In a forest plot the numbers of four tree species are as follows: Species A = 30, Species B = 15, Species C = 10, Species D = 5. Calculate the Simpson’s diversity index ( $1 - D$ ).

medium 2 marks Class 12 · Biology · Biodiversity and Conservation

Answer

0.664 (approx)

The correct answer is 0.664 (approx) — Step 3: Sum these values: $870 + 210 + 90 + 20 = 1190$ . Step 4: Compute $N (N - 1)$ : $60 \times 59 = 3540$ . Step 5: Find $D = \frac{1190}{3540} \approx 0.336$ . Step 6: The diversity index is $1 - D = 1 - 0.336 = 0.664$ . Step 7: Round to three decimal places giving 0.664.

Step-by-step solution

Step 1: Compute the total number of individuals $N$ = 30+15+10+5 = 60.
Step 2: Calculate $n_{i} (n_{i} - 1)$ for each species: A: 30×29 = 870; B: 15×14 = 210; C: 10×9 = 90; D: 5×4 = 20.
Step 3: Sum these values: $870 + 210 + 90 + 20 = 1190$ . Step 4: Compute $N (N - 1)$ : $60 \times 59 = 3540$ . Step 5: Find $D = \frac{1190}{3540} \approx 0.336$ . Step 6: The diversity index is $1 - D = 1 - 0.336 = 0.664$ . Step 7: Round to three decimal places giving 0.664.

Common mistake: Using

N^{2}

instead of

N (N - 1)

in the denominator

Concept tested: Simpson’s diversity index

Published 26 September 2026 · How this solution was prepared and checked

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In a forest plot the numbers of four tree species are as follows: Species A = 30, Species B = 15, Species C = 10, Species D = 5. Calculate the Simpson’s diversity index (1−D).

Step-by-step solution

In a forest plot the numbers of four tree species are as follows: Species A = 30, Species B = 15, Species C = 10, Species D = 5. Calculate the Simpson’s diversity index ( $1 - D$ ).