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Species diversity indices

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					Species diversity indices
Are these two communities equally diverse?

               Site 1   Site 2
        Sp A   12       49
        Sp B   11       1
        Sp C   14       1
        Sp D   13       1
 3 Ways to include abundance in
       species diversity

1. Plot the distribution of individuals
   amongst species.

2. Summarize both abundance and species
   richness in a single index.

3. Examine the evenness of the distribution
   of individuals amongst species
1. Plot the distribution of abundance
           amongst species
Three models have been proposed:
• Log-series
• Broken stick
• Log-normal

All are supported by data

None have a good theoretical explanation
(save Stephen Hubbell’s neutral model, 2001)

Hard to tell apart statistically!
                                  Log-series

Most species are represented by only a couple
of individuals (i.e. rare). Only a few highly-
abundant (i.e. common) species.
Log abundance




                100
                                    Straight line predicted
per species




                10




                1

                      1   2   3

                    Linear species rank (1=most abundant)
                           Broken-stick
   • More equitable distribution of abundances amongst
   species than log-series.

   • Like log series most species have a fairly low
   abundances.
abundance per




                50

                40
                                Straight line predicted
species




                30
Linear




                20

                10

                      1   10    100

                     Log Species rank (1=most abundant)
                                  Log-series revisited
                                    “Most species are rare”




                                                Number of species
Log abundance




                100
per species




                10




                1

                      1   2   3
                                                                    Log abundance class per
                    Linear species rank                             species
                    (1=most abundant)
                                Log-normal
Most species are do NOT have abundances of only a
few individuals, but rather have intermediate
abundances (on a log scale! Still low)
  Number of species




                                                        Log normal

                      Log abundance class per species
                                       2003 class mite data
Essentially number of species




                                    Log2 abundance class

                                PRIMER “Geometric class plot”
                                   2003 class mite data
Linear abundance per species




                                      Log species rank


                               PRIMER “Dominance plot”
2. Summarize everything in one index
Some indices output by PRIMER (formulas in Krebs
                 and Magurran)

   • Simpson’s (1-lambda, or 1-D in Krebs)

   • Shannon-Wiener

   • Alpha (a parameter from log series)

   • Margalef d
         Shannon-Wiener =
sum (-Proportion spA * ln (prop spA)+
  (-Proportion spB*ln(prop spB)...)


          Site 1   Site 2    Site 1 Site 2
                             -p*lnp -p*lnp
 Sp A     12       49          0.34    0.06
 Sp B     11       1           0.33    0.08
 Sp C     14       1           0.36    0.08
 Sp D     13       1           0.35    0.08
 sum                           1.38    0.28
              Which index?

Read Krebs and Magurran and consider:

- Sensitivity to differences in sample size.

- Do you want differences in rare or abundant
species to be emphasized?

- Do you want differences in species richness or
evenness to be emphasized?

- How does log-normal vs. log-series affect?

- Performance in other studies (what works?).
   3. Measure evenness
        separately

Pielou’s J: Comparison of actual Shannon-Wiener
with Shannon-Wiener if species had equal
proportion (log S).

•Close to 1: very even distribution of abundances
amongst species

•Close to 0: very uneven
        Site 1   Site 2   Site 1 Site 2
                          -p*lnp -p*lnp
Sp A 12         49          0.34    0.06
Sp B 11         1           0.33    0.08
Sp C 14         1           0.36    0.08
Sp D 13         1           0.35    0.08
Sum (Shannon-Wiener)        1.38    0.28
Log S                       1.39    1.39
J’                          1.00    0.20
Smarties revisited!


1. Count your smarties. Each colour is a different
species.


2. Does your distribution fit log-series or log-normal?
(Use log 2 abundance classes to make bar graph).


3. Calculate the following diversity/evenness indices:

 Simpson’s
 Shannon-Wiener
 Pielou’s J

				
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