Calculate and interpret Simpson’s index
Use the supplied Simpson’s index formula and interpret higher values as greater diversity.
A Level; Cambridge International Biology 9700, 2028–2030. Written responses are self-checked; this does not certify supervised fieldwork or practical competence.
Before you begin
- Classification compares shared characteristics; populations occupy environments and contain variation.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What does a higher Simpson’s diversity value indicate in this formula form?
What you will learn
- Calculate Simpson’s index from the number of individuals in each type
- Interpret different index values and compare samples
Build the explanation
For counts nᵢ of each type and total N, the supplied formula is D=1−Σ[nᵢ(nᵢ−1)]/[N(N−1)]. It accounts for both the number of types and their relative abundance. For this form, values closer to 1 indicate greater diversity; values closer to 0 indicate lower diversity dominated by fewer types.
Use evidence within scope
Use a complete count from a comparable sample, check that Σnᵢ=N and preserve parentheses. Compare sites sampled with the same method and effort; an index is an estimate and does not describe every ecological feature.
Pause and explain
Why should D values from unequal sampling effort be compared cautiously?
Worked example
Counts are 5, 3 and 2 individuals. Calculate D using the supplied formula.
Show the worked solution
- N=10.
- Σn(n−1)=20+6+2=28.
- D=1−28/(10×9).
Answer D≈0.69. The value should be interpreted as an estimate for the sampled community.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A sample has counts 4 and 4. Find N and Σn(n−1).
Give me a hint
Identify the required evidence and sequence the reasoning.
Compare my reasoning
- N=4+4.
- Calculate 4×3 for each type.
N=8 and Σn(n−1)=12+12=24, using each species count separately.
Look for these in your work
- Relevant evidence selected
- Reasoning linked to conclusion
Two equally sampled sites have D=0.81 and D=0.36. Which has greater estimated diversity?
Give me a hint
Use the supplied example or data to justify a conclusion.
Compare my reasoning
- Use the stated interpretation for this formula.
- The value closer to 1 is higher.
The site with D=0.81 has greater estimated diversity in this formula form.
Look for these in your work
- Concept applied
- Limit or assumption stated
Why should D values from unequal sampling effort be compared cautiously?
Give me a hint
Apply the concept in a new context and qualify its limits.
Compare my reasoning
- The sample may represent the communities differently.
- Use comparable methods and effort.
Unequal effort can miss rare types in the smaller sample and alter relative counts, so the estimates are less directly comparable.
Look for these in your work
- New context handled
- Conclusion appropriately bounded
Common mistakes
- Using N for each species count
- Treating the index as a direct species count
What can you explain now?
What does a higher Simpson’s diversity value indicate in this formula form?
Compare with the explanation
Greater diversity in the sample
The value rises when types are more numerous or more evenly represented.
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Make it stick
What do the counts nᵢ, total N and the resulting Simpson index describe?
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