Question

According to the Shannon Diversity Index, which of the five blocks above, with each containing 36 squares, would show the greatest diversity? The different shades represent different species, and more squares of a shade represent higher abundance. Use the figures to answer the following question. Five blocks are shown. Block 1 has 18 white squares and 18 light gray squares. Block 2 has 9 white squares, 18 light gray squares, and 9 dark gray squares. Block 3 has 23 light gray squares and 13 dark gray squares. Block 4 has 6 white squares, 2 light gray squares, 4 dark gray squares, and 24 black squares. Block 5 has 9 white squares, 9 light gray squares, 9 dark gray squares, and 9 black squares. According to the Shannon Diversity Index, which of the five blocks above, with each containing 36 squares, would show the greatest diversity? The different shades represent different species, and more squares of a shade represent higher abundance. 5 2 1 4

Answer 1

Block 5

Explanation:

The Shannon Diversity Index rewards larger numbers of species and more even distribution of species. On the face of it, Block 5, with its uniform distribution among 4 species, should have the highest index. When we do the calculation, we find this is the case. (see attachments)

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The SDI is the negative of the total of the products of relative frequency and the natural log of that relative frequency.