Community Diversity Index Calculator (Shannon / Simpson / Chao1)

The most common α-diversity metrics in microbiome and ecology studies all have short formulas, but they measure different things — conflating them can lead to opposite conclusions.

Let pᵢ = nᵢ / N be the relative abundance of species i, and S the observed species richness:

Shannon index　H = −Σ pᵢ ln pᵢ
Reflects both species richness and evenness. Sensitive to rare species — a few extra low-abundance species will noticeably increase H.

Simpson index　D = Σ pᵢ²
The probability that two randomly drawn individuals belong to the same species, so higher D means lower diversity. Common variants: 1 − D (Gini-Simpson) and 1/D (inverse Simpson). Simpson is dominated by abundant species and is insensitive to rare ones.

Pielou evenness　J = H / ln S
Divides H by the effect of species richness, capturing only how evenly abundances are distributed; ranges from 0 to 1.

Chao1 richness estimator　Uses the count of singletons (F₁, species seen once) and doubletons (F₂, species seen twice) to estimate unobserved species. This tool applies the bias-corrected form:

Chao1 = S + F₁(F₁ − 1) / (2(F₂ + 1))

The bias-corrected form is used instead of the classic S + F₁²/(2F₂) because the classic formula divides by zero when F₂ = 0.

Three things you must know:

1. Samples with different sequencing depths cannot be compared directly. Greater depth captures more rare species, inflating both Shannon and Chao1. Rarefy or apply another normalization method before comparing.
2. Chao1 requires count data. Computing Chao1 on relative abundances or fractional rarefied counts is meaningless, because the definitions of singleton and doubleton depend on true integer counts.
3. Singletons in amplicon data are often sequencing errors. Many pipelines remove them upstream — which substantially distorts Chao1. Verify whether your pipeline filtered singletons before reporting this metric.