Four tree species are recorded in a forest plot with the following number of individuals: Species A=40, Species B=25, Species C=15, Species D=10. Calculate the Shannon diversity index $H^{'}$ for this community (use natural logarithm).

medium 3 marks Class 12 · Biology · Biodiversity and Conservation

Answer

1.26

The correct answer is 1.26 — Round to two decimal places: $1.26$ .

Step-by-step solution

Compute total individuals: $40 + 25 + 15 + 10 = 90$ .
Calculate proportions: $p_{A} = 40/90 = 0.4444$ , $p_{B} = 25/90 = 0.2778$ , $p_{C} = 15/90 = 0.1667$ , $p_{D} = 10/90 = 0.1111$ .
Compute $p_{i} l n p_{i}$ for each species: $0.4444 l n 0.4444 = - 0.361$ , $0.2778 l n 0.2778 = - 0.356$ , $0.1667 l n 0.1667 = - 0.299$ , $0.1111 l n 0.1111 = - 0.245$ .
Sum these values: $- 0.361 - 0.356 - 0.299 - 0.245 = - 1.261$ .
Take the negative of the sum to get $H^{'}$ : $- (- 1.261) = 1.261$ .
Round to two decimal places: $1.26$ .

Common mistake: Using log base 10 instead of natural logarithm

Concept tested: Shannon diversity index calculation