Shannon Index

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```					Shannon Index

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
In other words, the higher the “H” value __________________________
_________________________________________________________
Shannon Index

Shannon Index Calculation
Sample I         pi      Ln(pi)    pi*ln(pi)
Species
A         24             -0.81
B         20             -0.99
C         7              -2.04
D         3              -2.89

Total     54     1           H'=

Sample II
A         48
B         40
C         14
D         6

Total     108    1           H'=

Sample III
A         24             -0.88
B         20             -1.06
C         7              -2.11
D         3              -2.96
E         3              -2.96
F         1              -4.06

Total     58     1           H'=

Note that:
Note that the index is invariant with respect to sample size, but rare
In other words, the higher the “H” value __________________________
_________________________________________________________
Shannon-Weiner Diversity Index Lab

Background: The Shannon Index is a measurement used to compare diversity
between habitat samples. This comparison can be between two different habitats
or a comparison of one habitat over time. The actual formula for the Shannon-
Weiner Diversity Index is:

Other Shannon measurements include “S” which is the number of species present
in the sample, and E which is the evenness of those species. If the E value is 1, the
species are equally present in the habitat. The formula to find E is: E = H/ln(S).

Procedure: Fill a dixie cup with Trail Mix 1 and a separate Dixie cup with Trail Mix
2. Mark your cups so you know which is from which “habitat.” Assume each type of
food is a new species in the habitat. You will need to use a copy of the natural log
tables or visit:
http://www.ajdesigner.com/phpnaturallog/natural_log_equation_y.php

Fill in the charts for each Habitat using Shannon’s Diversity Index.

Habitat One:

Species (i)   Number of      Pi (number       Ln(Pi)        Pi *ln(Pi)
that species   of that
species/total)
in sample

_____Total     Should add       Use the       H = _____
from all       up to 1.0        natural log   (add this
column and
species                         table         remove the -)

Questions from Habitat One:
1. What is the H value and what use would this value have if I did a second sample from this
habitat three years from now (assuming it was real animals and not food!)?

2. What would be the E value (evenness) for this habitat?
Habitat Two:

Species (i)   Number of      Pi (number       Ln(Pi)        Pi *ln(Pi)
that species   of that
species/total)
in sample

_____Total     Should add       Use the       H = _____
from all       up to 1.0        natural log   (add this
column and
species                         table         remove the -)

Questions from Habitat two:
1. What is the H value for habitat two?

2. Compare the H value of habitat one and two and use that comparison to describe which
habitat has more diversity to it.

3. What is the E value for Habitat two?

4. List two advantages to using a Shannon Index instead of simply a population count to
determine diversity.

5. List two disadvantages to using a Shannon Index to determine diversity.

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