Answer:
Explanation:
The Shannon diversity index (H') is a measure of the diversity of a community, and is calculated using the formula:
H' = - Σ(pi * ln(pi))
where pi is the proportion of individuals in the community belonging to the i-th species, and ln is the natural logarithm.
Higher values of H' indicate greater diversity, and H' approaches 1 as the diversity of the community approaches 0.
To determine which sample has a Shannon diversity index closer to 1, we need to calculate the H' values for both samples.
Let's call the two species in the samples A and B. From the information given, we know that:
Sample a has two species, and 42% of the individuals belong to species A.
Sample b has two species, and 93% of the individuals belong to one of the species (let's assume this is species A).
For sample a, we can calculate the proportion of individuals belonging to species B as:
1 - 0.42 = 0.58
So the proportions pi for sample a are:
pA = 0.42
pB = 0.58
Using these values, we can calculate the H' value for sample a as:
H' = - [(0.42 * ln(0.42)) + (0.58 * ln(0.58))] = 0.985
For sample b, we know that 93% of the individuals belong to species A, so the proportion of individuals belonging to species B is:
1 - 0.93 = 0.07
So the proportions pi for sample b are:
pA = 0.93
pB = 0.07
Using these values, we can calculate the H' value for sample b as:
H' = - [(0.93 * ln(0.93)) + (0.07 * ln(0.07))] = 0.209
Since a higher value of H' indicates greater diversity, we can see that sample a has a Shannon diversity index closer to 1. Therefore, sample a is the sample with a Shannon diversity index closer to one.