Ecologists investigated changes in grassland communities on large islands off the coast of Scotland between 1975 and 2010 - AQA - A-Level Biology - Question 4 - 2017 - Paper 3

Calculate n(n-1) for each species and sum them:

• For Hydrocotyle vulgaris: $3(3-1) = 6$
• For Plantago maritima: $19(19-1) = 342$
• For Ranunculus acris: $3(3-1) = 6$
• For Hieracium pilosella: $3(3-1) = 6$
• For Callicorg cuspidatum: $10(10-1) = 90$
• For Prunella vulgaris: $16(16-1) = 240$
• For Pseudoscleropodium purum: $6(6-1) = 30$

Summing these gives:

$\Sigma(n(n-1)) = 6 + 342 + 6 + 6 + 90 + 240 + 30 = 720$

Using the formula for the index of diversity:

$d = \frac{N(N-1)}{\Sigma(n(n-1))}$

We substitute N and \Sigma(n(n-1)):

$d = \frac{59(59-1)}{720} = \frac{59 \times 58}{720} = \frac{3422}{720} \approx 4.92$