Species Richness Estimator

Estimate true species richness from sample data using nonparametric estimators.

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Why Singletons Predict What You Missed

Chao1 rests on a simple insight: the number of species seen exactly once tells you how many you have not seen at all. If most species in your sample are singletons, sampling is clearly incomplete. If almost none are, you have probably found nearly everything.

Chao1 = Sobs + f1² / (2f2)
PatternInterpretation
Many singletons, few doubletonsLarge undetected richness
Few singletonsNear-complete inventory
f2 = 0Formula undefined — use the bias-corrected form

The estimator is a lower bound, not a point estimate. True richness is at least Chao1 and often higher, particularly when sampling is sparse. This is why it should be reported with confidence intervals rather than as a single number.

Coverage and Rarefaction

Good–Turing coverage ≈ 1 − f1/n

Coverage estimates the proportion of individuals in the community belonging to species you actually detected. Ninety-nine percent coverage sounds excellent, yet it can still conceal many rare species — because rare species contribute few individuals by definition.

Comparing richness between samples of unequal size is invalid, since larger samples always yield more species. Rarefaction subsamples to a common size to make comparison meaningful. Increasingly, coverage-based standardisation is preferred, since equal sample size does not guarantee equal completeness across communities of different evenness.

Worked Examples

Example 1: Forest birds: Sobs=50, f1=20, f2=8, n=200
Chao1=50+400/16=75
Result: 25 more species estimated
41% of species undetected with this sample
Example 2: High coverage: f1=2, f2=3, Sobs=50
Chao1=50+4/6=50.7
Result: Near-complete inventory
Low singletons = good sampling completeness
Example 3: Why sequencing depth misleads
99.6% coverage but 40 singletons in 150 OTUs
Result: Substantial undetected richness
Coverage is high because rare taxa contribute few reads. A quarter of observed OTUs being singletons signals incomplete sampling.
Example 4: Why rarefaction is needed
Sample A: 5,000 reads, 120 OTUs. Sample B: 20,000 reads, 180 OTUs
Result: Not directly comparable
B may be no richer, merely sampled four times deeper. Subsampling B to 5,000 reads gives a fair comparison.

Common Mistakes

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Treating Chao1 as a point estimate

It is a lower bound. True richness is at least Chao1 and frequently higher, especially with sparse sampling. Report confidence intervals.

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Comparing raw richness across sample sizes

Larger samples always detect more species. Rarefy to a common size, or better, standardise by coverage.

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Using the standard formula when f2 = 0

The estimator is undefined with no doubletons. The bias-corrected variant handles this case.

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Assuming high coverage means complete sampling

Coverage weights by individuals, so rare species contribute little. Ninety-nine percent coverage can still miss many species.

Frequently Asked Questions

Why Chao1?
Minimum lower bound estimator of true richness. Uses ratio f1²/2f2 (rare species frequency). Assumes: closed population, no individual heterogeneity. For heterogeneous detection: use abundance-based coverage estimator (ACE) or iNEXT rarefaction/extrapolation.
Rarefaction?
Standardize species counts to equal sample size. Random subsample n individuals from sample: count expected species. Compare across sites with different sampling effort. Rarefaction curve: species vs sample size. Saturates = good sampling.
What does Chao1 estimate?
Total species richness including undetected species, using the ratio of singletons to doubletons. It is a lower bound rather than a point estimate.
Why do singletons indicate incomplete sampling?
Species seen once are those on the edge of detection. Many singletons imply many more species just below the detection threshold.
What is rarefaction?
Subsampling to a common number of individuals or reads so richness can be compared fairly. Larger samples otherwise always appear richer.
Does high coverage mean complete sampling?
No. Coverage weights by individuals, and rare species contribute few. A sample can have 99% coverage while missing many rare species.