1. Introduction to the analysis of community data
Vojtech Novotny
Czech Academy of Science, University of South Bohemia & New Guinea Binatang Research Center

2. Ecological analysis of community samples
typical data format:

3. Some of the questions you can ask about the samples:
How many species?
How many individuals?
What species are common / rare?
How different are the sites in their species composition?
How different are the species in their distribution?

4. Presence – absence characteristics: number of species and sites

5. Species accumulation curve

6. How many
species?
Corrected estimate for missing species
Chao1
S + singletons2/(2*doubletons)
S – number of species sampled

7. Courtesy
Jonathan Coddington .

8. Courtesy
Jonathan Coddington

9. No. of species often depends on the number of individuals:
samples with more individuals have also more species
Rarefraction:
Comparing the number of species in a random selection of the same number of individuals from each sample

10. describing distribution of individuals among species
Diversity measures:
describing distribution of individuals among species
Simpson’s index: the probability that two individuals chosen from your sample will belong to the same species
Berger-Parker’s index: share of the most common species

11. Diversity estimate:
Simpson’s diversity: 1- ∑[ni(ni-1)/N(N-1)]
ni – number of individuals from species i, N – total number of individ.
Berger-Parker’s Index: nmax/N
nmax = abundance of the most common species, N – total no. of individ.

12. Na = (p1a + p2a + ... + pna)1/(1-a)
Diversity: Hill’s numbers
Na = (p1a + p2a pna)1/(1-a)
a = Hill’s number
p1, ... , pn = proportional abundance of species 1, 2, ... n
N-∞ = reciprocal of the proportional abundance of the rarest species
N0 = number of species
N1 = eH where H = Shannon diversity index
N2 = 1/D where D = Simpson’s index
N∞ = reciprocal of the proportional abundance of the commonest species

14. Alpha, beta and gamma diversity
alpha diversity
beta diversity
gamma diversity
 = avg + 
avg = 16.6
 = 20
= = 3.4 α β γ

16. X Y Community similarity estimate:
Jaccard similarity: shared species/[total species X + Y]
Jaccard similarity = A/(A+B+C)
X, Y - samples
X Y

17. Similarity indices
Koleff et al J anim Ecol 72:367

18. incorporate differences in species richness
Jaccard
Sorensen
"Broad sense" measures
incorporate differences in species richness
as well as differences in composition
Lennon et al.
"Narrow sense" measures
independent of differences in species richness 1-
Example 1
a = 10, b = 10, c = 100
Jaccard = 10/120 = 0.08
Sorensen = 20/130 = 0.15
Lennon = 1- 10/20 = 0.5
Example 2
a = 10, b = 10, c = 1000
Jaccard = 10/1020 = 0.010
Sorensen = 20/1030 = 0.019
Lennon = 1- 10/20 = 0.5
Koleff et al J anim Ecol 72:367

20. EstimateS data format, saved as TXT file

21. CJ = a / (a + b + c) CS = 2a / (2a + b +c) Chao1
S + singletons2/(2*doubletons)
S = number of species sampled
Jaccard CJ
CJ = a / (a + b + c)
a = richness in first site, b = richness in second site, j = shared species
Sorenson CS
CS = 2a / (2a + b +c)
Simpson's Index (D) measures the probability that two individuals randomly selected from a sample will belong to the same species

22. Jaccard Coefficient
number of shared species as proportion of total number of species in the two SUs
ranges from 0 (no species in common) to 1 (the SUs have identical species lists)
SU 2
Present
Absent
SU 1 a b c d

23. Sørenson Coefficient like Jaccard, ignores shared absences SU 2
Present
Absent
SU 1 a b c d

24. Quantitative Version of Sørenson (Bray-Curtis) Similarity

25. Morisita-Horn CmH Not influenced by sample size & richness
Highly sensitive to the abundance of common spp.
CmH = 2S(ani * bni) / (da + db)(aN)(bN)
aN = total # of indiv in site A
ani = # of individuals in ith species in site A
da = Sani2 / aN2