Download Species Diversity

1. Introduction
Species diversity (sometimes called species heterogeneity), a characteristic unique to the community level of
biological organization, is an expression of community
structure. The most useful measures of species diversity
incorporate consideration of both the number of species
(richness) and the distribution of individuals among the
species (evenness).
A community is said to have a high species diversity
if many equally or nearly equally abundant species are
present. On the other hand, 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 (example A in Table 5B. I). The minimum possible
diversity among 100 individuals would occur if there
were 9 1 individuals belonging to one of the species and
only one individual in each of the other nine species
(example C in Table 5B.1). In the latter case, the typical
species in the community is relatively rare. so that Patil
and Taillie ( 1982) refer to species diversity as average
rarity of species within a community and relate diversity
measures to the probability of interspecitic encounters.
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. This is still the subject of considerable
discussion; some ecologists have supported the concept
of species diversity as a measure of community stability
(the ability of community structure to be unaffected by
disturbance of its components), while others have concluded that there is no simple relationship between
diversity and stability. Some ecologists have also used
diversity as an index of the maturity of a community on
the premise that communities become more complex and
more stable as they mature. However. this assumption is
probably applicable only in certain ecological communities. Diversity in some groups of organisms has been
correlated with latitude. climate. productivily, and geography (Schluter and Ricklefs. 1993). The concept of
diversity of organisms (biodiversity) is important to the
field of conservation biology (see Meffe and Carroll,
1997; Primack, 1997).
On the following pages. we shall discuss species diversity, assuming that all individuals in a biological collection can be identified to species. If such identification
is not possible or practical (for example. in a class exer-
Species Diversity
cise), then other taxonomic groups may be used. (For
example. we may speak of genus or family diversity.)
Indeed, specific identification is not needed for most
comparative studies; the individuals collected may
simply be identified as taxon 1. taxon 2, and so on, as long
as such nomenclature is consistent from collection to
collection. If you want to compare diversity indices of
different communities or subcommunities, try to obtain
the same-sized sample from each. This is because all
measures of diversity depend to some extent on the number of species collected, which depends in turn on sample
size.
Diversity is usually considered for only certain subcommunities at a time rather than for an entire ecological
community. Great differences among organism sizes
make diversity measures difficult to interpret in largescale studies. Thus. we speak of the species diversity of
birds. insects, or algae, or the species diversity in the soil
or on tree trunks. Section 2A.8 discusses quantifying the
diversity of habitats. and Section 5B.4 refers to diversity
as a measure of niche width.
Section 5A.3 presents the relative-abundance
curve and the lognormal curve, which express the distribution of individuals among species. These plots may
be used to show species diversity graphically. Typically.
however. it is best to express quantitative measures of
diversity as discussed in Section 5B.2.
A large number of measures of diversity have been
proposed and many are in contemporary use. Of those
mentioned in the next section, we recommend that the
student concentrate on the Simpson index (D,, in Section
58.2.2) and the information-theoretic indices ( H a n d H',
in Section 58.2.3).
Analysis of Communities
178
Table 5B.1 Various Diversity Indices Computed for
Hypothetical Situations of N Individuals Distributed
among s Species, with n, Individuals in the ith Species.
Examples A, B, and C have identical values of N and
s. Example D has the same s and species distributioti
as A, but with a larger N . Example E has the same N
and evenness as e-rumple A, but a smaller s.
(Logarithms used are base 10.)
2. Measures of Species Diversity
2.1 Numbers of Species and Individuals The simplest measure of species diversity is the number of species
(s), or the species richness. Several indices of diversity
have been proposed that incorporate both s and N, the
total number of individuals in all the species; for
example, Margalef's index:
Hypothetical Examples
Species Abundance
A
B
C
D
E
D, =
s- l
log N
(Margalef, 1957). which is very similar to the index of
Gleason ( 1922):
S
D,<,=
log N
and Menhinick's index:
-
-
number of spccics
N, numbcr of individuals
D,, Margalcf divcrsity
D,, Glcason divcrsity
D,, Mcnhinick divcrsity
s,
10
10
100 100
4.50 4.50
5.00 5.00
1.00 1.00
If random sample:
I, Simpson dominancc 0.09
D,, Simpson divcrsity 0.9 I
tl,, invcrsc ol' 1
1 1 .OO
0.16
0.84
6.23
10
100
4.50
5.00
1.00
10
5
1000 100
3.00 2.00
3.33 2.50
0.32 0.50
0.83 0. I0
0.17 0.90
I .I 0 0 9
0. I9
0.81
5.2 1
I f entire community:
A.Simpsondominancc
A,. Simpson divcrsity
6,,invcrsc 01' A
0.10
0.90
10.00
0.17
0.83
5.92
0.83 0.10 0.20
0.17 0.90 0.80
1.21 10.00 5.00
H. Brillouin diversity
H'. Shannon diversity
S', cqually abundant
0.02
1 .OO
10.0
0.79
0.86
7.2
0. I8 0.99 0.66
0.22 1 .OO 0.70
1.7 10.0 5.0
spccics
maximu~nL),
El,, cvcnncss. using I),
tl,,,,, maximum 11,
r,,, cvcnncss, using 11,
1,,,,,,, ~ n a x i ~ ~ 1,
lu~n
E,, cvcnncss. using A,
6,,,,,, maximum 6,
e , ~cvcnncss.
,
using 6,
H,,,,,, maximum H
J, cvcnncss. using H
I - J. dominancc.
using H
H,,,,', maximum H '
J'. cvenncss. using H'
I - J'. dominancc.
using H '
I),,,,,,,
0 9 I 0.9 1 0.9 1 0.90 0.8 I
1.00 0.92 0. I9 I .OO I .OO
1 1 .OO 1 1 .OO 1 1 .OO 10.09 5.2 1
1 .OO 0.57 0. l l
I .OO I .o()
0.90 0.90 0.90 0.90 0.80
1 .OO 0.92 0.19 1 .OO 1 .OO
10.00 10.00 10.00 10.00 5.00
1 .OO 5 9 0.12 1 .OO 1 .OO
0.92 0.92 0.92 0.99 0.66
1 .OO 0.86 0.20 1 .OO 1 .OO
0.0
1 .OO
1.00
0.14
1 .OO
0.86
0.80
1.00
0.22
0.0 0.0
1 .OO 0.70
1 .OO 1 .00
0.0
0.14
0.78
0.0
0.0
(Menhinick, 1964). But measures such as s, D,,, L),, and
Dl,are inadequate because they do not allow us to differentiate between the diversities of different communities
having the same s and N. (For instance. examples A, B,
and C in Table 5B. I are declared equally diverse by such
indices.) And species richness is directly related to
sample size, with larger samples likely to contain more
species. 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.
2.2 Simpson's Index
Simpson1 (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. He showed that if two individuals are taken at random from a community, the probability that the two will belong to the same species is
I Simpson's approach was to apply to ecology a diversity measure
introduced in a n econometric context in 19 12 by Gini (Bhargava
and Uppuluri. 197.5: Rao, 1982). so that one sces occasional refercnces to the Gini index or Gini-Simpson index.
Species Diversity
Table 5B.2 A Hypothetical Set of Species Abundance
Data, Used in the Text to Illustrate the Calculation of
Various Diversity Indices.
Species,
i
Abundance,
Relative
Abundance,
ni
Pi
The quantity 1 is, therefore, a measure of dominance2
(the concentration of N individuals among s species). A
collection of species with high diversity will have low
dominance, and
namely
is a good measure of diversity3(expressing the probability
of two randomly selected individuals belonging to different species). For the data of Table 5B.2,
Some ecologists have inverted Simpson's dominance
index to arrive at a measure of diversity:
179
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. It is also an expression of how many
equally abundant species would have a diversity equal to
that in the observed collection. The index d , is preferable
to D, in comparing collections in which the values of D,
are very close to 1.0 and nearly the same. (For example,
two collections yielding values of D, of 0.96 and 0.98
would give us d , values-with more discrimination-of
25.00 and 50.00, respectively.) Levins ( 1968) proposed
the inverse of Simpson's diversity index as a measure of
niche breadth, but others have since presented measures
that are preferable for that purpose (see, for example,
Feinsinger et al., 1981 ).
Hurlburt (1971) severely criticized most diversity
indices (including those that follow), but praised the
characteristics of the above indices as being biologically
meaningful, with D, referring to the probability of interspecific encounter (which he calls PIE). This is the
probability of an individual in the community encountering a member of another species. He relates this concept
to specific kinds of encounters, such as competition and
predation.
The above considerations of 1, D,, and d , assume that
the data at hand are a random sample from a community
or subcommunity. There are occasions when this is not
the case, as when we have data from an entire community
or subcommunity (e.g., a laboratory culture of animals or
scavengers at an animal carcass) rather than from a sample, or when we do have a sample but it is known to be a
nonrandom representation of a community or subcommunity. In such cases, the appropriate Simpson measure
of dominance is
or, equivalently,
where
'The quantity Zn,(n, - I ) in the numerator of 1 may be computed as
Zn,' - N, which may prove simpler on some calculators. Morisita's
measure of dispersion (Section 4C.3.4) is computationally related to
I. That is. a large 1 implies an aggregation of individuals in only a
few species, whereas a small value of 1 denotes a more uniform distribution of individuals among species.
'Hurlburt (1971) computes D,as X(ni/N)[(N - n,)/(N - I)]; but
Equation 6 is simpler. Mclntosh (1967) has proposed
as a
dominance measure from which diversity indices may be derived.
that is, pi is the proportion of the total number of individuals occurring in species i. And the diversity indices
analogous to D, and d , are
180
Analysis of Communities
and
"
I
N'
g =-=An;'
Table 5B.3 Factors to Convert between Logarithmic
Bases 2, e, and 10. (For example, a value of 0.86
computed itsing base 10 is equivalent 10 a value of
(0.86)(2.3026) = 1.98 using base e.)
-
respectively, which may also be written as
2
Toconvertto
A,
-
-
-
--
To Convert from
e
10
= I - AP2
and
2.3 Information-Thearetic Indices
Measures ofspecies diversity bascd on information theory (introduced to
ecologists by MacArthur. 1955. and Margalcf. 1958) are
related to the concept of uncertainty. In a spccit.s aggregation of low diversity (e.g.. example C in 'Table 5B. I ),
we can be relatively certain of the identity o f a species
chosen at random. (In this example. i t will probably be a
member of speeics I.) In a highly diverse community.
however (e.g., example A in 'Fable 5B. I ), it is difticult to
predict the identity of a randomly picked individual.
Thus. high diversity is associated with high uncertainty
and low diversity with low uncertainty. And some authors have equated uncertainty with entropy.
Information-theoretic measures also allow LIS to consider and calculate measures of hierarchical diversity.
Consider example A in Table 5B. 1. I f the I O species were
each ol' a different genus. this would intuitively imply a
greater diversity than it' they were all o f the same genus.
To learn more :tbout niensuing hierarchical diversity. taking inlo ilccount the distribution of species within genera.
genera hithin liimilics. and so on. consult Piclou ( 1975.
1977).
Two kinds of ecological collections must bc considcred. The lirst is where our species-abundance data compose a sample taken at random from a community or
subcommunity. In the second kind of collection (c.g..
with a rotting log subcommunity o r some laboratory situations). we know the total number of indivitlunls in n
collection ol' s p c c ~ c swithout resorting to samples. O r we
may have obtained a nonrandom sample (thus nonrepreaentativc of its community or subcommunity): in these
cases. the sample must also be considered a complete
enumeration. For cxample. trap (Sections 3D.5 and
3E.3.1 ). arrilicial substrate (Section 3E.2.5). and seine
(Section 3E.3.5) sampling typically favor the collection
of certain species. Thus. these collections do not exhibit
species compositions and abundances that accurately
reflect those of the sampled community.
If our data are a random sample of species abundances from a larger community .or subcommunity of
interest, then we may appropriately use the Shannon"
diversity indcx (Shannon 1 1948 I):
H ' = -Sp, log
(15)
17,.
where 17, is as in Equation 10: the proportion of the total
number of individuals that belong to species i. For this
calculation. one may use any logarithmic base: bases 10
and c are the commonest. although communications engineers (from whom the index has been borrowed) use
base 2. Thc selection of a particular logarithmic base is
immaterial as long as it is consistent; H ' computed in one
base may be converted to H' for another base by consulting Table 5B.3. In Appendix D. Table D. I gives logarithms and Table D.2 gives logarithms of proportions.
For the data in Table 5B.2.
H'
=
-[0.588 log 0.588 t- 0.294 log 0.294
+ 0.1 18 log 0.1 181
= -[0.588( -0.23 1 )
+ 0. I 18( -0.928
+ 0.294( -0.532)
)]
= -[-i).
136 - 0.156 - 0.1 101
= 0.40.
A little algebraic manipulation arrives at an equivalent
equation:
H'
=
( N log N
-
\'[I!, log ,rJ)/N.
(
16)
This equation allows us to compute H' without ti rst converting abundances (11,) to proportions (I),).both saving
time and avoiding rounding errors. Table 5B.4 is very
'This often less properly called the Shannon-Wcavcr or ShannonWicncr indcx. Ibr C. E. Shannon's cqua~ionreceived somc inspiralion from N. Wicncr and some clarilication from W. W. Weaver
(Pcrkins. 19821. Shannon did not apply his mcasurc lo ecological
systems.
Species Diversity
-3
Table 5B.4 Values of ni log n, (or N log N ) for Use in Equation 16. *
"If values for
rl,
(or N I largcr than 409 arc nccdcd. consult Lloyd et al. ( 1968) or Zar ( 1974:JOl-404) or usc Appendix D. Table D. I .
181
Analysis of Communities
182
conveniently used with this equation. For the above data
from Table 5B.2.
H'
=
[85 log 85 - (50 log 50
+ I0 log 10)]/85
+ 25 log 25
The computation of factorials-such
as 6 ! =
(6)(5)(4)(3)(2)= 720-is
tedious, and the numbers
typically become unwieldy. Therefore, H is much more
conveniently calculated using logarithms:
H = (log N!
- C[log n,!])/N,
(20)
with the aid of Table 5B.5. For our Table 5B.2 example,
+ log 25! + log 10!)]/85
= [ I 28.450 - (64.483 + 25.19 1 + 6.560)]/85
H = [log 85! - (log 50!
As noted above, the Shannon diversity index. H ' . is
appropriate when you have a random sample of species
abundances from a larger aggregation. say a random
sample of an entire community. Such a sample runless
extremely large) will probably not contain representatives of each species in the entire community. So. typically. our observed value of s is biased. an underestimate
of the number of species in the entire community. However, the lack of data on rare species has little et'fect on
the value of H ' (although it has serious effect on H,;,,,,and
J', discussed in Section 5B.2.4).
H' may also be calculated for data other than abundances, for example. to express habitat heterogeneity
(Section 2A.8) or the diversity of biomass (Section 6A),
or of coverage (Sections 3A. 3B, and 3C). Also note that
Equations 8, 9, 13, 14. and 15 may be used with relative
measures (e.g.. relative abundance or relative biomass).
Another way of depicting species diversity is to express the number of equally abundant species that would
produce the value of H' of the observed sample. This
measure may be represented as
wher-c Ll is the logarithmic base used in computing H'
(e.g.. 10. c. or 3- ). For cxample B in Table 5B. 1 .
Now Ict us consider a set of species-abundance data
that is considered a nonrandom sample. For such a set. or
Ihr collcctecl tlat;~that arc ;In entire community or subcolnmunity. tlo not use H' ( Pielou. 1966a. 1966b. 1967.
1975); instead use the Brillouin (1962) index:
= 32.216/85
= 0.38.
As with H'. the logarithmic base used is immaterial as
long as it is consistent. H values in one base may be
converted to those in another by using Tablc 5B.3.
The units of H and H' are unimportant (and probably meaningless) to the ecologist. 'These indices are used
only in a relative fashion, that is, to determine which
species assemblages are more or less diverse than others.
Washington ( 1984) summarizes many uses and interpretations of H and H ' .
2.4 Evenness The diversity indices in Sections 5B.2.2
and 5B.2.3 take into account both the species richness
( I he number of species) and the evenness of t hc individuals' distribution among the species. Separate measures
of these two components of diversity are often desirable.
Richness can be expressed simply as the number of species. Evenness may be expressed by considering how
close a set of observed species abundanccs are to those
l'rorn an aggregation of species having maximum possible
diversity for a given N and s.
The ~naximumpossible diversity I'or a collection of N
individuals in a total of s species exists when thc N individuals are distributed as evenly as possible among the s
species, that is. when each n , = Nl's. The maximum possible values of D,, d,. A,. H. and If' are as follows:
where 11 (capital Greek pi) means to take the product.
just as E ~neansto take the sum: thus, we can write
Equation 18 as
a,,,<,.V= .s.
H,,,, = [log N!
-
(s - r) log c! - r log ( c
+
(24)
1) !]IN,
(25)