Biodiversity Index
Simpson's Index of Diversity.
This public page keeps the free explanation visible and leaves premium worked solving, advanced walkthroughs, and saved study tools inside the app.
Core idea
Overview
Simpson's Index of Diversity (D) measures the probability that two individuals randomly selected from a sample will belong to different species. It integrates species richness and evenness into a single value, where a result closer to 1 indicates high diversity and a value closer to 0 indicates a monoculture.
When to use: Use this formula when evaluating the ecological health of a habitat or comparing different biological communities. It is best suited for scenarios where you have a sample representing the total population and want to account for the dominance of specific species rather than just the total number of species.
Why it matters: This index is a standard metric in conservation biology for identifying resilient ecosystems that can better withstand environmental changes. High biodiversity indices often correlate with complex food webs and greater ecosystem stability, helping scientists prioritize areas for environmental protection.
Symbols
Variables
D = Diversity Index, (n/N)^2 = Sum of (n/N)^2
Walkthrough
Derivation
Understanding Biodiversity Index (Simpson’s Index idea)
Biodiversity indices combine species richness and evenness into a single value, so a habitat dominated by one species scores lower than a balanced habitat.
- The sample is representative of the habitat.
- Individuals are identified and counted accurately.
Define Totals:
Count the total number of individuals N and the count for each species .
Use Proportions to Include Evenness:
Convert each species count into a proportion of the total so dominance can be detected.
Example Index Form (Simpson-style):
Square each species proportion, sum them, then subtract from 1. The value increases when individuals are spread more evenly across species.
Note: Some boards use an alternative equivalent form. Always use the exact formula required by your specification.
Result
Source: AQA A-Level Biology — Biodiversity
Free formulas
Rearrangements
Solve for
Make D the subject
D is already the subject of the formula.
Difficulty: 1/5
Solve for
Make Sigma (n/N)^2 the subject
Start from Biodiversity Index. To make Sigma (n/N)^2 the subject, clear N, then simplify to isolate Sigma (n/N)^2.
Difficulty: 4/5
The static page shows the finished rearrangements. The app keeps the full worked algebra walkthrough.
Visual intuition
Graph
The graph is a downward-sloping linear line with a y-intercept of 1 and a constant negative slope of -1, passing through the points (1, 0) and (0, 1). In biological terms, a small x-value indicates a high diversity index, while a large x-value represents a low diversity index. The most important feature is the inverse linear relationship, which means that any increase in the sum of the squared proportions results in an identical decrease in the diversity index.
Graph type: linear
Why it behaves this way
Intuition
Imagine a bag of marbles, where each marble represents an individual organism and its color represents its species; the index quantifies the chance of pulling out two marbles of different colors from the bag.
Signs and relationships
- 1 - ...: The subtraction from 1 transforms the probability of selecting two individuals of the *same* species into the probability of selecting two individuals of *different* species, which is the core definition of diversity for
- ^2: Squaring the proportion (n/N) gives disproportionately more weight to dominant species. This means that a few very common species will significantly increase the probability of picking the same species, thereby lowering
Free study cues
Insight
Canonical usage
Simpson's Index of Diversity (D) is a dimensionless quantity, representing a probability or an index value derived from counts of individuals.
Common confusion
Students sometimes mistakenly attempt to assign units such as 'species' or 'individuals' to the Simpson's Index, when it is fundamentally a dimensionless probability or ratio.
Dimension note
The index is dimensionless because it is calculated from ratios of counts of individuals (n/N). Both the numerator and denominator represent counts of individuals, effectively cancelling out any implicit 'units' and
Unit systems
One free problem
Practice Problem
A biologist surveying a coastal tide pool finds 2 species: 15 sea anemones and 35 hermit crabs. Calculate the Biodiversity Index (D) for this community.
Solve for:
Hint: First find the total population N, then calculate the sum of (n/N)² for both species before subtracting from 1.
The full worked solution stays in the interactive walkthrough.
Where it shows up
Real-World Context
When comparing diversity between two habitats, Biodiversity Index is used to calculate Diversity Index from Sum of (n/N)^2. The result matters because it helps compare populations or ecosystems and decide whether the system is growing, stable, or under stress.
Study smarter
Tips
- Calculate the total population size N by summing the counts (n) of every species present.
- The term (n/N) represents the relative abundance of a single species in the community.
- Ensure you square each individual relative abundance before summing them together.
- Always subtract the final sum of squares from 1 to obtain the Index of Diversity (D).
Avoid these traps
Common Mistakes
- Confusing D with the sum term.
- Using percentages instead of proportions.
Common questions
Frequently Asked Questions
Biodiversity indices combine species richness and evenness into a single value, so a habitat dominated by one species scores lower than a balanced habitat.
Use this formula when evaluating the ecological health of a habitat or comparing different biological communities. It is best suited for scenarios where you have a sample representing the total population and want to account for the dominance of specific species rather than just the total number of species.
This index is a standard metric in conservation biology for identifying resilient ecosystems that can better withstand environmental changes. High biodiversity indices often correlate with complex food webs and greater ecosystem stability, helping scientists prioritize areas for environmental protection.
Confusing D with the sum term. Using percentages instead of proportions.
When comparing diversity between two habitats, Biodiversity Index is used to calculate Diversity Index from Sum of (n/N)^2. The result matters because it helps compare populations or ecosystems and decide whether the system is growing, stable, or under stress.
Calculate the total population size N by summing the counts (n) of every species present. The term (n/N) represents the relative abundance of a single species in the community. Ensure you square each individual relative abundance before summing them together. Always subtract the final sum of squares from 1 to obtain the Index of Diversity (D).
References
Sources
- Wikipedia: Simpson index
- Britannica: Simpson's diversity index
- Ecology: From Individuals to Ecosystems (Begon, Townsend, Harper)
- Magurran, Anne E. Ecological Diversity and Its Measurement. Princeton University Press, 2004.
- Begon, Michael, Colin R. Townsend, and John L. Harper. Ecology: From Individuals to Ecosystems. Wiley-Blackwell, 2006.
- AQA A-Level Biology — Biodiversity