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A tool for computing diversity and consideration on differences between diversity indices

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Diversity represents a key concept in ecology, and there are various methods of assessing it. The multitude of diversity indices are quite puzzling and sometimes difficult to compute for a large volume of data. This paper promotes a computational tool used to assess the diversity of different entities. The BIODIV software is a user-friendly tool, developed using Microsoft Visual Basic. It is capable to compute several diversity indices such as: Shannon, Simpson, Pielou, Brillouin, Berger-Parker, McIntosh, Margalef, Menhinick and Gleason. The software tool was tested using real data sets and the results were analysed in order to make assumption on the indices behaviour. The results showed a clear segregation of indices in two major groups with similar expressivity.
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Journal of Landscape Management (2014) Vol.:5 / No. 2
- 78 -
original research paper
A tool for computing diversity and consideration on differences between diversity indices
Ciprian Palaghianu
Abstract
Diversity represents a key concept in ecology, and there are various methods of assessing it. The
multitude of diversity indices are quite puzzling and sometimes difficult to compute for a large volume
of data. This paper promotes a computational tool used to assess the diversity of different entities. The
BIODIV software is a user-friendly tool, developed using Microsoft Visual Basic. It is capable to
compute several diversity indices such as: Shannon, Simpson, Pielou, Brillouin, Berger-Parker,
McIntosh, Margalef, Menhinick and Gleason. The software tool was tested using real data sets and
the results were analysed in order to make assumption on the indices behaviour. The results showed
a clear segregation of indices in two major groups with similar expressivity.
Keywords: heterogeneity, assessing diversity, Shannon index, Simpson index, Menhinick index
Introduction
The keywords such as biodiversity, diversity or
heterogeneity are extensively used in
ecological studies. So diversity, as a measure
of heterogeneity still represents an important
concept in ecology despite all the new trends
in this field. The pioneer work of Gleason
(1922), Shannon (1948), Simpson (1949) or
Pielou (1969) was continued later in numerous
studies.
There are different aspects of diversity that can
be assessed at landscape level, population
level or even regarding to certain individual
attributes. But why diversity is such an
important feature? That is because diversity
and heterogeneity of a system are frequently
related to its superior stability. A more complex
and diverse system can manifest a higher
resilience to external disturbances.
In forestry, due to a relatively low number of
tree species in the stands located in the
temperate region, the researchers rather focus
on structural or dimensional diversity. This type
of diversity is also related to a higher structural
stability and the interest in this particular field
was constant in the last decades (Zenner &
Hibbs, 2000; Pommerening, 2002; Zenner,
2005; Davies & Pommerening, 2008).
But whatever the theme of the study is, the
measurement of diversity still remains a
puzzling issue. There is a huge diversity
regarding the possibility of assessing diversity.
Ecology offers a great variety of techniques
and indices for measuring this highly
appreciated feature. And this represents in fact
a genuine problem, a scientifically dilemma,
because it is quite challenging to decide which
method or index is more suited to use in your
research.
Although there are several comprehensive
comparative studies that debate on the quality
and sensitivity of the main diversity indices
(Staudhammer & LeMay, 2001; Pommerening,
2006; Lexerod & Eid, 2006), the verdict is still
unclear, and it was not established the
superiority of one particular index.
This paper is not trying either to set a verdict,
but it might cast some light on various aspects
regarding computing and interpreting indices
values.
Material and methods
The computational process required by the
diversity indices is rather complex and difficult,
especially for large amount of data. So the
need for a computer becomes evident. The
advancement in spreadsheets has made this
procedure more approachable, but even with
the help of such software (e.g. Microsoft Excel)
several numerical operations require further
knowledge of VBA coding (Visual Basic for
Applications). This fact might become limitative
for some researchers, so I have developed a
computational tool used to assess the
diversity. BIODIV software is a standalone
program which was coded using Microsoft
Visual Basic and it’s based on earlier personal
studies (Palaghianu & Avăcăriţei, 2006).
BIODIV has a graphic user-friendly interface
and uses the input data from an MS Excel
worksheet (Figure 1).
Using BIODIV, the productivity of computation
increase, the researchers have a convenient
method of data input and the results are rapidly
and easy obtained and saved in a
spreadsheet.
The input data consists in classes and their
frequency. Using this data, the last version of
the software is capable to compute several
diversity indices such as: Shannon, Simpson,
Pielou, Brillouin, Berger-Parker, McIntosh,
Margalef, Menhinick and Gleason.
Journal of Landscape Management (2014) Vol.:5 / No. 2
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Fig. 1: The BIODIV software interface
a) The Shannon index (H)
This is one of the most frequently used
biodiversity index. It originates from the
information theory as a measure of entropy
(Shannon, 1948) and sometimes it is
incorrectly mentioned as Shannon-Wiener or
Shannon-Weaver index.
S
i
ii ppH
1
ln
,
Nnp ii /
where the
same notations are used for all the following
expressions:
H - is the value of Shannon index
i
p
- is the proportion of each class
i
n
- the frequency for the class i
S - the total number of classes
N - the total number of observations
The minimum value of the index is 0 when all
the observations belong to a single class. The
maximum value equals ln (1/S) and it can be
reached when the observations are equally
divided between all the classes.
b) Evenness or Pielou Index (E)
This index represents a standardization form of
the Shannon index, displaying the relations
between the class frequencies (Pielou, 1969).
The evenness equals one when the class
frequencies are similar and it tends to zero
when the majority of observations belong to a
single class.
)ln(S
H
E
c) Brillouin index (HB)
Generally, the value of this index is relatively
closed to Shannon index, but it is always lower
(Magurran, 2004). From the mathematical
perspective, this index is superior in sensitivity
to Shannon and that is why it is recommended
by many. But the complex and intricate
formulae as well as the unexpected results
biased by the observation volume discourage
the researchers in using it.
N
nN
HB
S
i
i
1
)!ln()!ln(
d) The Simpson index (D) is a widely used
index that takes into account not only the
number of classes, but also the proportion of
each class (Simpson, 1949). In general, there
are three alternatives of these indices (D, 1-D
and 1/D).
2
i
pD
,
Nnp ii /
,
In this version, the Simpson index (D)
represents the possibility that two randomly
observations belong to the same class. The
minimum value is 1/S (where S is the total
number of classes) and the maximum is 1.
The diversity Simpson index (1 D) represents
the possibility that two randomly observations
belong to different classes. The minimum value
is 0 and the maximum is 1-(1/S).
The Simpson reciprocal index (1/D) expresses
the number of classes with a high weight which
leads to a specific value of Simpson index D.
The minimum is 1 and the maximum reach S
value.
e) Berger-Parker index (d)
This index simplifies the diversity assessing,
using as reference the dominance or the
maximum proportion of a class (Berger &
Parker, 1970). Its value does not take into
account the number of classes but it is highly
influenced by the equity. The minimum value is
1/S in case of a uniform distribution of
observations between classes and the
maximum extent to 1 for grouping of
observations to a single class.
f) McIntosh index (DMI) is another evaluation
form of dominance (McIntosh, 1967), but the
index is rather infrequently used due to its
computing complexity. Furthermore its
ecological interpretation is controversial.
NN
nN
D
S
i
i
MI
1
2
g) Margalef index (DMg) is clearly inspired by
the Gleason coefficient (Margalef, 1958) and it
is commonly used due to its simplicity. The
index value is not biased by the class
frequencies but depends on the number of
Journal of Landscape Management (2014) Vol.:5 / No. 2
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classes. The minimum value drops to 0 for the
grouping of all observations to a single class.
)ln(
1
N
S
DMg
h) Menhinick index (DMn) resulted after a
comparative study on diversity indices
(Menhinick, 1964). His author developed the
index considering the influence on diversity of
the analysis scale therefore the index value is
not taking into account class frequencies.
N
S
DMn
g) Glisson coefficient (Kgl) is one of the earliest
indices of diversity (Gleason, 1922),
consequently influenced many other indices
afterward. Its value is less dependent on the
analysis scale due to its logarithmic
expression.
K gl = (S 1) / log(N)
The BIODIV software was tested on real data
sets. It was analysed the structural diversity of
a sapling population from a natural
regeneration spot located in Flămânzi Forest
District, parcel 50A, Botoşani County,
Romania. The species composition consists of
30% sessile oak, 20% oak, 30% common
hornbeam, 10% small-leaved linden and 10%
common ash. The biometric features (height,
diameter, crown insertion height and two crown
diameters) of all 7253 saplings and seedlings
were collected from a network of ten
permanent sampling plots (7 x 7 m).
Results and Discussion
Using BIODIV, all the diversity indices prior
mentioned were computed on classes of
diameter, height, crown volume and exterior
surface of the crown. The evaluation was
made separately by species and one
evaluation grouped all the saplings, regardless
of species, by the four biometric features.
In Table 1 there are presented only the indices
values for the whole population of saplings,
regardless of species.
Further, a correlation matrix was computed,
using all the indices values, in order to
establish the indices relationships and similar
behaviours (Table 2 and 3). The correlation
coefficients have large values, as expected,
indicating strong associations between indices
and statistically all the relationships can be
designated as highly significant (***).
Tab. 1: Diversity indices values
Index / feature
diameter
height
crown
volume
crown
surface
Simpson (D)
0,240
0,157
0,974
0,785
Simpson (1-D)
0,760
0,843
0,026
0,215
Simpson (1/D)
4,164
6,351
1,027
1,273
Shannon (H)
1,610
1,973
0,084
0,461
Pielou (E)
0,610
0,729
0,036
0,186
Brillouin (HB)
1,606
1,967
0,082
0,458
Berger-Parker (d)
0,358
0,199
0,987
0,881
McIntosh (Dmi)
0,516
0,610
0,013
0,115
Margalef (DMg)
1,462
1,575
1,012
1,237
Menhinick (DMn)
0,164
0,176
0,117
0,141
Gleason (Kgl)
1,014
1,092
0,702
0,858
Tab. 2: Correlations between diversity indices
1-D
H
HB
d
1-D
1
0,995
0,994
-0,994
H
0,995
1
1,000
-0,996
HB
0,994
1,000
1
-0,996
d
-0,994
-0,996
-0,996
1
Dmi
0,997
0,998
0,997
-0,998
DMg
0,785
0,798
0,801
-0,774
DMn
0,778
0,768
0,761
-0,760
Kgl
0,785
0,798
0,801
-0,774
Tab. 3: Correlations between diversity indices
DMi
DMg
DMn
Kgl
1-D
0,997
0,785
0,778
0,785
H
0,998
0,798
0,768
0,798
HB
0,997
0,801
0,761
0,801
d
-0,998
-0,774
-0,760
-0,774
Dmi
1
0,776
0,782
0,776
DMg
0,776
1
0,573
1,000
DMn
0,782
0,573
1
0,573
Kgl
0,776
1,000
0,573
1
Analysing the mathematical substantiation of
the indices, their values for the different
features and the correlations between indices,
segregation in two main groups was observed.
The first group encompass Shannon, Simpson,
Brillouin, Berger-Parker and McIntosh indices.
Nearly functional relationships between this
indices were detected, with high values of the
coefficient of correlation (over 0,990 ***). The
relation between Shannon and Brillouin index
Journal of Landscape Management (2014) Vol.:5 / No. 2
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is quite functional with a correlation value of
1,00 ***, anticipated by their mathematical
similarity.
The second group is an atypical one,
encompassing Gleason, Margalef and
(questionable) Menhinick indices. We record
another expected functional relationship
between two indices: Gleason and Margalef.
Indices from this cluster are strongly influenced
by Gleason (1922) approach therefore they
don’t take into account the proportion of the
classes. Menhinick index strays from both
groups, but mathematically it is closer related
to the second one, justifying its classification.
Comparing the expressivity of the two groups,
the indices from the first group might be
consider superior, due to their higher
mathematically complexity. Their values are
based not only on the number of classes and
observation, but also on the class proportions.
The differences between the indices from the
first group are not significant considering their
expressivity. Although Shannon index has
constantly higher absolute values compared
with the rest of the indices, this does not imply
a greater sensitivity.
Conclusion
I consider that BIODIV software might improve
the productivity of diversity analysis and it is
quite user-friendly even for the unexperienced
users. The software tool was tested on real
data and the results revealed interesting
differences and similarities in the behaviour of
the studied indices. The results showed a clear
segregation of indices in two major groups with
different expressivity. Generally, the first group
has a more complex mathematic foundation
and it seems more sensitive in assessing
diversity. However there is no justification for
using a whole collection of indices, because all
of them share a similar responsiveness. It is
sufficient to use only one index from the first
group, and I would recommend Shannon or
Simpson due to their notoriety which increases
the possibility to compare the results. The
Simpson index, by all its three versions, offers
a better flexibility and has even a better
ecological interpretation. Nevertheless, the
results can be seriously altered by the way
classes are formed.
As a final mention, BIODIV is non-commercial
software, and it can be used without any
restrictions by researchers.
References
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Planktonic Foraminifera in Deep-Sea
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Davies, O., Pommerening, A., (2008), The
contribution of structural indices to the
modelling of Sitka spruce (Picea sitchensis)
and birch (Betula spp.) crowns, Forest Ecology
and Management 256, 6877;
Gleason, H.A., (1922), On the relation between
species and area, Ecology 3 (2), 158-162;
Lexerod, N.L., Eid, T., (2006), An evaluation of
different diameter diversity indices based on
criteria related to forest management planning,
Forest Ecology and Management 222, 1728;
Magurran, A.E., (2004), Measuring Biological
Diversity, Blackwell Publishing;
Margalef, R., (1958), Information theory in
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McIntosh, R.P., (1967), An index of diversity
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Pommerening, A., (2006), Evaluating structural
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Shannon, C.E., (1948), A mathematical theory
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Staudhammer, C.L., LeMay, V.M., (2001),
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Acknowledgement
This work has been mainly supported by the
Romanian National Authority for Scientific
Research, UEFISCDI, Grant PNII-PT-PCCA-
2011-3.2-1574, no.119/2012 (STROMA).
The views expressed herein are exclusively
those of the author.
Author’s contact
Eng. Ciprian Palaghianu, Ph.D.,
Department of Silviculture and Environmental
Protection, Forestry Faculty,
Stefan cel Mare University of Suceava
Universitatii Street, 13, Suceava, Romania
Phone: (+40) 0745 614 487
Email: cpalaghianu@usv.ro

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"Measuring Biological Diversity assumes no specialist mathematical knowledge and includes worked examples and links to web-based software. It will be essential reading for all students, researchers, and managers who need to measure biological diversity."--BOOK JACKET.
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