Download Biodiversity Indexes Biodiversity Indices Simpson`s Diversity Index

3/12/2011
Biodiversity Indexes
Characteristics effecting biodiversity
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Shanni Liang
Amanda Ye
Anny Lam
Olena Borkovska
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Biodiversity Indices
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Simpson's Diversity Index
Shannon Index
Sorensen Similarity Index
Menhnick's Index
Number of species
Number of individuals from all species
Biological interactions between species
(competition, mutualism, amensalism,
symbiosis)
Availability of food supply/ Amount of energy
reaching the ground
Human impact (Rate of extinction/ degree of
endangerment
Climate/Temperature Sensitivity
Simpson's Diversity Index
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Used to quantify biodiversity of a habitat
Takes into account the number of species
present and the relative abundance of
each specie
Represents probability that two randomly
selected individuals from the habitat will
not be from the same specie
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Formula for Simpson's Index
Shannon Index
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n is the total number of organisms of a particular
species
N is the total number of organisms of all species
D represents a range between 0 and 1, 0 being no
diversity and 1 represents infinite diversity
As species richness and evenness increases so
does the diversity
Sorensen’s Similarity Index
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Index measure of beta
diversity
Ranges from 0 when there
is no species overlap , to 1
when the same species
are found in both
communities
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S1 is the total number of
species found in the first
community
S2 is the number of
individuals found in the
second community
C is the number of species
common to both
communities
H = Σ (pl) |ln pl|
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H = the Shannon diversity
index
Pi = fraction of the entire
population made up of
species i
S = numbers of species
encountered
∑ = sum from species 1 to
species S
Menhnick’s Index
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Measures Diversity in
categorical data
Takes into account
number of species and
evenness of species
May be used for habitat
comparison
V l off index
Value
i d ranges
from low species
evenness and richness
to high species
evenness and richness,
between 1.5 and 3.5
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Menhnick’s Index measures species
richness, which is a measure of a number of
species found in a sample
D = s√N
s is the number of species represented in a
sample
N is the total number of organisms found in a
sample
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Our Biodiversity Index
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We have eleven species, total number of individuals is 353
To get reproduction rate we multiply food consumption by 3
To get Proportion of each species, we divide the number of individuals
in each specie by the total number of individuals
We than multiply reproduction rate by pi and take natural log of the
product in order to identify how reproduction rate effects proportion of
each specie
Take an Absolute value of natural log of product Pi and R in order for
p
results to be positive
Final step to calculate biodiversity, we multiply the product of Pi and R
and product of natural log of Pi and R
Original Equation
H = Σ (pl) |ln pl|
Our Equation
H = Σ R (pl) |ln (R) pl|
Food consumption/av
ailability
pi (individual proportion of total)
Rate of Reproduction R*Pi
Ln(R*Pi)
Biodiversity (pi*R) |ln pi*R|
|ln pi *R|
A
75
0
0
0.21246459
0
0
0
0
B
59
0.5
1.5
0.16713881
0.2507082
‐3.1723961
3.1723961
0.795345769
C
42
0.75
2.25
0.11898017
0.2677054
‐3.4466667
3.4466667
0.922691217
D
36
1
3
0.101983
0.305949
‐3.4672859
3.4672859
1.060812698
E
30
1.5
4.5
0.08498584
0.3824363
‐3.426464
3.426464
1.310404062
F
28
2
6
0.07932011
0.4759207
‐3.2767676
3.2767676
1.559481476
G
25
2
6
0.07082153
0.4249292
‐3.503425
3.503425
1.488707505
H
24
25
2.5
75
7.5
0 06798867
0.06798867
0 509915
0.509915
‐3.3619254
3 3619254
3 3619254
3.3619254
1 714296255
1.714296255
I
14
3
9
0.03966006
0.3569405
‐4.2575969
4.2575969
1.5197088
J
12
4
12
0.03399433
0.407932
‐4.2782162
4.2782162
1.745221325
K
8
4
12
0.02266289
0.2719547
‐5.0891464
5.0891464
1.384017146
Total
353
13.50068625
Food Consumption vs Biodiversity
Food Consumption vs Rate of Reproduction
4
35
3.5
14
Rate of Reproduction
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Species
# Indiv
idual
s
y = 3x
12
3
2
R = 1
10
2.5
Food
cons umpti on/avai l a
bi l i ty
Bi odi versi ty (pi *R)
|l n pi *R|
8
2
6
4
1.5
2
1
pi (i ndi vi dual
0
0
2
4
Food consumption
6
0.5
0
1
2
3
4
5
6
7
8
9 10 11
3