Species diversity indices

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Species diversity indices
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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
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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

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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 Hubbells neutral model, 2001)
• Hard to tell apart statistically!

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Log-series
Most species are represented by only a couple of
individuals (i.e. rare). Only a few
highly-abundant (i.e. common) species.
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Straight line predicted
Log abundance per species
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1
1
2
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Linear species rank (1most abundant)
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Broken-stick

• More equitable distribution of abundances
  amongst species than log-series.
• Like log series most species have a fairly low
  abundances.

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Log-series revisited
Most species are rare
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Log abundance per species
Number of species
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1
1
2
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Log abundance class per species
Linear species rank (1most abundant)
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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
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2003 class mite data
Essentially number of species
Log2 abundance class
PRIMER Geometric class plot
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2003 class mite data
Linear abundance per species
Log species rank
PRIMER Dominance plot
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2. Summarize everything in one index
Some indices output by PRIMER (formulas in Krebs
and Magurran)

• Simpsons (1-lambda, or 1-D in Krebs)
• Shannon-Wiener
• Alpha (a parameter from log series)
• Margalef d

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Shannon-Wiener sum (-Proportion spA ln (prop
spA) (-Proportion spBln(prop spB)...)
Site 1 Site 2 Site 1 -plnp Site 2 -plnp
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
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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?).
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3. Measure evenness separately

• Pielous 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

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Site 1 Site 2 Site 1 -plnp Site 2 -plnp
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) Sum (Shannon-Wiener) Sum (Shannon-Wiener) 1.38 0.28
Log S 1.39 1.39
J 1.00 0.20
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• 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
• Simpsons
• Shannon-Wiener
• Pielous J