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Introduction to the analysis of community data
Vojtech Novotny
Czech Academy of Science, University of South Bohemia & New Guinea Binatang Research Center
Ecological analysis of community samples
typical data format:
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?
Presence – absence characteristics: number of species and sites
Species accumulation curve
21
19
No. of species .
17
15
13
11
9
Site accummulation 1-2-3-4-5
Randomised sites
7
5
1
2
3
No. of sites
4
5
How many
species?
Corrected
estimate for
missing species
Chao1
S + singletons2/(2*doubletons)
S – number of species sampled
Courtesy
Jonathan Coddington
.
Courtesy
Jonathan Coddington
No. of species often depends on the number of individuals:
samples with more individuals have also more species
No. of species
25
20
Rarefraction:
15
Comparing the number
of species in a random
selection of the same
number of individuals
from each sample
10
5
observed
rarefraction 36 ind.
0
0
100
200
300
400
No. of individuals
500
600
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
0.6
Site 1
Berger-Parker index
0.5
0.4
0.3
0.2
0.1
0
0.00
Site 5
0.05
0.10
0.15
0.20
Simpson's index
0.25
0.30
0.35
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.
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
Alpha, beta and gamma diversity
alpha diversity
beta diversity
 = avg + 
gamma diversity
avg = 16.6
 = 20
α
 = 20 - 16.6 = 3.4
β
γ
Community similarity estimate:
Jaccard similarity: shared species/[total species X + Y]
Jaccard similarity = A/(A+B+C)
X, Y - samples
X
Y
Similarity indices
Koleff et al. 2003 J anim Ecol 72:367
"Broad sense" measures
incorporate differences in species richness
as well as differences in composition
Jaccard
"Narrow sense" measures
independent of differences in species richness
Example 1
a = 10, b = 10, c = 100
Jaccard = 10/120 = 0.08
Sorensen = 20/130 = 0.15
Lennon = 1- 10/20 = 0.5
Sorensen
Lennon et al.
1-
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. 2003 J anim Ecol 72:367
EstimateS data format, saved as TXT file
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
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)
a
J
S 
abc
SU 1
SU 2
Present Absent
Present
a
b
Absent
c
d
Sørenson Coefficient
• like Jaccard, ignores shared absences
S
BC
2a

2a  b  c
SU 1
SU 2
Present Absent
Present
a
b
Absent
c
d
Quantitative Version of Sørenson
(Bray-Curtis) Similarity
S
BC
jk

2W jk
T j  Ts k


2 min X ij , X ik
i 1
s
s
X X
i 1
ij
i 1
ik

• 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