Solved: Index of Diversity, refer to Example.Index of

QUESTION:

Index of Diversity, refer to Example.Index of DiversityOne 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.Suppose a sample of a small community shows two species with 50 individuals each.a. Find the index of diversity H.________________b. What is the maximum value of the index of diversity for two species?________________c. Does your answer for part a equal ln 2? Explain why.