1. Species diversity indices

2. Are these two communities equally diverse?
Site 1
Site 2
Sp A 12 49
Sp B 11 1
Sp C 14
Sp D 13

3. 3 Ways to include abundance in species diversity
Plot the distribution of individuals amongst species.
Summarize both abundance and species richness in a single index.
Examine the evenness of the distribution of individuals amongst species

4. 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!

5. Log-series
Most species are represented by only a couple of individuals (i.e. rare). Only a few highly-abundant (i.e. common) species.
100
Straight line predicted
Log abundance per species 10 1 1 2 3
Linear species rank (1=most abundant)

6. Broken-stick
More equitable distribution of abundances amongst species than log-series.
Like log series most species have a fairly low abundances.
Log Species rank (1=most abundant)
Linear abundance per species
Straight line predicted 1 10
100 20 30 40 50

7. Log-series revisited “Most species are rare” Number of species
100
Log abundance per species
Number of species 10 1 1 2 3
Log abundance class per species
Linear species rank (1=most abundant)

8. 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

9. 2003 class mite data Essentially number of species
Log2 abundance class
PRIMER “Geometric class plot”

10. 2003 class mite data Linear abundance per species Log species rank
PRIMER “Dominance plot”

11. 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

12. Site 1 Site 2 -p*lnp Sp A 12 49 0.34 0.06 Sp B 11 1 0.33 0.08 Sp C 14
Shannon-Wiener =
sum (-Proportion spA * ln (prop spA)+
(-Proportion spB*ln(prop spB)...)
Site 1
Site 2
-p*lnp
Sp A 12 49
0.34
0.06
Sp B 11 1
0.33
0.08
Sp C 14
0.36
Sp D 13
0.35
sum
1.38
0.28

17. 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?).

18. 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

19. Site 1
Site 2
-p*lnp
Sp A 12 49
0.34
0.06
Sp B 11 1
0.33
0.08
Sp C 14
0.36
Sp D 13
0.35
Sum (Shannon-Wiener)
1.38
0.28
Log S
1.39 J’
1.00
0.20

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