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Introduction to the analysis of community data
Vojtech NovotnyCzech Academy of Science, University of South Bohemia & New Guinea Binatang Research Center
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?
5
7
9
11
13
15
17
19
21
1 2 3 4 5
No. of sites
No
. o
f sp
ecie
s .
Site accummulation 1-2-3-4-5 Randomised sites
Species accumulation curve
How many species?
Corrected estimate for missing species
Chao1 S + singletons2/(2*doubletons) S – number of species sampled
No. of species often depends on the number of individuals:samples with more individuals have also more species
0
5
10
15
20
25
0 100 200 300 400 500 600
No. of individuals
No
. o
f sp
ecie
s
observedrarefraction 36 ind.
Rarefraction:
Comparing the number of species in a random selection of the same number of individuals from each sample
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 speciesBerger-Parker’s index: share of the most common species
0
0.1
0.2
0.3
0.4
0.5
0.6
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
Simpson's index
Ber
ger
-Par
ker
ind
ex
Site 1
Site 5
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/Nnmax = abundance of the most common species, N – total no. of individ.
alpha diversity
beta diversity
gamma diversity
αβ
γ
= avg +
= 20
avg = 16.6
= 20 - 16.6 = 3.4
Alpha, beta and gamma diversity
Community similarity estimate:Jaccard similarity: shared species/[total species X + Y]Jaccard similarity = A/(A+B+C)X, Y - samples
X Y
Chao1 S + singletons2/(2*doubletons) S = number of species sampled
Simpson's Index (D) measures the probability that two individuals randomly selected from a sample will belong to the same species
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)
SU 2
Present Absent
SU 1Present a b
Absent c d
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)
cba
aS
J
SU 2
Present Absent
SU 1Present a b
Absent c d
cba
aS
2
2BC
Sørenson Coefficient
• like Jaccard, ignores shared absences
Quantitative Version of Sørenson (Bray-Curtis) Similarity
s
iik
s
iij
s
iikij
XX
XX
11
1
,min2kj
jkjk TT
WS
2BC