Use this biodiversity measure when counts or incidences were collected with comparable sampling effort and the estimator matches the study design. It can summarize richness, dominance, evenness, or compositional difference.

Observed species

An integer count greater than or equal to 0, expressed in species.

Sample count

An integer count greater than or equal to 1, expressed in samples.

Singletons

An integer count greater than or equal to 0, expressed in species.

The implementation follows this calculation rule: Compute the limited richness proxy Sobs + singletons divided by sample count. A full bootstrap richness estimator requires each species' observed incidence frequency.^[1]

Bootstrap estimate

The calculated bootstrap estimate in species.

Different diversity indices weight rare and common taxa differently. Detection probability, sample coverage, taxonomic resolution, zero counts, and unequal effort can dominate comparisons; proxy estimators are not interchangeable with their full published forms. The output is explicitly an estimate or proxy; preserve that label when reporting it.

Report observed richness, abundance or incidence data, and sampling effort beside the index. Coverage-based rarefaction, accumulation curves, and more than one Hill-number order provide a fuller view of community structure.

• ACE Proxy Estimator

  Compute the singleton-doubleton proxy Sobs + F1 squared divided by 2 F2, substituting one when F2 is zero. This is not the full abundance-based coverage estimator, which requires the rare-species frequency distribution.

• Chao1 Estimator

  Estimate total species richness from singletons and doubletons in a single sample using the Chao1 estimator.

• ACE Bias Corrected

  Estimate abundance-based species richness with ACE using the species observed at most ten times, their total individuals, singleton count, and the rare-frequency moment sum i(i-1)f_i. ACE is undefined when every rare individual is a singleton.