Simpson Diversity Index (D = 1 − Σpᵢ²)

Simpson Diversity Index (D = 1 − Σpᵢ²) | Online Free Tool | Elysia Tools

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category: Health
Input types: textarea
Output type: json
Sample coverage: 4
API ready: Yes

Overview

Enter species abundance counts (one per line, or separated by commas or spaces) to compute Simpson-family diversity metrics. The calculator returns Gini–Simpson D = 1 − Σpᵢ², dominance λ = Σpᵢ², the reciprocal 1/λ (effective species number), and Simpson evenness from the observed richness and total N.

When to use

You have raw species counts from a plot, transect, or lab sample and need D, λ, 1/λ, and evenness in one step.
You want the probability that two random individuals belong to different species, plus the equivalent number of equally common taxa.
You need to compare community structure when literature uses different Simpson conventions (λ, 1 − λ, or 1/λ).

How it works

1Paste positive abundance counts for each species; zeros and empty lines are ignored. At least two species with positive counts are required.
2The tool converts counts to proportions pᵢ, then computes λ = Σpᵢ², Gini–Simpson D = 1 − λ, the reciprocal 1/λ, and evenness (1/λ)/S.
3Results include richness S, total N, the proportion vector, and a short interpretation of dominance versus evenness.
4All four Simpson-family values are reported so you can match the definition used in your field.

Use cases

Summarize plot or quadrat counts into Gini–Simpson D and effective species number for biodiversity reports.
Check whether a community is dominated (high λ, low 1/λ) or relatively even before comparing sites.
Convert lab or field species tallies into λ, D, 1/λ, and evenness for ecology coursework or papers.

Examples

1. Five-species mixed stand

Field ecologist

Background

A 100-stem inventory of a mixed forest plot recorded five taxa with counts 40, 25, 20, 10, and 5.

Problem

Need Gini–Simpson D, dominance λ, effective species number, and evenness instead of richness alone.

How to use

Paste the five counts into Species counts, one per line (or as a comma-separated list).

Outcome

S = 5, N = 100, λ = 0.2750, D = 0.7250, 1/λ ≈ 3.64 effective species, evenness ≈ 0.73 — abundance is spread across taxa rather than dominated by one.

2. Near-monoculture sample

Lab technician

Background

A culture or plot is visually dominated by one taxon; counts are 90, 5, and 5.

Problem

Quantify how strongly one species holds probability mass and how few effective species remain.

How to use

Enter the three abundances in the counts field.

90
5
5

FAQ

What counts can I enter?

One non-negative abundance per species, separated by new lines, commas, or spaces. Only positive counts contribute to richness and the indices.

What is Gini–Simpson D?

D = 1 − Σpᵢ² is the probability that two randomly drawn individuals belong to different species. It ranges from 0 (complete dominance) toward 1 (high diversity).

How is the reciprocal 1/λ interpreted?

1/λ is the Hill number of order 2: the number of equally common species that would produce the same λ. It is easier to compare across communities than D.

What is Simpson evenness?

Evenness is (1/λ)/S. Values near 1 mean abundances are similar; lower values indicate a few taxa dominate.

Why do some papers call λ the Simpson index?

Literature uses λ, 1 − λ, or 1/λ interchangeably. This tool reports all three so you can match the convention in your source.

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Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Overview

When to use

How it works

Use cases

Examples

1. Five-species mixed stand

2. Near-monoculture sample

FAQ

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