Chapter 16 Handout on Diversity Index Calculation |
BIOL 4120 Principles of Ecology |
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Harned Hall 301 (615) 963 - 5782 |
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The equations for each calculation are given in both the notes and in the textbook. As they are fairly simple and no new notation is introduced, the equations will not be given here. To follow the tables, have the equations in front of you or go back to the webpage for Chapters 15&16.
Simpson's Index and Berger-Parker index
Notice that the three communities differ
Simpson and Berger/Parker Indices | ||||
Sample I | ni*(ni-1) | /N*(N-1) | ||
Species | ||||
A | 24 | 552 |
0.193 |
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B | 20 | 380 |
0.133 |
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C | 7 | 42 |
0.015 |
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D | 3 | 6 |
0.002 |
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Simpson's = | ||||
Total | 54 | 0.342 | 2.92 |
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N*(N-1) | 2862 | Berger-Parker= | ||
2.25 |
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Sample II | ||||
A | 48 | 2256 |
0.195 |
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B | 40 | 1560 |
0.135 |
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C | 14 | 182 |
0.016 |
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D | 6 | 30 |
0.003 |
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Simpson's = | ||||
Total | 108 | 0.349 | 2.87 |
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N*(N-1) | 11556 | Berger-Parker= | ||
2.25 |
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Sample III | ||||
A | 24 | 552 |
0.167 |
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B | 20 | 380 |
0.115 |
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C | 7 | 42 |
0.013 |
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D | 3 | 6 |
0.002 |
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E | 3 | 6 |
0.002 |
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F | 1 | 0 |
0.000 |
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Simpson's = | ||||
Total | 58 | 0.298 | 3.35 |
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N*(N-1) | 3306 | Berger-Parker= | ||
2.42 |
Both of these indices are the reciprocal of the book's formulations
Note that:
Shannon Index
The three communities are the same as above
Shannon Index Calculation | ||||
Sample I | pi | Ln(pi) | pi*ln(pi) | |
Species | ||||
A | 24 | 0.44 | -0.81 | -0.36 |
B | 20 | 0.37 | -0.99 | -0.37 |
C | 7 | 0.13 | -2.04 | -0.26 |
D | 3 | 0.06 | -2.89 | -0.16 |
Total | 54 | 1 | H'= |
1.15 |
Sample II | ||||
A | 48 | 0.44 | -0.81 | -0.36 |
B | 40 | 0.37 | -0.99 | -0.37 |
C | 14 | 0.13 | -2.04 | -0.26 |
D | 6 | 0.06 | -2.89 | -0.16 |
Total | 108 | 1 | H'= |
1.15 |
Sample III | ||||
A | 24 | 0.41 | -0.88 | -0.37 |
B | 20 | 0.34 | -1.06 | -0.37 |
C | 7 | 0.12 | -2.11 | -0.26 |
D | 3 | 0.05 | -2.96 | -0.15 |
E | 3 | 0.05 | -2.96 | -0.15 |
F | 1 | 0.02 | -4.06 | -0.07 |
Total | 58 | 1 | H'= |
1.36 |
Note that:
Note that the index is invariant with respect to sample size, but rare species add to it
Brillouin Index
Brillouin Index Calculation | ||||
Sample I | ln(n!) | |||
Species | ln(N!) = | |||
A | 24 | 54.8 | 164.3 | |
B | 20 | 42.3 | ||
C | 7 | 8.5 | ln(N!) - sum = | |
D | 3 | 1.8 | 56.9 | |
Total | 54 | 107.4 | divide by N = | |
HB = |
1.05 | |||
Sample II | ln(N!) = | |||
A | 48 | 140.7 | 400.9 | |
B | 40 | 110.3 | ||
C | 14 | 25.2 | ln(N!) - sum = | |
D | 6 | 6.6 | 118.2 | |
Total | 108 | 282.8 | divide by N = | |
HB = |
1.09 | |||
Sample III | ||||
A | 24 | 54.8 | ln(N!) = | |
B | 20 | 42.3 | 180.5 | |
C | 7 | 8.5 | ||
D | 3 | 1.8 | ln(N!) - sum = | |
E | 3 | 1.8 | 71.2 | |
F | 1 | 0.0 | ||
divide by N = | ||||
Total | 58 | 109.2 | HB = |
1.23 |
Note that:
Note that the sample size affects the magnitude of the index, unlike the Shannon index
Last Updated April 10, 2006