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Biodiversity Indices
Species Richness, Simpson’s, and Shannon-Weaver…oh my…
What is Biodiversity?

In its simplest form, biological diversity is the variety of different types of
organisms present and interacting in an ecosystem. One could say that more
species equals more diversity, although a closer look will soon require us to
qualify that statement. There are, in fact many more factors beyond a simple
count of species that determine whether biodiversity is higher or lower in any
given ecosystem.
Species Richness

Species richness (S) is a measure of the number of species found in a sample.
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Since the larger the sample, the more species we would expect to find, the
number of species is divided by the square root of the number of individuals
in the sample. This particular measure of species richness is known as D, the
Menhinick's index.

D = s/√N

s = the # of different species

N = total # of individuals
Simpson’s Index, Index of Biodiversity,
and Reciprocal

The term 'Simpson's Diversity Index' can actually refer to any one of 3 closely
related indices.

Simpson's Index (D) measures the probability that two individuals randomly
selected from a sample will belong to the same species (or some category
other than species). There are two versions of the formula for calculating D.
Either is acceptable, but be consistent.

D = SUM n(n-1) / N (N-1)
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The value of D ranges between 0 and 1

With this index, 0 represents infinite diversity and 1, no diversity. That is, the
bigger the value of D, the lower the diversity. This is neither intuitive nor
logical, so to get over this problem, D is often subtracted from 1 to give:
Continued…

Simpson's Index of Diversity 1 – D

The value of this index also ranges between 0 and 1, but now, the greater the
value, the greater the sample diversity. This makes more sense. In this case,
the index represents the probability that two individuals randomly selected
from a sample will belong to different species.

Another way of overcoming the problem of the counter-intuitive nature of
Simpson's Index is to take the reciprocal of the Index:

Simpson's Reciprocal Index 1 / D

The value of this index starts with 1 as the lowest possible figure. This figure
would represent a community containing only one species. The higher the
value, the greater the diversity. The maximum value is the number of species
(or other category being used) in the sample. For example if there are five
species in the sample, then the maximum value is 5.
Simpson’s Interpretation

D is a measure of dominance, so as D increases, diversity (in the sense of
evenness) decreases. Thus, Simpsonʼs index is usually reported as its
complement 1-D (or sometimes 1/D or –lnD). Since D takes on values between
zero and one and approaches one in the limit of a monoculture, (1-D)
provides an intuitive proportional measure of diversity that is much less
sensitive to species richness.
Shannon-Weaver

This diversity measure came from information theory and measures the order
(or disorder) observed within a particular system. In ecological studies, this
order is characterized by the number of individuals observed for each species
in the sample plot (e.g., biofilm on a plexiglass disc). It has also been called
the Shannon index and the Shannon-Weaver index.
Similar to the Simpson index, the first step is to calculate Pi for each category
(e.g., species). You then multiply this number by the log of the number. While
you may use any base, the natural log is commonly used (ln). The index is
computed from the negative sum of these numbers. In other words, the
Shannon-Wiener index is defined as:

H = - SUM [Pi x lnPi], where Pi = ni/N
S-W Interpretation

Typical values are generally between 1.5 and 3.5 in most ecological studies,
and the index is rarely greater than 4. The Shannon index increases as both
the richness and the evenness of the community increase. The fact that the
index incorporates both components of biodiversity can be seen as both a
strength and a weakness. It is a strength because it provides a simple,
synthetic summary, but it is a weakness because it makes it difficult to
compare communities that differ greatly in richness.

Due to the confounding of richness and evenness in the Shannon index, many
biodiversity researchers prefer to stick to two numbers for comparative
studiescombining a direct estimate of species richness (the total number of
species in the community, S) with some measure of dominance or evenness.
The mostcommon dominance measure is Simpsonʼs index.