Trees, Timber and Trade
Ecology Workshop #2 Community Analysis: Species Diversity Indices
Introduction
Species diversity (sometimes called species heterogeneity) is an expression of community structure. A
community is said to have high species diversity if many equally or nearly equally abundant species are
present. Conversely, if a community is composed of a very few species, or if only a few species are
abundant, then species diversity is low. For example, if a community had 100 individuals distributed among
10 species, then the maximum possible diversity would occur if there were 10 individuals in each of the 10
species. The minimum possible diversity would occur if there were 91 individuals belonging to one species
and only one individual in each of the other nine species.
High species diversity indicates a highly complex community, for a greater variety of species allows for a
larger array of species interactions. Thus, population interactions involving energy transfer (food webs),
predation, competition, and niche apportionment are theoretically more complex and varied in a community
of high species diversity. There is general agreement among ecologists that high species diversity is
correlated with community stability; the ability of community structure to be unaffected by disturbance of
its components. However, a few maintain that there is no simple relationship between diversity and stability.
Objectives
The objectives of this exercise are to:

To introduce you to two of the most popular species diversity indices; Simpson's Index, and
Shannon's Index,

Gain expertise in computing species diversity indices from a real data set and interpret the results
Measures of Species Diversity
Simpson Index
A good measure of diversity should take into account both the number of species and the evenness of
occurrence of individuals in the various species. Simpson's Index (1949) considered not only the number of
species (s) and the total number of individuals (N), but also the proportion of the total that occurs in each
species. This diversity index is an expression of the number of times one would have to take pairs of
individuals at random from the entire aggregation to find a pair from the same species. This diversity index
is the inverse of Simpson's dominance index and is expressed as:
Ds =1 -
n
2
i
-N
N(N  1)
where:
Ds = Simpson's Index of Diversity
N = total number of individuals of all species
ni = total number of individuals of a species
Table 1: Hypothetical species abundance data used to illustrate the calculation of various diversity indices.
Species (i)
1
2
3
N
Frequency (ni)
50
25
10
85
Relative Abundance (pi)
50/85 = 0.588
25/85 = 0.294
10/85 = 0.118
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Example 1: Using the data in Table 1 as an example for calculating the Simpson Index (Ds) yields the
following:
Ds
n
=1 -
2
i
-N
N(N  1)
= 1 - 3140/7140
= 1 - 0.439
= 0.56
Simpson’s Index is the probability that any two individuals, chosen randomly from the same site, would be
different species. As diversity increases, Ds increases.
Shannon Index
The Shannon Index is another widely employed species diversity index. Derived from information theory, it
measures the degree of uncertainty in a sampling event. That is, if diversity is low, then the certainty of
picking a particular species is high. If diversity is high, then it is difficult to predict the identity of a
randomly picked individual. The mathematical expression of the Shannon Diversity Index is shown below:
H = (N log N - ∑ni log ni) /N
where:
H = the Shannon Index of Diversity
Example 2: Using the data in Table 1 as an example for calculating the Shannon Index yields:
H = [85 log 85 - (50 log 50 + 25 log 25 + 10 log 10)] /85
= [164.001 - (84.949 + 34.949 + 10.000)]/85
= 34.103/85
= 0.40
The Shannon Index (H) is appropriate when you have a random sample of species abundance's from a larger
community or sub-community of interest. Such a sample (unless extremely large) may not contain
representatives for each species in the entire community. However, the lack of data on rare species has little
effect on the value of H.
Exercise
Calculate Simpson’s and Shannon’s Indices for the data given below.
Sample Data Sets
Species I
II III
A
10 25 37
B
10
7
1
C
10
4
1
D
10
4
1
Q1. How do the two indices vary between the sites? Do they both give you the
same information?
Q2. Calculate Simpson’s Index for one of the data sets given out in class.
Compare the relative diversity of the sites. There are two data sets, both from
Fort Lewis. The first data are from a plot in a transition zone between prairie and
forest that was sampled over a period of years. The second data are from three
different sites, a prairie, a transition between prairie and forest, and a forest site. Make a statement about the
relative diversity of the sites your group analyzes.
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Time Sequence Data for Prairie/ Forest Transition
Sum of CountOfPlant Acronym
COMMON NAME
Bareground
Barren fesc ue
Bicolored linanthus
Blue-eyed grass
Brack en fern
Broadpetal strawberry
California oatgrass
Camas
Canadian bluegrass
Casc ara
Cleavers
Colonial bentgrass
Common speedwell
Common vetch
Creeping snowberry
Cut-leaved microseris
Douglas fir
English plantain
Field chickweed
Field woodrush
Hairy cat's-ear
Hop clover
Hound's tongue hawkweed
Idaho fescue
Junegrass
Kentucky bluegrass
Klamath weed
Least hop clover
Litter Forb
Litter Grass
Litter Shrub
Litter Tree
Little hairgrass
Long stolon sedge
Long-stalked geranium
Miner's lettuce
Missouri goldenrod
Moss
Nuttall's violet
Oregon sunshine
Ox-eye daisy
Pacific bromegrass
Pennywort
Pomo-celery
Quack grass
Red fescue
Rosy puss ytoes
Scot's broom
Self-heal
Serviceberry
Showy fleabane
Sick le keeled lupine
Silver hairgrass
Slender cinquefoil
Small-flowered deervetch
Snowberry
Soft brome-grass
Sour weed
Spreading dogbane
Sweet cicely
Velvet grass
Wall bedstraw
Western buttercup
White-topped aster
Yarrow
Grand Total
Year
1994 1996 1998 1999 2001 Grand Total
2
2
1
5
6
3
2
5
2
2
13
4
7
1
1
26
8
7
15
9
4
43
4
1
4
9
7
6
13
1
1
2
2
6
1
7
62
58 114
26
28
288
1
1
2
4
2
2
5
4
1
14
1
1
3
1
4
20
52
60
36
26
194
4
8
1
13
1
1
2
1
2
3
1
3
4
1
1
3
1
1
5
19
26
28
6
8
87
3
3
11
4
1
3
19
2
2
5
4
13
2
7
9
1
1
11
10
1
14
39
75
4
1
4
1
10
1
2
5
8
16
1
1
2
32
40
16
17
10
115
1
1
2
1
1
1
1
1
2
2
3
8
1
1
3
2
1
2
2
10
4
2
1
7
3
3
3
1
8
3
15
8
2
6
14
5
35
2
2
5
5
4
14
1
1
47
20
97
35
59
258
2
2
2
10
8
16
4
40
1
1
3
6
4
13
1
1
1
1
1
3
6
1
7
1
1
1
1
5
7
3
1
1
2
7
5
2
7
1
1
29
3
6
38
4
4
2
5
3
3
13
1
1
2
7
4
1
4
16
281 296 466 249 228
1520
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Data for Fores t, Prairie and Prairie/ Forest Transition
Sum of No. indivuals
Common name
Bigleaf sandwort
Blue ryegrass
Brack en fern
Broadpetal strawberry
California oatgrass
Camas
Cleavers
Colonial bentgrass
Columbia bromus
Common vetch
Douglas fir
Duff Tree
English plantain
Evergreen violet
Field chickweed
Foam flower
Hairy cat's-ear
Hound's tongue hawkweed
Idaho fescue
Inside-out flower
Junegrass
Kentucky bluegrass
Kinnikinnick
Klamath weed
Least hop clover
Litter Forb
Litter Grass
Litter Shrub
Litter Tree
Long stolon sedge
Miner's lettuce
Moss
Nine-leaf lomatium
Nodding fescue
Oregon sunshine
Ox-eye daisy
Pacific dogwood
Pennywort
Pomo-celery
Poverty danthonia
Quack grass
Red fescue
Red huckleberry
Salal
Scot's broom
Scouler's harebell
Serviceberry
Silver hairgrass
Slender cinquefoil
Small-flowered deervetch
Sour weed
Starflower
Sweet vernal grass
Sword fern
Trailing blackberry
Twinflower
Velvet grass
Wall lettuce
Western buttercup
White-flowered hawkweed
White-topped aster
Yarrow
Grand Total
Location
Forest
Prairie
Transition Grand Total
7
2
9
1
4
1
7
1
30
2
1
91
1
48
2
6
1
28
1
26
1
1
2
1
6
1
1
53
1
8
16
9
8
2
3
1
1
11
3
16
39
1
22
24
1
10
1
3
2
1
4
1
4
7
3
2
1
4
3
5
1
6
4
1
4
8
16
4
59
4
1
1
1
2
2
1
2
12
69
68
17
9
2
6
1
3
2
1
191
1
4
228
2
447
7
2
10
4
1
13
2
106
2
4
117
1
1
1
3
1
7
1
61
16
9
11
2
1
1
11
58
1
22
35
1
5
1
4
9
5
4
3
9
1
1
10
4
8
75
4
4
1
1
1
5
2
12
69
68
17
15
2
4
2
3
5
866