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Simpson's Diversity Index

Measure biodiversity using Simpson’s index.

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Core idea

Overview

Simpson's Diversity Index is a statistical measure used to quantify the biodiversity of a habitat by accounting for both species richness and evenness. It calculates the probability that two individuals randomly selected from a sample will belong to different species, with values ranging from 0 for a monoculture to 1 for infinite diversity.

When to use: This index is best used when comparing two distinct ecological communities or tracking the impact of environmental changes on a single site over time. It is particularly effective for large datasets where calculating relative abundance is more informative than simply counting the number of species present.

Why it matters: Biodiversity is a key indicator of ecosystem health and resilience; higher diversity typically suggests a more stable environment capable of withstanding stressors. Conservationists use this metric to identify habitats requiring protection and to measure the success of restoration projects.

Symbols

Variables

D = Simpson's Diversity Index, n = Individuals in Species, N = Total Individuals, Diversity Index = Diversity Index

Simpson's Diversity Index
Variable
Individuals in Species
Variable
Total Individuals
Variable
Diversity Index
Diversity Index
Variable

Walkthrough

Derivation

Formula: Simpson's Diversity Index (D)

Simpson’s index estimates diversity by considering both richness and evenness. Higher values indicate greater diversity (for the D form given here).

  • Sample is representative.
  • Individuals are correctly identified and counted.
1

Identify Variables:

You need the total number of organisms and the count for each species.

2

State One Common A-Level Form:

For each species, compute , sum across species, then subtract from 1.

Note: Some boards use . Always use the form your exam board specifies.

Result

Source: OCR A-Level Biology A — Biodiversity

Visual intuition

Graph

Graph unavailable for this formula.

The graph displays a linear relationship where the diversity index y increases at a constant one-to-one rate as the Simpson's Diversity Index D increases. For a biology student, this means that higher values of D represent a more diverse ecosystem, while lower values indicate reduced biodiversity. The most important feature of this curve is that the linear relationship means any change in D results in an identical change in the diversity index, showing a direct proportional connection between the two.

Graph type: linear

Why it behaves this way

Intuition

Imagine randomly drawing two organisms from a habitat; the index quantifies the likelihood that these two organisms will represent different species, reflecting the variety and balance of life present.

Simpson's Diversity Index; the probability that two individuals randomly selected from a sample will belong to different species.
A higher D value signifies greater biodiversity, reflecting more species and/or a more even distribution of individuals among species.
The number of individuals of a particular species within the sample.
Represents the abundance of a single species.
The total number of individuals of all species in the sample.
Represents the total size of the ecological community being sampled.
n/N
The proportional abundance of a specific species.
Indicates how common a single species is relative to the entire community.
Simpson's Index of Dominance; the probability that two individuals randomly selected from the sample will belong to the *same* species.
A higher value means a few species dominate the community, indicating lower diversity.

Signs and relationships

  • 1 - sum(n/N)^2: The subtraction from 1 transforms the 'probability of picking two of the same species' (sum(n/N)^2) into the 'probability of picking two *different* species'.

Free study cues

Insight

Canonical usage

Used to calculate a dimensionless index of biodiversity, where the input quantities 'n' and 'N' are counts of individuals.

Common confusion

A common mistake is attempting to assign physical units to the index D, or to the counts 'n' and 'N' beyond simply 'individuals' or 'counts'. The 'n/N' ratio must always be dimensionless.

Dimension note

Simpson's Diversity Index is inherently dimensionless, as it is derived from ratios of counts of individuals. The value represents a probability and ranges from 0 to 1.

Unit systems

count · Represents the number of individuals belonging to a specific species.
count · Represents the total number of individuals across all species in the sample.
dimensionless · Simpson's Diversity Index, a probability value between 0 and 1.

One free problem

Practice Problem

An island ecosystem contains 2 species of lizards. There are 50 individuals of the first species and 50 individuals of the second species, for a total of 100 lizards. Calculate the Simpson's Index of Diversity (D).

Individuals in Species50
Total Individuals100

Solve for:

Hint: Divide the count of each species by the total population, square those values, sum them, and subtract from 1.

The full worked solution stays in the interactive walkthrough.

Where it shows up

Real-World Context

When comparing biodiversity across two habitats, Simpson's Diversity Index is used to calculate Diversity Index from Simpson's Diversity Index, Individuals in Species, and Total Individuals. The result matters because it helps compare populations or ecosystems and decide whether the system is growing, stable, or under stress.

Study smarter

Tips

  • Ensure the sum of all individual species counts (n) is exactly equal to the total population size (N).
  • A value of 0 means no diversity (only one species exists), while values closer to 1 indicate high diversity.
  • Always square the relative abundance (n/N) for each species individually before calculating the total sum.
  • The index specifically measures the probability that two random individuals will be different species.

Avoid these traps

Common Mistakes

  • Using raw counts without dividing by N.
  • Forgetting the final 1 - sum step.

Common questions

Frequently Asked Questions

Simpson’s index estimates diversity by considering both richness and evenness. Higher values indicate greater diversity (for the D form given here).

This index is best used when comparing two distinct ecological communities or tracking the impact of environmental changes on a single site over time. It is particularly effective for large datasets where calculating relative abundance is more informative than simply counting the number of species present.

Biodiversity is a key indicator of ecosystem health and resilience; higher diversity typically suggests a more stable environment capable of withstanding stressors. Conservationists use this metric to identify habitats requiring protection and to measure the success of restoration projects.

Using raw counts without dividing by N. Forgetting the final 1 - sum step.

When comparing biodiversity across two habitats, Simpson's Diversity Index is used to calculate Diversity Index from Simpson's Diversity Index, Individuals in Species, and Total Individuals. The result matters because it helps compare populations or ecosystems and decide whether the system is growing, stable, or under stress.

Ensure the sum of all individual species counts (n) is exactly equal to the total population size (N). A value of 0 means no diversity (only one species exists), while values closer to 1 indicate high diversity. Always square the relative abundance (n/N) for each species individually before calculating the total sum. The index specifically measures the probability that two random individuals will be different species.

References

Sources

  1. Wikipedia: Simpson index
  2. Campbell Biology
  3. Britannica: Simpson's diversity index
  4. AQA Biology A-level Textbook by Glenn Toole and Susan Toole
  5. Ecology: From Individuals to Ecosystems by Michael Begon, Colin R. Townsend, and John L. Harper
  6. OCR A-Level Biology A — Biodiversity