Question

A community of plants contains three species. On a collecting trip, you find that 80 plants are species A, 60 are species B, and 60 are species C. Based on this sample, what is the Shannon index of the plant community?

a. [0.8 (ln 0.8) + 0.6 (ln 0.6) + 0.6 (ln 0.6)]
b. ‒[0.8 (ln 0.8) ‒ 0.6 (ln 0.6) + 0.6 (ln 0.6)]
c. ‒[0.4 (ln 0.4) + 0.6 (ln 0.3) + 0.6 (ln 0.3)]
d. ‒[0.4 (ln 0.4) + 0.3 (ln 0.3) + 0.3 (ln 0.3)]

Answer 1

To calculate the Shannon Index for the plant community, use the formula H = -[p(A) * ln(p(A)) + p(B) * ln(p(B)) + p(C) * ln(p(C))], with p representing the proportion of each species. The correct Shannon Index based on the given number of plants is -[0.4 * ln(0.4) + 0.3 * ln(0.3) + 0.3 * ln(0.3)], which corresponds to option d.

Step-by-step explanation:

The student is asking about calculating the Shannon Index, a measure of biodiversity within a given plant community. To calculate the Shannon Index (H), you need to determine the proportion (p) of the total for each species, multiply this by the natural logarithm (ln) of the proportion, sum all these values for each species, and take the negative sum. With 200 total plants (80 species A, 60 species B, and 60 species C), the proportions are 0.4, 0.3, and 0.3 respectively. Therefore, the correct Shannon Index is:

H = -[p(A) * ln(p(A)) + p(B) * ln(p(B)) + p(C) * ln(p(C))]

H = -[0.4 * ln(0.4) + 0.3 * ln(0.3) + 0.3 * ln(0.3)]

The correct answer is option d: –[0.4 (ln 0.4) + 0.3 (ln 0.3) + 0.3 (ln 0.3)].