This is the one page in the sub-topic with a calculation on it. You will be given Simpson’s formula in the exam, so what is being tested is whether you can organise the data, apply it correctly, and say what the answer means.
📘 What you need to know
Species richness is the number of species in a community or defined area.
Richness alone can be misleading, because it ignores how many individuals each species has.
Species evenness is the evenness of abundance across the different species.
Species diversity combines richness and evenness, which is why conservationists prefer it.
Simpson’s diversity index quantifies diversity so communities can be compared.
A higher D means greater richness and evenness. The lowest possible value of D is 1.
The index is only useful for comparing two similar habitats, or the same habitat over time.
Richness is not enough
Species richness is the number of species in a community or defined area. It is sometimes a useful way to compare the biodiversity of different areas, but it can also be a misleading indicator, because it takes no account of the number of individuals of each species.
Once the abundance of each species has been recorded, you can calculate species diversity, which looks at the number of species and the species evenness — how evenly abundance is spread across them.
Area 2 is dominated by one species, and one of its species is represented by a single individual. Richness cannot see either fact.
Species diversity is a much more informative measurement than richness, and conservationists usually favour it because it takes both richness and evenness into account.
Simpson’s diversity index
Biological communities can be described and compared using diversity indices — mathematical tools that quantify the diversity of species within a community. They measure the variety of species present as well as their relative abundances, so you can compare different communities or track changes in one community over time. The commonly used one is Simpson’s index.
Simpson’s diversity index
D = N(N − 1) ÷ Σ n(n − 1) D = Simpson’s diversity index N = total number of individuals sampled n = number of individuals of each species
WE 1
Calculating Simpson’s index for two river sites
Students used kick sampling to collect and count invertebrates at two sites along a river. Calculate Simpson’s diversity index for each site and compare them. (6 marks)
Species
Site A: n
Site A: n(n−1)
Site B: n
Site B: n(n−1)
Mite
14
182
0
0
Snail
9
72
0
0
Leech
3
6
26
650
Worm
0
0
6
30
Flat worm
132
17 292
9
72
Mayfly nymph
43
1 806
0
0
Olive mayfly nymph
154
23 562
0
0
Midge larva
0
0
10
90
Blackfly larva
77
5 852
0
0
Caddis larva
15
210
1
0
Fish
1
0
0
0
Freshwater shrimp
211
44 310
6
30
Water hog louse
0
0
40
1 560
Total
N = 659
93 292
N = 98
2 432
Step 1: work out n(n−1) for every species
For each species, multiply its count by one less than its count. Freshwater shrimp at Site A: 211 × 210 = 44 310. Species with 0 or 1 individuals contribute nothing.
Step 2: total the columns
Site A: N = 659 and Σn(n−1) = 93 292. Site B: N = 98 and Σn(n−1) = 2 432.
Site A: D = 659 × 658 ÷ 93 292 = 433 622 ÷ 93 292 = 4.65Site B: D = 98 × 97 ÷ 2 432 = 9 506 ÷ 2 432 = 3.91Step 3: interpret
Site B has the lower species diversity. Site A has both more species present and a more even spread of individuals among them.
Site A: D = 4.65 Site B: D = 3.91quote D to two decimal places and always say which site is more diverse
What the number means
D has no fixed maximum, so a value is only meaningful next to another value from a comparable place or time.
The value of D is higher where there is greater richness (more species) and greater evenness (similar abundances).
The lowest possible value of D is 1.
The index is only useful when comparing two similar habitats, or the same habitat over time.
You will be given Simpson’s formula in the exam, so do not waste revision time memorising it. What you must be able to do is set the data out in a table, compute n(n−1) for every species without dropping one, total both columns, and then say clearly which community is more diverse and why. Most marks lost here are arithmetic slips, not conceptual errors.
A note on the data. Some versions of this classic dataset swap the leech and worm counts between the data table and the working. It makes no difference to the answer, because 6 × 5 and 26 × 25 are both added into the same total either way — but it is a useful reminder to check your own transcription before you start multiplying.
More worked examples
WE 2
Richness versus diversity
Two areas each contain four tree species. Explain why they may still differ in species diversity. (3 marks)
Step 1: what is the same
Both areas have the same species richness, because richness counts only the number of species present.
Step 2: what richness misses
Richness does not take into account the number of individuals of each species, so it cannot detect dominance or rarity.
Step 3: the difference
If one area is dominated by a single species and contains a very rare species with only one individual, its species evenness is lower. Since species diversity combines richness and evenness, that area has lower diversity.
Identical richness, different evenness, therefore different diversitythis is exactly why conservationists prefer diversity to richness
WE 3
Limits of the index
State one limitation of using Simpson’s diversity index to compare two ecosystems. (2 marks)
The limitation
The index is only useful when comparing two similar habitats, or the same habitat over time.
Why this matters
Different habitat types naturally support different numbers and distributions of species, so a difference in D between, say, a river and a woodland reflects the habitats being different rather than one being degraded.
D is a comparative measure, not an absolute scorethis limitation is stated explicitly in the syllabus, so it is a reliable mark
💡 Exam tips
The formula is given in the exam. Practise applying it, not reciting it.
Set out a table with an n(n−1) column and fill in every species, including zeros.
Remember species with 0 or 1 individuals contribute 0 to the sum.
Quote D to two decimal places and state which community is more diverse.
Say the lowest possible value of D is 1.
Note the limitation: only compare similar habitats or the same habitat over time.
⚠ Common mistakes
Using n(n−1) for N as well, or vice versa. N is the grand total; n is per species.
Dropping species with zero counts. Include them in the table so nothing is missed.
Forgetting that a species with one individual contributes 0. 1 × 0 = 0.
Reporting D with no comparison. A single value on its own means little.
Assuming higher richness always means higher D. Evenness can outweigh it.
Comparing unlike habitats. The index is not designed for that.
Up next: Managing Biodiversity in Practice. You can now measure biodiversity. The next page is about who collects that data at global and local scales, and what gets done with it.
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