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
species add to it
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
species add to it.
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.