Solution Found!
Index of Diversity, refer to Example.Index of DiversityOne
Chapter 2, Problem 83A(choose chapter or problem)
Problem 83A
Index of Diversity, refer to Example.
Index of Diversity
One measure of the diversity of the species in an ecological community is given by the index of diversityH, where
and P1, P2, . . . , Pn are the proportions of a sample belonging to each of n species found in the sample. Source: Statistical Ecology. For example, in a community with two species, where there are 90 of one species and 10 of the other, P1 = 90/100 = 0.9 and P2 = 10/100 = 0.1, with
Verify that H ≈ 0.673 if there are 60 of one species and 40 of the other. As the proportions of nspecies get closer to 1/n each, the index of diversity increases to a maximum of ln n.
Find the value of the index of diversity for populations with n species and 1/n of each if
a.n = 3;
b.n = 4.
c. Verify that your answers for parts a and b equal ln 3 and ln 4, respectively.
Questions & Answers
QUESTION:
Problem 83A
Index of Diversity, refer to Example.
Index of Diversity
One measure of the diversity of the species in an ecological community is given by the index of diversityH, where
and P1, P2, . . . , Pn are the proportions of a sample belonging to each of n species found in the sample. Source: Statistical Ecology. For example, in a community with two species, where there are 90 of one species and 10 of the other, P1 = 90/100 = 0.9 and P2 = 10/100 = 0.1, with
Verify that H ≈ 0.673 if there are 60 of one species and 40 of the other. As the proportions of nspecies get closer to 1/n each, the index of diversity increases to a maximum of ln n.
Find the value of the index of diversity for populations with n species and 1/n of each if
a.n = 3;
b.n = 4.
c. Verify that your answers for parts a and b equal ln 3 and ln 4, respectively.
ANSWER:
Solution
Step 1 of 3
In this problem, we have to determine the index of diversity for populations with n species with each of them being equal to