Q.42 A forest has four different tree species (A, B, C and D) and their numbers are:

A = 60; B = 20; C = 10 and D = 10.

The Shannon biodiversity index of the trees in this forest is________________. (rounded

off to 2 decimals)

Shannon Biodiversity Index Calculation: Forest Trees Example

The Shannon biodiversity index measures species diversity by accounting for both richness and evenness in a community. For the given forest with trees A=60, B=20, C=10, D=10, the index calculates to 1.07 when rounded to two decimals.

Formula and Steps

The Shannon index H′=−∑piln⁡(pi)H′=−∑piln(pi), where pipi is the proportion of each species. Total trees = 100, so proportions are A: 0.60, B: 0.20, C: 0.10, D: 0.10.

• Compute: -[0.60×ln(0.60) + 0.20×ln(0.20) + 0.10×ln(0.10) + 0.10×ln(0.10)] = -[-0.392 -0.224 -0.230 -0.230] = 1.076.

• Rounded: 1.07, indicating moderate diversity due to dominance by species A.

Step-by-Step Computation

1. Proportions: pA=60/100=0.6pA=60/100=0.6, pB=0.2pB=0.2, pC=pD=0.1pC=pD=0.1.

2. Ln values: ln(0.6)≈-0.510, ln(0.2)≈-1.609, ln(0.1)≈-2.303.

3. Products: 0.6×-0.510=-0.306, 0.2×-1.609=-0.322, 0.1×-2.303=-0.230 (twice).

4. Sum = -1.076, negate for H’=1.076≈1.07.

Interpretation Guide

Higher values show greater diversity; 0 means one species dominates fully. Here, 1.07 reflects low evenness from A’s 60% share, unlike equal distribution (max H’=1.39 for 4 species).

• Low (<1): Heavy dominance.

• Moderate (1-2): Several species, uneven.

• High (>2): Even, rich communities.

Common Mistakes in Options

No explicit options provided, but typical MCQ traps include:

• Using log10 instead of ln: Yields ~0.47 (wrong base).

• Forgetting negative sign: Positive sum error.

• Simpson index confusion: 1−∑pi2=0.681−∑pi2=0.68 (different metric).

• Incorrect total (e.g., unnormalized): Leads to ~1.92.