use Simpson’s index of diversity (D) to calculate the biodiversity of an area, and state the significance of different values of D (the formula for Simpson’s index of diversity will be provided, as shown in the Mathematical requirements)

Published by Patrick Mutisya · 14 days ago

Cambridge A‑Level Biology 9700 – Biodiversity: Simpson’s Index of Diversity (D)

Biodiversity – Simpson’s Index of Diversity (D)

Learning Objective

Students will be able to use Simpson’s index of diversity (D) to calculate the biodiversity of a given area and interpret the ecological significance of different D values.

Key Concepts

  • Biodiversity: the variety of living organisms within a particular habitat or ecosystem.

  • Species richness (S): the number of different species present.

  • Species evenness: how equally individuals are distributed among the species.

  • Simpson’s index of diversity (D): a quantitative measure that combines species richness and evenness.

Mathematical Requirement

Simpson’s index of diversity is calculated using the following formula:

\$\$

D = 1 - \frac{\displaystyle\sum{i=1}^{S} ni (n_i - 1)}{N (N - 1)}

\$\$

where:

  • \$S\$ = total number of species in the sample.

  • \$n_i\$ = number of individuals of species \$i\$.

  • \$N\$ = total number of individuals of all species (\$N = \sum{i=1}^{S} ni\$).

Step‑by‑Step Calculation

  1. List each species and count the number of individuals (\$n_i\$).

  2. Calculate \$N\$, the sum of all \$n_i\$ values.

  3. For each species, compute \$ni (ni - 1)\$.

  4. Sum the values from step 3 to obtain \$\displaystyle\sum ni (ni - 1)\$.

  5. Insert the values into the formula and solve for \$D\$.

  6. Interpret the resulting \$D\$ value (see the interpretation table below).

Worked Example

Consider a woodland plot in which four species of trees have been recorded as follows:

SpeciesNumber of individuals (\$n_i\$)\$ni (ni - 1)\$
Oak (A)4040 × 39 = 1560
Birch (B)3030 × 29 = 870
Hazel (C)2020 × 19 = 380
Willow (D)1010 × 9 = 90

Calculate the totals:

  • \$N = 40 + 30 + 20 + 10 = 100\$

  • \$\displaystyle\sum ni (ni - 1) = 1560 + 870 + 380 + 90 = 2900\$

Insert into the formula:

\$\$

D = 1 - \frac{2900}{100 \times 99} = 1 - \frac{2900}{9900} = 1 - 0.2939 \approx 0.706

\$\$

Interpretation of Simpson’s Index (D)

The value of \$D\$ ranges from 0 to 1:

Range of \$D\$Ecological Significance
0 ≤ \$D\$ < 0.2Very low diversity – community dominated by one or two species.
0.2 ≤ \$D\$ < 0.5Low to moderate diversity – a few species are common, others are rare.
0.5 ≤ \$D\$ < 0.8Moderate to high diversity – relatively even distribution of individuals among species.
0.8 ≤ \$D\$ ≤ 1.0Very high diversity – no single species dominates; high evenness.

In the example above, \$D \approx 0.71\$, placing the woodland in the “moderate to high diversity” category. This indicates a fairly even distribution of individuals among the four tree species, suggesting a healthy and resilient ecosystem.

Suggested diagram: A pie chart or bar graph showing the proportional abundance of each species in the example, illustrating how evenness contributes to a higher \$D\$ value.