Shannon wiener index

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Oct 29, 2013 (3 years and 7 months ago)

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FROM : http://www.cyberwaysandwaterways.com/en/index.jhtml

Theory of Species Diversity
Species diversity is an expression of community structure and is a characteristic unique to the
community level of organization. A community demonstrates a high species diversity if many
equally or nearly equally abundant species are present. If a community is composed of only a
few species, or if only a few species are abundant, then species diversity is low.
High species diversity indicates a complex community in which a high degree of species
interaction is possible. For this reason, communities with higher diversities typically
have higher levels of energy transfer (food webs), predation, competition and niche
availability. In several ecological community studies, species diversity has been construed as a
measure of community stability in which low or changing species diversity may indicate a
stressed or unstable environment. However, many ecologists argue that there is no direct
correlation between species diversity and community stability or community stress.
The theory of species diversity takes into account three different ecological phenomena (i.e.,
species richness, relative abundance and community evenness). When viewed separately, each
of these parameters can reveal valuable ecological insight. However, when viewed cumulatively
through studies of species diversity indices, these parameters combine to give an excellent
overall picture of community structure.
SPECIES RICHNESS

The first of the three parameters contained within the theory of species diversity is the total
number of species present in a community, or its species richness. A high species richness
indicates a complex community in which a high degree of species interaction is possible. For
this reason, communities that possess a high species richness can be said to have
higher levels of energy transfer (food webs), predation, competition and niche
availability, than other similar communities that exhibit low species richness. However,
species richness does not take into account the number of individuals per species or the
evenness of the individuals within each species. For this reason, this method is generally not
used singularly to describe detailed community characteristics rather it is sometimes loosely
used to make initial inferences on the condition of a given community. By qualitatively
determining the number of species present in a community, limited assumptions as to the
"health" and community structure of an environment can be made.
RELATIVE ABUNDANCE
The second parameter contained within the theory of species diversity relates to the number of
individuals within each species, or the relative abundance of individuals within a given
community. If one accepts the theory that when species richness is high that higher levels of
energy transfer are possible, then the idea that if within each species the number of individuals
is also high then higher levels of energy transfer within the community should be higher
still.
Relative abundance calculations show the percentage of individuals within each species present
in a community and how that species relates numerically to the abundance of any other species
present in that community. Calculations of this type are valuable to ecologists because they
reveal ecological patterns that indicate which species is dominant or least dominant, or if there
is an even distribution of individuals within the community. The following is an example of
relative abundance calculations from theoretical data.
Species Number of
Individuals per
Species (Ti)
PERCENT TOTAL
Ti/T*100=(A)
DOMINANCE
RANK

Species A 5 5/76*100=6.58% 4
Species B 10 10/76*100=13.16% 3
Species C 5 5/76*100=6.58% 4
Species D 30 30/76*100=39.47% 1
Species E 20 20/76*100=26.32% 2
Species F 5 5/76*100=6.58% 4
Species G 1 1/76*100=1.32% 5
TOTAL(T) 76 100%
COMMUNITY EVENNESS
The third parameter contained within the theory of species diversity relates to the evenness of
the number of individuals within each species or its community evenness. Communities that
exhibit more even numbers of individuals within the total number of species present are thought
to be closer to a state of equilibrium than those in which the numbers of individuals is less
even. Because the energy flow within ecological systems is constantly changing, consistent
patterns of evenness within a given community can be equated with community
stability. Communities that historically exhibit good community stability can, over time,
become less stable through the introduction of natural/unnatural alterations to the system
and/or introductions of highly competitive species.
SPECIES DIVERSITY INDICES
A large number of species diversity indices have been proposed, and many are in contemporary
use. It has been observed that there are two basic groups of species diversity indices: those
that are affected most by the occurrence of rare species in the community and those that are
most sensitive to the relative abundance of the species within the community. The first group is
best utilized when observations of slight changes in community interactions within rare species
are desired. This first group is also most highly affected by variations in sample size. Measures
in the second group tend to be more accurate for examining the affects of one or more changing
parameters on the study community as a whole.
The Shannon and Simpson indices are the two most widely used species diversity
indices for examining overall community characteristics. Both are derived from a
function used in the field of information (mainly insurance companies) and have been
adapted by ecologists to describe the average degree of uncertainty of predicting the
species of an individual picked at random from the community. The uncertainty of
occurrence increases both as the number of species increases and as the individuals
are distributed more and more evenly among the species already present.


Biodiversity Step 1 / Biodiversity Monitoring Form
The 4empowerment projects are designed to allow students from many different schools along a
given watershed to share, compare and discuss each other's sampling station results. For this
reason, it is necessary for each school to report their individual biodiversity results so that they
represent the same amount of area/volume sampled. In addition to allowing these results to be
discussed and compared on the same area/volumetric level, correcting your data will also help
to eliminate bias (a kind of built in standard error present in all scientific studies). The following
steps should be used in order to achieve standardized results:
 Use the Shannon-Wiener formula for each replicate; then, average those numbers so
that you have a mean H' for the entire system.
 Determining the proper correction factor in order for your data to represent the number
of given individuals you would expect to find in 1.0 m
3
of water.
 Apply the conversion factor to your data.
First, (for each individual sample taken)
 Remove all flora/fauna from your sampling device being careful to retain ALL sample
materials
 Identify and count all species using accurate and precise laboratory procedures
 Record each species found [Note: initially it is not necessary to know the exact
scientific name of the organism found as long as all like species are identified to the
same generic level (example: fish A...B...etc.)]
 Record the number of individuals within each species
 Record the dimensions of the sampling device used
 Record the distance the device was pulled through the water (Note: this measurement
should be the same for all replicates, otherwise, it will be necessary to calculate a
correction factor for each sample taken)
The following is an example of a correctly reported sample:
BIODIVERSITY MONITORING FORM
Biodiversity Step 1
Sampling Technique:
Kick Net

Seine (optional)
Date: 04-02-1999
Length Of Pull (meters): 3.0m
School: Riverside High School
Test Site: San Felipe River sampling station
Replicate Number: 1of 3 (circle one)
Time (military): 09:30
Seine/Kick net dimensions: .25m * .45m
Monitoring Group: Extreme Team
Species
Green Darter
Red Darter
Mosquito Fish
Dragonfly Nymph A

Whirligig beetle
Amphipod A
Number of Individuals Collected

5
2
4
1
2
15

Biodiversity Step 2 / Correction Factor Determination Form
Because each sampling station located along the study system will utilize slightly
different sampling methods, it is necessary to determine the correction factor for your
sampling device. Therefore, ALL biodiversity data needs to reflect the estimated
number of species and organisms found within a standardized unit of water (i.e. 1.0
m3).
The process of standardizing data or formulating a correction factor is important so
that each individual school participating in the project will be able to interpret, utilize,
and compare each other's river monitoring data. NOTE: Correction factors need only
be computed once for each sampling station and technique unless the
sampling device or volume of water sampled is changed.
DETERMINING THE DESIRED VOLUME
1. Using the information from your BIODIVERSITY MONITORING FORM, determine
the area of your sampling device. Since both the kick net and seine are both
rectangles (when fully submerged in the water), the formula will be:
Width of net * Height of net = Area of net
A. Using the information from your BIODIVERSITY MONITORING FORM,
determine the volume of water sampled through the sampling device. The
formula will be:
Area of net * Distance net was pull through water = Volume of water
sampled
B. Now that the volume of water filtered through either the seine or the kick
net has been determined, a correction factor must be calculated in order
that an estimated average of how many organisms found in your samples
are expected to be found in 1.0 m3 of water.
Since we know that 1.0 m
3
of water contains 100 cm (width)* 100 cm
(height) *100 cm (depth), we know that there are 1,000,000 cm
3
in 1.0
m
3
. THIS IS OUR DESIRED VOLUME
1,000,000 cm
3

DETERMINING THE ACTUAL VOLUME SAMPLED
1. From our sample BIODIVERSITY MONITORING FORM, we recorded our net
dimensions as:
.25 m * .45 m or converting to cm = 25 cm * 45 cm = 1,125.00 cm
2

2. From our sample BIODIVERSITY MONITORING FORM we recorded our length of
pull as 3.0 m. In order to obtain the ACTUAL VOLUME FOR ONE REPLICATE of
water filtered we multiply by 300 cm to get the number of cm
3
. The resulting
equation is:
1,125.00 cm
2
* 300 cm = 337,500 cm
3

3. From our sample BIODIVERSITY MONITORING FORM we recorded that we had
three replicates. We must now multiply our results by three to get the ACTUAL
VOLUME FOR ALL REPLICATES.
337,500.00 cm
3
* 3 = 101,250.00 cm
3

THIS IS OUR ACTUAL VOLUME FOR ALL REPLICATES
1,012,500 cm
3

(Note: This number will change for each sampling technique used.)
DETERMINING THE CORRECTION FACTOR
In order to determine the correction factor for converting the number of organisms found in
1,012,500 cm
3
to the number of organisms you would expect to find in 1,000,000 cm
3
, we
divide the DESIRED VOLUME by the ACTUAL VOLUME FOR ALL REPLICATES.
1,000,000 cm
3
/ 1,012,500. cm
3
= .9877
The correction factor for this sampling technique is:
.9877




Biodiversity Step 3 / Species Diversity Worksheet
The Shannon and Simpson indices are the two most widely used species diversity indices for
examining overall community characteristics. Both are derived from a function used in the field
of information (mainly insurance companies) and have been adapted by ecologists to describe
the average degree of uncertainty of predicting the species of an individual picked at random
from the community. The uncertainty of occurrence increases both as the number of species
increases and as the individuals are distributed more and more evenly among the species
already present.
THE SHANNON-WIENER SPECIES DIVERSITY INDEX
The Shannon-Wiener species diversity index, when properly manipulated, will always result in a
diversity value (H') ranging between 0 (indicating low community complexity) and 4 (indicating
high community complexity). It is not necessary to key all organisms to their specific species
nomenclature (i.e. organisms which can not be expediently identified may be assigned numeric
values such as species 1, 2, 3, etc.). However, in order to derive accurate diversity values, all
organisms should be keyed to the lowest possible like taxonomic level. The following is an
example of the Shannon-Wiener formula and how it should be used.


N = Total # individuals in all species
N
i
= # of individuals in each species
3.322= Conversion factor from base 10 to base 2
H' = Diversity (0-4)
REPLICATE #: DATE: LOCATION:
Species N
i
log N
i
N
i
(log N
i
)
Cheatocerus sp. 15 1.17 17.55
Skeletonema sp. 20 1.3 26.00
Thallassiomena sp. 17 1.23 20.90
Cosinodiscus sp. 19 1.28 24.32
Sagitta sp. 12 1.08 12.96
N =83
N
i
(log N
i
) =
101.73





For each replicate, apply the Shannon-Wiener formula separately; then, find the mean
(average) H' (species diversity). Then go on to find the standard deviation of that average H' if
you choose to. Details for standard deviation are on Biodiversity Step 3 forms. The purpose of
replication is to quantify the degree of variability in the sampling scheme.

Biodiversity Step 4 / Data Compliation Form
From your individual BIODIVERSITY MONITORING FORM for each sample and the
CORRECTION FACTOR DETERMINATION FORM, (Biodiversity Step 2), complete the
following.
 Compile the inworksheetation from each replicate onto the DATA COMPILATION
FORM
 Add together the number of individuals found in each species
 Divide the number of individuals found in each species by the number of replicates
 Multiply each of your averaged the number of individuals found in each species by your
calculated CORRECTION FACTOR
 Compute the estimated percentage of individuals within each species in 1.0 m
3
of
water.
 Rank your percentages according from most dominant species to the least dominant
species
The following is an example of a correctly filled in DATA COMPILATION FORM:
DATA COMPILATION FORM
Biodiversity Step 4
Correction Factor (c.f.) = .9877
Species Number of
individuals in each
replicate
Total # of
ind. in each
species
Total # ind. in
each species
divided by # reps.

# indiv in
all reps. *
c.f.
% total
per m
3

Dom
rank
1 2 3 4 5 (.9877)
Green
Darter
5 4 1

10 3.33 3.289 30.25 1
Red Darter 2 6 0

8 2.67 2.637 24.25 2
Mosquito
Fish
0 2 3

5 1.67 1.6495 15.18 3
Dragonfly
Nymph A
1 0 4

5 1.67 1.6495 15.18 3
Whirligig
beetle
0 0 3

3 1.0 .9877 9.08 4
Amphipod A

0 2 0

2 .67 .6610 6.06 5

Total X X X

X X 10.874 100 % X