Download Diversity Indices

Diversity Indices
• Usually used as biodiversity (as in species), but can apply to
other data where you count the number of times a
particular category occurs (e.g. nest shape).
• Comprises two components
• Species Richness: the number of species in an ecosystem.
• Species Evenness: a measure of how abundances are
distributed among the species.
• These are commonly combined into a single diversity index,
making interpretation really, really difficult.
Which sample is more diverse?
RNA Sequencing Study
700
Number of Unique Sequences
600
500
400
300
200
100
0
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Total number of reads
• Pyrosequencing reads thousands of genetic sequences from a sample
• How many unique sequences are there? It depends on how many
total sequences you count.
• Number of species encountered in some way depends on the
number of individuals counted.
Species Richness
Margalef (1958)
S −1
R1 =
ln( n )
S
Menhinick (1964) R2 =
n
n=number of individuals
S= number of species
€
These are based on some presumed relationship between S and n
which may or may not hold for your case.
€
Species Richness
A better way...
Rarefaction
Habitat
9
20
36
N
50
122
62
S
14
38
8
• Based on your actual data
• Computes probabilities of encountering a
species at n individuals.
1.8
Rarefaction Curve
1.7
Menhinick
1.6
10
1.5
1.4
1.3
1.2
1.1
1
0
10
Number of Species
9
20
30
8
2.1
40
7
50
60
70
80 2.05
2
1.95
6
1.9
Margalef
1.85
5
1.8
1.75
1.7
4
1.65
1.6
3
0
10
20
0
30
10
20
40
30
50
Sample Size
40
50
60
60
70
70
80
80
“Diversity” Indices
Evenness and Richness Combined
S
Simpson’s index
n i ( n i −1)
λ=∑
i=1 n ( n −1)
ni=number of individuals of species i
n = total number of individuals counted
S = total number of species
€
Shannon’s Index
€
S
⎡⎛ n i ⎞ ⎛ n i ⎞⎤
H ʹ′ = −∑⎢⎜ ⎟ ln⎜ ⎟⎥
⎝ ⎠ ⎝ n ⎠⎦
i=1 ⎣ n
Evenness Indices
Pielou (1975)
H ʹ′
E1 =
ln(S)
a.k.a. J’
H ʹ′
Sheldon (1969)
€
Heip (1974)
€
Hill (1973)
€
Alatalo (1981)
e
E2 =
S
H ʹ′
e −1
E3=
S −1
1/ λ
E 4 = H ʹ′
e
1/ λ) −1
(
E5 = H ʹ′
e −1
dominance → 1
dominance → 0
But how different is different?
Actual Shannon
Diversity
1) download the Biodiversity File from the web site
2) for each sample (TET38, S3 and ARIES 46) calculate
the following:
a) Margalef and Menhinick species richness
b) Shannon and Simpson diversity indices
c) Hill’s evenness index