Community Diversity – Measures and Techniques
What is the best way to describe community diversity? Is it:
1. Species richness – the total number of species encountered
in samples (or in the entire community if sampled areas are
combined to determine the asymptotic richness)…or…
2. A measure of species diversity. There are many suggested
measures (see Table 9.2, pg.216). The most widely used
are:
a. Simpson’s Index (or a direct derivative from it),
b. Shannon-Weiner Information Theory diversity (or a
derivative),
c. Brillouin’s index,
d. Pielou’s index
e. Fisher’s 
Simpson’s index is:
s
D  1 /  pi2
i 1
This index generally emphasizes the more common species in
the value of the index. Those species contribute more to the
sum of squares of proportions, while rare species contribute
little. If there are no really common species, then the index
works well.
This index also does not require full knowledge of the
community to make statistical comparisons. Russell Lande
showed that there is an unbiased version of this index (N is
the number of individuals sampled):
D
1 N
1  N  pi2
Shannon-Weiner Information Theory diversity is:
s
H '    pi ln 2 pi
i 1
As long as the same base is used, you don’t really have to
determine logs base 2, but that is the theoretical requirement.
This index places greater emphasis on rare species.
To try to portray the distribution of species abundances, H’ is
frequently compared with the maximum possible value,
which would be found if all species were equally abundant.
If all species were equally abundant:
s
1 1
H '   s ln  
s
i 1 s
 ln1  ln s  ln s
The ratio H’/ln s is called evenness. Since the index is based
on logs, the Shannon-Weiner index is sometimes ‘corrected’
by presenting eH’, though this ‘correction is not common in
the literature.
The problem with information theory is that to make
appropriate statistical comparisons you need to know how
many total species comprise the community. Then the
comparisons you make are between individual samples and
the total community. Differences are subjected to typical
kinds of statistical analysis. The basic index and evenness
measures are described as “biased”.
Yet this remains probably the most commonly used index of
diversity.
Brillouin’s index is:
s
ln N !
HB 
 ln n !
i 1
i
N
This index also emphasizes the effect of rare species. Note
that it uses ni, the number of individuals in the species, and
can’t be used with alternative measures like biomass.
Brillouin’s index also has an evenness ratio. The formula is
too complicated to insert here; look it up if you want to use
Brillouin’s index in a research context.
Pielou’s index is closely related to Brillouin’s, and similarly
provides a better indication of rare species contribution than
common species. It is:
N!
log 2 s
i 1 ni !
HP 
N
There is one last index that has fallen out of favor recently. It
isn’t even listed in the text, but can be very valuable in low
diversity or early successional communities. Fisher’s index is
called , and requires iterative calculation using the number
of species and the number of individuals. It comes from
Fisher’s log series estimate of community structure,
sometimes called a ‘broken stick’ model.
There are actually two steps to determine . First you need to
know the number of species and number of individuals in
your samples. From this information you calculate x:
S 1 x

(  ln(1  x ))
N
x
Then you use the calculated x to further calculate :
N (1  x )

x
In practice there is no explicit equation solution for x, so a
computer program (not really very complicated) is used to get
x, and from it calculating  is straightforward.
Sampling schemes in community studies
The text considers first a European approach in which a large
sample plot, called a relevé, is subjectively chosen to represent
the community. A species-area curve is constructed by
collecting samples representing a series of ‘nested’ quadrats,
slowly expanding the total area sampled within the relevé.
This approach typically uses species richness as the measure
of diversity.
In North American ecology, the typical method is to collect
data from randomly placed, small quadrats. Some ecologists
instead use regularly placed (evenly spaced) quadrats. While
sizes vary depending on the community, typically the quadrats
range in area from ¼ m2 to around 1 m2. In forests, it is
obvious that larger sample areas would be required.
The data (numbers of individuals or biomass of each species)
is then used to calculate (and compare) any of the diversity
statistics.
What shape should these quadrats be?
There are arguments among ecologists about this. One view is
to use square quadrats. This approach is frequently used when
vegetation is to be mapped, so that distances between
individuals and species is being collected. A rigid frame
supports a clear plexiglas sheet marked with grid squares.
Sheets of thin clear plastic can be laid over the support, and
plants mapped onto the sheet.
On the other hand, if biomass or numbers of individuals are
the data of interest, circular quadrats are more frequently
used. Hoops enclosing the appropriate area can be tossed to
randomize placement.
One of the arguments advanced to support using circular,
rather than square quadrats, is that if there are spatial
gradients in the distribution of species, the corners of the
square (or rectangular) quadrats will ‘pick up’ species more
likely to differ from the basic pattern within the sample area
than is the case with circular sample areas.
A completely different approach is to collect samples along a
transect, which is a long line (e.g. an extended tape measure).
Species or the numbers of individuals of species can be
counted if the occur within some specific distance (10 cm, 20
cm, 1m) on either side of the line. This is called the belt
transect approach.
A related approach uses the line-intercept method. Now you
only count those individuals whose bodies ‘make contact’
with the transect line.
In addition to quantitative data in the form of numbers or
biomass, there are other approaches used in studies of
distributions, rather than abundances.
In this case, data can take the form of frequencies of
occurrence. What fraction of quadrats in an area contain
species A? Is this fraction statistically similar to or different
from the fraction in another community.
A slightly more quantitative measure (but frequently only
approximated) is to use basal cover (or canopy cover for
trees). What area of ground is covered by the plant or plants of
a species? Using frame quadrats and plastic sheets, drawing
the area occupied by a species permits later use of various
tools to quantify cover.
There are also various systems dividing cover into ‘classes’:
The simplest classification is traceable to Braun-Blanquet, but
here are the three shown in the text:
The methods described thus far are hard (or impossible) to use
in studies of forests. There, plotless methods are usually
employed. One of the simplest is the point-centred quadrat
method:
Choose (usually using random number tables) a series of
random points distributed over the forest area being studied.
From each point use a compass to set basic compass
directions (basically axes) pointing N, S, E and W, dividing
the area around this point into four quarters. Measure the
distance (and record the species) closest to the point within
each quarter. Typically these distances are converted into local
densities for the species encountered.
In herbaceous or grassland communities, harvests to
determine biomass are readily completed. What do you do in a
forest?
There are two parts to generating an estimate of tree biomass:
1. Use triangulation methods to estimate the height of the tree.
2. Measure the DBH – diameter at breast height (a standard
height above ground).
Sometimes, for trees grown commercially, only the second
measure is needed. There are standardized tables to convert
DBH to biomass. However, in a natural forest trees may
extend vertically to reach the canopy while not having
grown to the same DBH. Then you need both measures to
estimate biomass.
The point-centred quadrat is the first technique presented that
also provides data about the spatial structure of the
community.
Another method is called Morishita’s index of dispersion.
To calculate it you are back to point-centred quadrats to study
the distribution of a species. The formula for the index is:
I  n
n
[i 1 mi   mi ]
n
2
n
i 1
n
i 1
i 1
[( mi ) 2   mi ]
where you measure the number of individuals within a given
radius (using different radii) of the focal (central) individual. n
is the number of focal individuals and mi is the number of
individuals within the radius of focal individual i.
While the Morishita index can take on a range of values, if:
I > 1 the population has a clumped distribution.
I = 1 the population is randomly distributed. and
I < 1 the population is ‘uniformly’ distributed.