A mangrove fish community consists of four species with the following counts: Species X = 25, Species Y = 15, 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 $N=25+15+10+5=55$.
2. Step 2: Compute relative abundances $p_i$: X = 25/55 = 0.4545; Y = 15/55 = 0.2727; Z = 10/55 = 0.1818; W = 5/55 = 0.0909.
3. Step 3: Compute $p_{i}ln{p}_i$ for each species: X: 0.4545 × ln(0.4545) = 0.4545 × (−0.789) = −0.358, Y: 0.2727 × ln(0.2727) = 0.2727 × (−1.299) = −0.354, Z: 0.1818 × ln(0.1818) = 0.1818 × (−1.704) = −0.310, W: 0.0909 × ln(0.0909) = 0.0909 × (−2.397) = −0.218.
4. Step 4: Sum these values: (−0.358) + (−0.354) + (−0.310) + (−0.218) = −1.240.
5. Step 5: Apply the negative sign: $H^{\prime }=-(-1.240)=1.240$. Step 6: Round to two decimal places giving 1.24.

Concept tested: Shannon diversity index

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