In a mangrove plot, four fish species have the following counts: Species X = 30, Species Y = 20, Species Z = 10, Species W = 5. Calculate the Shannon diversity index ($H^{\prime }$) using the natural logarithm.

Step-by-step solution

1. Step 1: Find total number of individuals: $N=30+20+10+5=65$.
2. Step 2: Compute relative abundances $p_i$ for each species:
3. $p_X=30/65=0.4615$
4. $p_Y=20/65=0.3077$
5. $p_Z=10/65=0.1538$
6. $p_W=5/65=0.0769$
7. Step 3: Compute each term $p_{i}ln{p}_i$:
8. $0.4615\times \ln (0.4615)=-0.3571$
9. $0.3077\times \ln (0.3077)=-0.3625$
10. $0.1538\times \ln (0.1538)=-0.2879$
11. $0.0769\times \ln (0.0769)=-0.1973$
12. Step 4: Sum the terms: $-0.3571-0.3625-0.2879-0.1973=-1.2048$
13. Step 5: Apply $H^{\prime }=-sum{p}_{i}ln{p}_i=1.2048$.
14. Step 6: Round to three decimal places: $H^{\prime }=1.205$.
15. Step 7: Final answer is $1.205$.

Concept tested: Shannon diversity index calculation

Published 28 September 2026 · How this solution was prepared and checked