In a mangrove plot, fish species counts are: Species A=50, Species B=30, Species C=15, Species D=5. Calculate the Shannon diversity index $H^{'}$ using natural logarithm.

easy 2 marks Class 12 · Biology · Biodiversity and Conservation

Answer

1.142

The correct answer is 1.142 — Step 5: Report $H^{'} = 1.142$ (rounded to three decimal places).

Step-by-step solution

Step 1: Compute total number of individuals $N = 50 + 30 + 15 + 5 = 100$ .
Step 2: Calculate relative frequencies $p_{i}$ : $p_{A} = 0.5,; p_{B} = 0.3,; p_{C} = 0.15,; p_{D} = 0.05$ .
Step 3: Compute each $p_{i} l n p_{i}$ : $0.5 l n 0.5 = - 0.34655,; 0.3 l n 0.3 = - 0.36119,; 0.15 l n 0.15 = - 0.28457,; 0.05 l n 0.05 = - 0.14979$ .
Step 4: Sum the absolute values: $0.34655 + 0.36119 + 0.28457 + 0.14979 = 1.14210$ .
Step 5: Report $H^{'} = 1.142$ (rounded to three decimal places).

Common mistake: Using log base 10 instead of natural logarithm or forgetting the negative sign

Concept tested: Shannon diversity index calculation