DIVERSITY INDICES: SHANNON'S H AND E
DIVERSITY INDICES: SHANNON'S
H AND E
Introduction: A diversity index is a mathematical measure of
species diversity in a community. Diversity indices provide more information
about community composition than simply species richness (i.e., the number of
species present); they also take the relative abundances of different species
into account (for an illustration of this point, see below, or introduction to SIMPSON'S D AND E).
Importance: Diversity indices provide important
information about rarity and commonness of species in a community. The ability
to quantify diversity in this way is an important tool for biologists trying to
understand community structure.
Question: How do we measure diversity?
Variables:
H
|
Shannon's
diversity index
|
S
|
total number of species in the
community (richness)
|
pi
|
proportion of S made up of the
ith species
|
EH
|
equitability (evenness)
|
Methods: The Shannon
diversity index (H) is another index that is commonly used to
characterize species diversity in a community. Like Simpson's index, Shannon's index accounts for both abundance and evenness
of the species present. The proportion of species i relative to the
total number of species (pi) is calculated, and then
multiplied by the natural logarithm of this proportion (lnpi).
The resulting product is summed across species, and multiplied by -1:
Shannon's
equitability (EH) can be calculated by dividing H by Hmax
(here Hmax = lnS). Equitability assumes a value
between 0 and 1 with 1 being complete evenness.
Example:
The graph below shows H and EH for four hypothetical communities, each consisting of 100 individuals. The communities are composed of 5, 10, 20 and 50 species, respectively. For each community H and EH have been calculated for the case in which individuals are distributed evenly among the different species (i.e., each species makes up an equal proportion of S), and for the case in which one species has 90% of the individuals, and the remaining individuals are distributed evenly. For example, in a community with 10 species in which the species contain equal numbers of individuals, p = 0.1 for each species. In a community with 10 species in which one species has 90% of the individuals, p = 0.9 for the dominant species, and p = 0.01 for the other nine species. The diamonds represent H and EHvalues for the first case (equal proportions), and the triangles represent values for H and EH for the second case (unequal proportions).
The graph below shows H and EH for four hypothetical communities, each consisting of 100 individuals. The communities are composed of 5, 10, 20 and 50 species, respectively. For each community H and EH have been calculated for the case in which individuals are distributed evenly among the different species (i.e., each species makes up an equal proportion of S), and for the case in which one species has 90% of the individuals, and the remaining individuals are distributed evenly. For example, in a community with 10 species in which the species contain equal numbers of individuals, p = 0.1 for each species. In a community with 10 species in which one species has 90% of the individuals, p = 0.9 for the dominant species, and p = 0.01 for the other nine species. The diamonds represent H and EHvalues for the first case (equal proportions), and the triangles represent values for H and EH for the second case (unequal proportions).
For
the first case, EH is always equal to one (complete evenness,
or equitability), but H increases dramatically as the number of species
increases, as we would expect. For the second case, in which one species makes
up 90% of the community, the picture is a little different. Here we can see
that although H does increase with increasing numbers of species, it
does so much more slowly than in the first case. Additionally, EH
decreases as species number increases (since one species always makes up 90% of
the community in the second case of this hypothetical example, the remaining
species make up some fraction of 10% of the community; as species number
increases this fraction becomes smaller and evenness decreases). H and EH
clearly give more information about these communities than would species number
(richness) alone.
The
following table contains data from a study of Costa Rican ant diversity (Roth et
al. 1994). The authors measured diversity in four different habitats
ranging very low levels of human disturbance (primary rain forest) to very high
levels of human disturbance (banana plantations) to assess the impacts of
different levels of disturbance on biological diversity. For each habitat
studied we will use data collected from one site within that habitat. The numbers
below represent relative proportions of each species (from Roth et al.
1994 [family names have been omitted]).
Interpretation: We can see from our results that the
diversity and evenness in this site from the undisturbed habitat (primary rain
forest) are much higher than in the site from the highly disturbed habitat
(banana plantation). The primary rain forest not only has a greater number of
species present, but the individuals in the community are distributed more
equitably among these species. In the banana plantation there are 23 fewer
species and over 80% of the individuals belong to one species, Solenopsis
geminata (the most common species in the primary rain forest, on the other
hand, makes up about 16% of the community [Pheidole sp. 15]).
Conclusions: Different levels of disturbance have
different effects on ant diversity. If our goal is to preserve biodiversity in
a given area, we need to be able to understand how diversity is impacted by
different management strategies. Because diversity indices provide more
information than simply the number of species present (i.e., they account for
some species being rare and others being common), they serve as valuable tools
that enable biologists to quantify diversity in a community and describe its numerical
structure
DIVERSITY INDICES: SIMPSON'S D AND E
Introduction: A diversity index is a mathematical measure of
species diversity in a community. Diversity indices provide more information
about community composition than simply species richness (i.e., the number of
species present); they also take the relative abundances of different species
into account. Consider two communities of 100 individuals each and composed of
10 different species. One community has 10 individuals of each species; the
other has one individual of each of nine species, and 91 individuals of the
tenth species. Which community is more diverse? Clearly the first one is, but
both communities have the same species richness. By taking relative abundances
into account, a diversity index depends not only on species richness but also
on the evenness, or equitability, with which individuals are distributed among
the different species.
Importance: Diversity indices provide important information
about rarity and commonness of species in a community. The ability to quantify
diversity in this way is an important tool for biologists trying to understand
community structure.
Question: How do we measure diversity?
Variables:
D
|
Simpson's diversity index
|
S
|
total number of species in the
community (richness)
|
pi
|
proportion of S made up of the
ith species
|
ED
|
equitability (evenness)
|
Methods: Simpson's diversity index (D)
is a simple mathematical measure that characterizes species diversity in a
community. The proportion of species i relative to the total number of
species (pi) is calculated and squared. The squared
proportions for all the species are summed, and the reciprocal is taken:
For
a given richness (S), D increases as equitability increases, and
for a given equitability D increases as richness increases. Equitability
(ED) can be calculated by taking Simpson's index (D)
and expressing it as a proportion of the maximum value D could assume if
individuals in the community were completely evenly distributed (Dmax,
which equals S-- as in a case where there was one individual per
species). Equitability takes a value between 0 and 1, with 1 being complete
evenness.
Siemann
et al. (1997) collected the following data on oak savanna arthropod
communities to investigate the effects of prescribed burning on arthropods. The
abundance data below represent the number of individuals per family (rather
than per species) collected in sweep-net sampling during a two year period
(1992-1993) (from Siemann et al. 1997).
Although
we do not have species data, we can calculate family diversity and equitability
using these data. The proportions (pi values) have been
calculated by dividing the number of individuals in a given family by the total
number of individuals collected in a year (8,561 in 1992 and 1,379 in 1993). To
calculate Simpson's D, we square each proportion (pi),
sum these squared values, and take the reciprocal (divide one by the sum). For
example, for the 1992 data, Simpson's D is calculated (1 / [0.0132
+ 0.0082 + 0.0002 + 0.0152 + ... + 0.0072])
= 8.732. We could then calculate the equitability (ED) quite
easily using the second equation above (ED = D / Dmax,
with Dmax = S). Here, we will use the number of
families in place of S, so that E = 8.732 / 31 = 0.2817.
Interpretation: What we have calculated is an index of
family diversity and evenness, rather than the standard index of species
diversity and evenness. Based on the value of 0.2817 calculated for ED,
we could describe the equitability, or evenness of individuals' distributions
among families, in this community as relatively low (recall that ED
assumes a value between 0 and 1, and 1 is complete equitability).
Conclusions: Simpson's D is one of many
diversity indices used by biologists. Others include the Shannon index (H),
the Berger-Parker index (d), Hill's N1, and Q-statistics.
Each of these indices has strengths and weaknesses. An ideal index would
discriminate clearly and accurately between samples, not be greatly affected by
differences in sample size, and be relatively simple to calculate. Biologists
often use a combination of several indices to take advantages of the strengths
of each and develop a more complete understanding of community structure.
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