The Simpson’s diversity index

The Simpson's index of diversity calculates biodiversity using the number of species and their relative abundances. That is, it takes both species richness and species evenness into account.

It is calculated as:

$D=1-(\sum {(\frac{n}{N})}^2)$

Where:

• $\text{n }=\text{ number of individuals of each species}$
• $\text{N }=\text{ total number of all individuals}$

D ranges from 0 to 1, with 1 representing maximum diversity.

Worked example - Calculating the Simpson’s diversity index

A biologist is assessing the biodiversity of two fields. field A contains 150 individual plants, consisting of 85 daisies, 35 buttercups, and 30 clovers. field B contains 150 individual plants, consisting of 55 daisies, 45 buttercups, and 50 clovers.

Calculate and compare the diversity indices for each habitat.

Step 1: Equation

$D=1-(\sum {\left(\frac{n}{N}\right)}^2)$

Step 2: Construct a table to calculate $\sum {\left(\frac{n}{N}\right)}^2$ for field A

Step 3: Substitution and correct evaluation for field A

$\text{diversity of field A }=1-(\sum {\left(\frac{n}{N}\right)}^2)$

$\text{diversity of field A }=1-0.4156\text{...}$

$\text{diversity of field A }=0.584\text{ (to 3 s.f.)}$

Step 4: Construct a table to calculate $\sum {\left(\frac{n}{N}\right)}^2$ for field B

Step 5: Substitution and correct evaluation for field B

$\text{diversity of field B }=1-(\sum {\left(\frac{n}{N}\right)}^2)$

$\text{diversity of field B }=1-0.3356\text{...}$

$\text{diversity of field B }=0.664\text{ (to 3 s.f.)}$

Step 6: Interpretation of result

the Simpson’s diversity index for field A is 0.584 and for field B it is 0.664, which indicates that field B has a higher species diversity compared to field A