Diversity Index Shannon's diversity index is a measure of

Chapter , Problem 6.4.118

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Diversity Index Shannon's diversity index is a measure of the diversity of a population. The diversity index is given by the formula H = -(PI log PI + P210g P2 + ... + Pl1log PH) where PI is the proportion of the population that is species 1, P2 is the proportion of the population that is species 2, and so on. (a) According to the U.S. Census B ureau, the distribution of race in the United States in 2000 was as follows: Race American Indian or Native Alaskan Asian Black or African American Hispanic Native Hawaiian or Pacific Islander White Source: u.s. Census Bureau Proportion 0.014 0.041 0.128 0.124 0.003 0.690 Compute the diversity index of the United States in 2000. (b) The largest value of the diversity index is given by H max = logeS), where S is the number of categories of race. Compute H max' H (c) The evenness ratio is given by Ef{ = --, where Hmax 0:5 EN :5 1. If Ef{ = 1, there is complete evenness. Compute the evenness ratio for the United States. (d) Obtain the distribution of race for the United States in 1990 from the Census B ureau. Compute Shannon's diversity index. Is the United States becoming more diverse? Why?