In a forest plot, four tree species have the following numbers of individuals: Species A = 40, Species B = 20, Species C = 15, Species D = 10. Calculate the Simpson’s diversity index ( $1 - D$ ).

easy 2 marks Class 12 · Biology · Biodiversity and Conservation

Answer

0.686

The correct answer is $0.686$ — Step 7: Final answer is $0.686$ .

Step-by-step solution

Step 1: Compute total number of individuals: $N = 40 + 20 + 15 + 10 = 85$ .
Step 2: Compute $n_{i} (n_{i} - 1)$ for each species:
$40 \times 39 = 1560$
$20 \times 19 = 380$
$15 \times 14 = 210$
$10 \times 9 = 90$
Step 3: Sum these values: $1560 + 380 + 210 + 90 = 2240$ .
Step 4: Compute denominator $N (N - 1) = 85 \times 84 = 7140$ .
Step 5: Calculate Simpson’s index $D = \frac{2240}{7140} \approx 0.3138$ .
Step 6: Compute $1 - D = 1 - 0.3138 = 0.6862$ , round to three decimals as $0.686$ .
Step 7: Final answer is $0.686$ .

Common mistake: Forgetting to subtract 1 from the total number when computing the denominator

Concept tested: Simpson’s diversity index calculation