³ /9n ₃ ² + 2n ₂ ² /3n ₃ .