Biodiversity Index Calculator

Biodiversity cannot be captured in a single number — but ecologists routinely need to compare sites, track change over time, and communicate diversity in a format comparable across studies. The three indices this calculator computes are complementary: Margalef captures how many species are present relative to sample size; Shannon captures both richness and evenness in an information-theoretic framework; and Simpson's captures the probability that two random individuals belong to the same species. The biodiversity index calculator provides all three simultaneously from the same input data.

The Three Indices: Formulas and Interpretation

Margalef Richness Index (d):

d = (S − 1) / ln(N)

where S = number of species, N = total number of individuals. Ranges from 0 upward; higher values indicate greater species richness relative to sample size. Reference: below 2.5 = low richness; 2.5–5.0 = medium; above 5.0 = high.

Shannon-Wiener Index (H'):

H' = −Σ pᵢ × ln(pᵢ) where pᵢ = proportion of individuals belonging to species i. Range: 0 to ln(S) maximum. Typical ecological values: 1.5–3.5; higher values indicate more equitable distribution of individuals across species.

Simpson's Diversity Index (1 − D):

D = Σ [nᵢ(nᵢ−1)] / [N(N−1)]; Simpson's diversity = 1 − D. Range: 0 (no diversity) to 1 (infinite diversity). D alone represents the probability two randomly selected individuals belong to the same species; 1−D is the complement — probability they belong to different species.

Use this online calculator for any species count and total individuals. The Shannon diversity calculator and biodiversity calculators provide focused analysis of individual indices.

Choosing Between Indices: What Each Captures

The three indices weight aspects of biodiversity differently:

• Margalef: primarily species richness (number of species); simple to compute from minimal data; strongly influenced by sample size; poor for comparing sites with very different sampling effort
• Shannon: balances richness and evenness; responds to changes in both species number and relative abundances; more sensitive to rare species than Simpson's
• Simpson's: dominated by the most abundant species; weighted toward common species; more sensitive to changes in dominant species abundances than rare species; the most robust to sampling effort differences

For environmental impact assessments (EIA), reporting all three is standard practice because they capture different facets of the biological community being protected.

Pielou's Evenness: The Complementary Metric

The Shannon index H' combines richness and evenness, making it difficult to distinguish which changes when communities shift. Pielou's evenness (J) isolates the evenness component:

J = H' / H'_max = H' / ln(S)

J ranges from 0 (one species dominates all individuals) to 1 (all species equally abundant). A site with H' = 2.5 and S = 20 species has J = 2.5/ln(20) = 2.5/2.996 = 0.835 — relatively even distribution. A site with H' = 1.0 and S = 20 species has J = 0.334 — very uneven, with one or few species dominating. Using H' and J together fully characterizes the richness-evenness contribution to Shannon diversity. The evenness index calculator computes Pielou's J separately.

Rarefaction: Comparing Sites with Different Sample Sizes

Direct comparison of species richness between sites sampled with different effort is misleading — more intensive sampling always finds more species. Rarefaction standardizes species counts to the same number of individuals by asking: how many species would we expect if we had sampled only n individuals from each site? The rarefied expected species count E(S_n) = S − Σ C(N−nᵢ, n) / C(N, n) where nᵢ is the count of species i and n is the standardized sample size. Rarefaction curves plotting E(S_n) vs. n allow valid comparison across sites with different total sampling effort.