Shannons diversity index is a measure of the diversity of a population. The diversity index is given
Question:
where p1 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 Bureau, the distribution of race in the United States in 2007 was as follows:
Race €¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦..€¦€¦€¦€¦€¦...................€¦€¦. Proportion
American Indian or Native Alaskan €¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦....€¦€¦. 0.015
Asian €¦.................€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦.€¦.. 0.042
Black or African American €¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦..€¦.....€¦. 0.129
Hispanic €¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦........ 0.125
Native Hawaiian or Pacific Islander €¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦...€¦€¦. 0.003
White €¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦. €¦€¦€¦€¦€¦€¦€¦€¦.................€¦€¦€¦... 0.686
Compute the diversity index of the United States in 2007.
(b) The largest value of the diversity index is given by Hmax = log(S), where S is the number of categories of race. Compute Hmax.
(c) The evenness ratio is given by EH = H/Hmax, where 0 ‰¤ EH ‰¤ 1. If EH = 1, there is complete evenness. Compute the evenness ratio for the United States.
(d) Obtain the distribution of race for the United States in 2010 from the Census Bureau. Compute Shannon's diversity index. Is the United States becoming more diverse? Why?
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