Transcript Measurement of Biological Diversity: Shannon

Measurement of
Biological Diversity:
Shannon Diversity Index
and
Shannon’s Equitability
Comparing the diversity found in two
or more habitats
What is Biological Diversity?
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(from Whitaker, 1960)
alpha diversity: diversity within a sample
beta diversity: diversity associated with
changes in sample composition along an
environmental gradient (between samples)
gamma diversity: diversity due to differences
among samples when they are combined into a
single sample (this tells us something about
how samples are collected – not about
communities in nature)
Biological Diversity Includes:
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Number of different species (species diversity)
Relative abundance of different species
(species evenness)
Ecological distinctiveness of different species,
e.g., functional differentiation – often done in
microbiology (Functional Diversity).
Evolutionary distinctiveness of different
species
(The last two of these are rarely addressed)
Why is Biological Diversity
Important?
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It is commonly believed that the more diverse
a system is, the more stable it will be.
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Studies with plants suggest that productivity
in more diverse plant communities is more
resistant to, and recovers more fully from, a
major drought.
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Diverse communities are more resistant to
invasion by exotic species than are less diverse
communities.
The Shannon Diversity Index
(SDI) – what is it?
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Claude Shannon was not a biologist – he was a
mathematician and communications engineer
who worked for Bell Laboratories.
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Shannon originated a field called Information
Theory.
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The Shannon Diversity Index is a
mathematical measure of species diversity in a
community.
What does the Shannon Diversity
Index tell us about biological
diversity?
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It provides information about community
composition beyond just species richness (how
many different species are present).
It also takes the relative abundance of each
species into account.
It provides important information about rarity
and commonness of species in a community.
The Variables examined when
calculating the SDI
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H = the SDI
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S = the total number of species in the
community (richness)
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pi = the proportion of S made up of the “ith”
species (the number of individuals of a
particular species divided by the total
number of all species)
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EH = Shannon’s Equitability (species
evenness).
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The SDI accounts for both abundance and
evenness of the species present.
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The proportion of species i relative to the total
number of species (we call it pi) is calculated,
and then multiplied by the natural logarithm of
this proportion (ln pi).
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The resulting product is summed across
species and multiplied by -1.
Let’s assume the following data set:
Species found
Beetle
Number
found
6
Proportion (pi)
(number ÷ total)
6/13 = 0.462
Earwig
3
3/13 = 0.231
Spider
2
2/13 = 0.154
Centipede
2
1/13 = 0.154
Total (Sum)
13
The formula for SDI is:
S
H   pi ln pi
i 1
Species
found
Beetle
Number Proportion (pi)
found (number ÷ total)
6
6/13 = 0.462
pi ln pi
- 0.357
Earwig
3
3/13 = 0.231
- 0.338
Spider
2
2/13 = 0.154
- 0.288
Centipede
2
1/13 = 0.154
- 0.288
Total
13
- 1.271
H = -1 times the sum of all pi ln pi
= -1 x -1.271 = 1.271
Now that we have calculated the SDI
for our sample, we can calculate
Shannon’s Equitability
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Shannon’s Equitability (EH) is a measure of
species evenness or relative abundance.
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Equitability assumes a value between 0 and 1,
with 1 being complete evenness (equal
numbers of every species in the sample).
Shannon’s Equitability for
our example would be:
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Shannon’s Equitability (EH) = SDI (H) divided
by the natural log of HMAX or…
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H/ln S (where S = 4)
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In this case, EH = 1.27/1.39 = .91
Knowing that EH is always between zero and
one, our sample has pretty high equitability.
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Now, let’s see how SDI and Equitability
change under different circumstances.
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Let’s look at how species richness and species
evenness affect SDI and Equitability.
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In the first situation, let’s look at four
imaginary samples where the number of
species differs, and where there are always an
equal number of each species in the sample.
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We’ll call these our “even” communities.
SDI and Equitability for “Even”
Communities (equal number of each
species in the sample)
Number of
Species in the
Sample
5
10
20
50
SDI
Equitability
1.61
2.31
3.00
3.91
1.0
1.0
1.0
1.0
But what if the number of species in each
sample are NOT equal (Equitability is low)?
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In this second situation, let’s look at four imaginary
samples where the number of species again differs,
and where there are always an unequal number of
each species in the sample.
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In this case, one species makes up 90% of the total
number of individuals in the sample and the
remaining species each make up an equal proportion
of the remaining 10%.
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We’ll call these our “uneven” communities.
SDI and Equitability for “Uneven”
Communities (one species makes up 90%
of the total sample and the rest each make
up an equal portion of the last 10%)
Number of
Species in the
Sample
5
10
20
50
SDI
Equitability
0.46
0.54
0.62
0.71
0.29
0.23
0.21
0.18
There are two methods to calculate
SDI – one uses natural log, the other
uses log base 10
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As it turns out, Microbiologists often use one method
(the natural log version) in their publications, while
botanists and biologists often use the log 10 version.
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Either way, you always use the same method when
you compare the SDI of one sample to that of another
to determine which has more diversity.
Calculating eH or the exponent
of SDI
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Finally, if we calculate the exponent of our
SDI or eH, we get a number between 1
and S for that sample. You can use your
calculator to do this (use the ex) function
and put your H (SDI) in for the x. You
can also do this in excel (see the Word file
that explains this). If, for example, you
have
Calculating eH or the exponent
of SDI
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What does this tell us? If, for example, you
have a sample with species richness of 12 and
your eH is approximately 8.5, this means that
your sample has the same evenness as a
perfectly even sample with 8.5 species. In other
words, your sample of 12 species is dominated
by about 8.5 species. If you had a sample with
S = 12 and your eH is 12, it is perfectly even
and not dominated by any species – they are
equally distributed.
Now you do it
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Using the numbers of ants from the pitfall
data, calculate the SDI, Evenness, Species
Richness, and exponent of SDI for three
forest types
Melina forest – sylvaculture forest
Primary forest – rainforest, never cut
Secondary forest – rainforest, selectively
logged 30 years ago