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COMMUNITY STRUCTURE EXERCISE Name
You must show your work on separate paper to get credit for the answer. Exercise 1 – Calculating Species Diversity
1. Calculate Simpson’s index and Shannon’s index for communities B and C. Fill in the table:
Community
Simpson’s index
Shannon’s index
A
4.21
1.51
B
C
2. Fill in the blank with the words indicated in parentheses following the blank.
For both indexes, greater evenness with the same richness provides a
(higher, lower, or the same) index value. (Compare A & B communities.)
When evenness is nearly identical, the community with the higher richness has a (higher, lower, the same) index value. (Compare B & C communities.)
Exercise 2 – Quantifying community similarity
1. Use Jaccard’s index to calculate the similarity between communities A and C and between communities B and C. Fill in the table:
Communities
Jaccard’s index
A & B
0.37
A & C
B & C
2. Based on these calculations, which communities are most like each other? Exercise 3 – Estimating the number of species in an area
1. Using the equation, estimate the number of species in communities B and C. Fill in the table:
Community
Number of species
A
13
B
C
2. Fill in the blank with the words indicated in parentheses following the blank:
The greater the number of species represented by a single individual, the (greater, lesser, the same) the estimated number of species in the community.
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Exercise 1: Calculating Species Diversity
Ecologists agree that communities with more species and greater evenness have higher species diversity. To quantify the species diversity of a community, we need a method of calculating a single value for species diversity. Over the years, numerous indices of species diversity have been created.Wewill consider the two that are most common and equally valid: Simpson’s index and Shannon’s index. Both indices incorporate species richness, which we abbreviate as S, and evenness. However, they do so in different ways.
To see how we calculate species diversity with either index, we can begin with data from three communities for which we have the absolute abundance for each of the species. From these data we can then calculate relative abundance for each of the five species in the community, which is denoted Pi. With these relative abundance data, we can calculate both Simpson’s index and Shannon’s index.
Table 1: The abundance of different mammal species in three communities:
Community A
Community B
Community C
Species
Absolute
abundance
Relative
abundance (pi)
Absolute
abundance
Relative
abundance (pi)
Absolute
abundance
Relative
abundance (pi)
Mouse
24
0.24
18
33
Chipmunk
16
0.16
22
33
Squirrel
8
0.08
20
33
Shrew
34
0.34
17
0
Vole
18
0.18
23
0
Total
abundance
100
1.0
100
1.0
99
0.99
S
5
5
5
5
3
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Simpson’s Index (D), measurement of species diversity, is given by the following formula:
D = 1
∑ (pi) ���� 2
����=1
In words, this formula means that we square each of the relative abundance values, sum these squared values, and then take the inverse of this sum. For example, for Community A, Simpson’s index ofspecies diversity is:
���� = 1
(0.24)2 + (0.16)2 + (0.08)2 + (0.34)2 + (0.18)2
���� = 1
0.238
���� = 4.21
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Simpson’s index can range from a minimum value of 1, which occurs when a community only contains one species, to a maximum value equal to the number of species in the community. This maximum value only occurs when all the species in the community have equal abundances.
Shannon’s index (H’), also known as the ShannonWiener index, is another measurement of species diversity given by the following formula:
In words, this formula means that we multiply each of the relative abundance values by the natural log of the relative abundance values, sum these products, and then take the negative of this sum. For example, in Community A, Shannon’s index is
= – [(-0.34) + (-0.29) + (-0.20) + (-0.37) + (-0.31)]
= – [-1.51]
= 1.51
Shannon’s index can range from a minimum value of 0, which represents a community that contains only one species, to a maximum value that is the natural log of the number of species in the community. As we saw with Simpson’s index, the maximum species diversity value occurs when all species in the community have the same relative abundances.
YOUR TURN Calculate Simpson’s index and Shannon’s index for communities B and C. Based on your calculations, how does species evenness and species richness affect the values of each index?
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Exercise 2: Quantifying Community Similarity
When ecologists examine the species living in different communities, they often quantify composition and richness. Although such data tell us about the species living in each community, they do not provide a measure of comparison. To address this need, ecologists have developed several indices of community similarity that can range from zero to one. A value of zero indicates that two communities have no species in common, whereas a value of one indicates that two communities have an identical composition of species.
One of the most common ways to quantify similarity is Jaccard’s index of similarity, developed by the Swiss botanist Paul Jaccard in 1901. Jaccard’s index is calculated using the following equation:
���� = ����
A + B + X
Where A represents the number of species present in ONLY community A, B represents the number of species found ONLY in community B, and X represents the number of species found in BOTH in communities A and B.
For example, consider the table below that lists the species of fish found in each of three stream communities that are at different stages of succession. We can use Jaccard’s index to calculate the similarity between Community A and Community B.
Species
Community A
Community B
Community C
Rainbow trout
X
X
Brook trout
X
X
Brown trout
X
X
Mudminnow
X
Common shiner
X
X
X
Creek shiner
X
White sucker
X
X
Johnny darter
X
X
Smallmouth bass
X
Mottled sculpin
X
X
������������ = 3
1 + 4 + 3
J AB = 0.37
This value indicates that there is relatively low similarity in the species composition of Communities A and B.
YOUR TURN Use Jaccard’s index to calculate the similarity between Communities A and C and between Communities B and C. Based on these calculations, which communities are the most similar to each other?
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Exercise 3: Estimating the Number of Species in an Area
As we have seen, ecologists often need to estimate how many species exist in an area. Since counting every individual is rarely possible, we must take a sample of an area to estimate how many species are present. One way to estimate the number of species in a sample is to graph the number of species that we observe as we increase our sample size. One would expect that the more we sample, the closer we will get to knowing the actual number of species in an area. Eventually, thecurv will reach a plateau so that any additional sampling will not discover additional species.A graph of the number of species observed in relation to the number of individuals sampled is known as a species accumulation curve.
A second way to estimate the number of species in an area is based on the number of rare species that are detected. When we sample many individuals in a community, we typically end up with a high number of individuals for each of the common species but we may detect only one or two individuals of rare species.
· We can estimate the number of species actually living in an area (S) by sampling the community to determine how many species are observed (Sobs), how many species are represented by two individuals (f2), and how many are represented by one individual (f1). In essence, species represented by two individuals are likely to be more common in the community than species represented by single individuals. We can therefore estimate the number of actual species that live in a community by starting with how many species we have observed and multiplying this by a ratio that incorporates the number of species represented by one versus two individuals:
·
���� = Sobs + ����1(����1 − 1)
2 (����2 + 1)
As you can see in this equation, the estimated number of species in a community increases with an increase in the number of species represented by a single individual and decreases with an increase in the number of species represented by two individuals. For example, consider the table on the following page that lists the number of individuals observed for 12 species sampled from three pond communities.
Using the data for Community A, we can estimate the actual number of species. In this community, we have observed 12 species. Two individuals were observed for each of two species, whereas one individual was observed for each of three species. Using our equation above:
���� = 12 +3(3 − 1)
2 (2 + 1)
S = 13
Based on these results, we conclude that although we observed 12 species, we estimate that the community actually contains 13 species.
YOURTURN Using The Equation, estimate the number of species that are present in Community B and Community C. Based on your results, how does the number of species represented by single individuals affect the estimated number of species in
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the community?
Species
Community A
Community B
Community C
Wood frogs
32
65
42
Green frogs
45
24
45
Newts
12
14
5
Spotted salamanders
15
17
12
Ramshorn snails
2
23
67
Pond snails
25
14
2
Amphipods
2
1
2
Isopods
1
1
0
Fingernail clams
9
1
0
Diving beetles
1
1
0
Water boatmen
5
1
0
Dragonflies
1
1
0
