Species diversity:rarefaction, evenness and indices

Are these two communities equally diverse?

Site 1 Site 2

Sp A 12 49

Sp B 0 1

Sp C 0 1

Sp D 0 1

Problem 1: Accounting for sample size

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

Problem 2: Accounting for abundance

Resampling techniques

• Can be used to estimate a statistic or parameter for a different sample size

• Can be used to estimate a statistic or parameter under the null hypothesis of no treatment effect

Smartie diversity!

• Suppose we found 5 colours represented in a sample of 10 smarties. Is this the same diversity (species richness) as in your sample?

Phyc 2003 Practice data setFr

eque

ncy

R

6

88

243

232

189

109

58

35

1910 9

1

-0.05-0.10-0.15-0.20 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

0.48

.477

Phyc 2003 Practice data setFr

eque

ncy

R

6

88

243

232

189

109

58

35

1910 9

1

-0.05-0.10-0.15-0.20 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

0.48

.477

1999

P= = 0.001

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

Problem 2: Accounting for abundance

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

Log-series distribution

Log abundance class per species

Num

ber

of s

peci

es

“Most species are rare”

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

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)

Log abundance class per species

Num

ber

of s

peci

es

Log normal

2003 class mite data

Log2 abundance class

Ess

entia

lly n

umbe

r of

spe

cies

PRIMER “Geometric class plot”

2. Summarize everything in one index

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

• Shannon-Wiener

• Alpha (a parameter from log series)

• Margalef d

Some indices output by PRIMER (formulas in Krebs and Magurran)

Site 1 Site 2 Site 1

-p*lnp

Site 2

-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 50 52 1.38 0.28

Shannon-Wiener =

sum (-Proportion spA * ln (prop spA)+

(-Proportion spB*ln(prop spB)...)

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).

Question: Why would Shannon-Wiener = logS if species equally abundant?

3. Measure evenness separately

Pielou’s J:

J = Shannon-Wiener / logS

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

• Close to 0: very uneven

Site 1 Site 2 Site 1

-p*lnp

Site 2

-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