1. Introduction

Species diversity (sometimes called species heterogene- ity), 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 abun- dant, 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 spe- cies (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), preda- tion. competition. and niche apportionment are theoreti- cally 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 con- cluded 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 communi- ties. Diversity in some groups of organisms has been correlated with latitude. climate. productivily, and geo- graphy (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 di- versity, assuming that all individuals in a biological col- lection 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 num- ber of species collected, which depends in turn on sample size.

Diversity is usually considered for only certain sub- communities at a time rather than for an entire ecological community. Great differences among organism sizes make diversity measures difficult to interpret in large- scale 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 dis- tribution 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 (Hand H' , in Section 58.2.3).

178 Analysis of Communities

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.)

Hypothetical Examples

Species Abundance A B C D E

- -

s , number of spccics 10 10 10 10 5 N, numbcr of individuals 100 100 100 1000 100 D,, Margalcf divcrsity 4.50 4.50 4.50 3.00 2.00 D,, Glcason divcrsity 5.00 5.00 5.00 3.33 2.50 D,, Mcnhinick divcrsity 1.00 1.00 1.00 0.32 0.50

I f random sample: I, Simpson dominancc 0.09 0.16 0.83 0. I0 0. I9 D,, Simpson divcrsity 0.9 I 0.84 0.17 0.90 0.81 tl,, invcrsc ol' 1 1 1 .OO 6.23 I . I 0 0 9 5.2 1

I f entire community: A.Simpsondominancc 0.10 0.17 0.83 0.10 0.20 A,. Simpson divcrsity 0.90 0.83 0.17 0.90 0.80 6,, invcrsc 01' A 10.00 5.92 1.21 10.00 5.00

H. Brillouin diversity 0.02 0.79 0. I8 0.99 0.66 H'. Shannon diversity 1 .OO 0.86 0.22 1 .OO 0.70 S' , cqually abundant 10.0 7.2 1.7 10.0 5.0

spccics I) ,,,,,,, maximu~n L), 0 9 I 0.9 1 0.9 1 0.90 0.8 I El,, cvcnncss. using I), 1.00 0.92 0. I9 I .OO I .OO tl,,,,, maximum 11, 1 1 .OO 1 1 .OO 1 1 .OO 10.09 5.2 1 r,,, cvcnncss, using 11, 1 .OO 0.57 0. l l I .OO I .o()

1 ,,,,,,, ~ n a x i ~ ~ l u ~ n 1, 0.90 0.90 0.90 0.90 0.80 E,, cvcnncss. using A, 1 .OO 0.92 0.19 1 .OO 1 .OO 6,,,,,, maximum 6, 10.00 10.00 10.00 10.00 5.00 e , ~ , cvcnncss. using 6, 1 .OO 5 9 0.12 1 .OO 1 .OO H,,, , , , maximum H 0.92 0.92 0.92 0.99 0.66 J, cvcnncss. using H 1 .OO 0.86 0.20 1 .OO 1 .OO I - J. dominancc.

using H 0.0 0.14 0.80 0.0 0.0 H,,,,', maximum H ' 1 .OO 1 .OO 1.00 1 .OO 0.70 J'. cvenncss. using H' 1.00 0.86 0.22 1 .OO 1 .00 I - J'. dominancc.

using H ' 0.0 0.14 0.78 0.0 0.0

2. Measures of Species Diversity

2.1 Numbers of Species and Individuals The sim- plest 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:

s - l D, = -

log N

(Margalef, 1957). which is very similar to the index of Gleason ( 1922):

S D,<, = -

log N

and Menhinick's index:

(Menhinick, 1964). But measures such as s, D,,, L),, and Dl, are inadequate because they do not allow us to differ- entiate 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 indi- viduals are taken at random from a community, the prob- ability 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 refer- cnces to the Gini index or Gini-Simpson index.

Table 5B.2 A Hypothetical Set of Species Abundance Data, Used in the Text to Illustrate the Calculation of Various Diversity Indices.

Relative Species, Abundance, Abundance,

i 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 differ- ent species). For the data of Table 5B.2,

Some ecologists have inverted Simpson's dominance index to arrive at a measure of diversity:

'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 dis- tribution 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.

Species Diversity 179

This diversity index is an expression of the number of times one would have to take pairs of individuals at ran- dom 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., 198 1 ).

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 in- terspecific encounter (which he calls PIE). This is the probability of an individual in the community encounter- ing 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 sam- ple, or when we do have a sample but it is known to be a nonrandom representation of a community or subcom- munity. In such cases, the appropriate Simpson measure of dominance is

or, equivalently,

where

that is, pi is the proportion of the total number of individ- uals occurring in species i . And the diversity indices analogous to D, and d , are

180 Analysis of Communities

and

I N' g = - = - " An;'

respectively, which may also be written as

A, = I - AP2

and

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.)

2.3 Information-Thearetic Indices Measures ofspe- cies 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 aggre- gation 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 au- thors have equated uncertainty with entropy.

Information-theoretic measures also allow LIS to con- sider 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 of the same genus. To learn more :tbout niensuing hierarchical diversity. tak- ing 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 consid- cred. The lirst is where our species-abundance data com- pose a sample taken at random from a community or subcommunity. In the second kind of collection (c.g.. with a rotting log subcommunity or some laboratory situ- ations). we know the total number of indivitlunls in n collection ol' spcc~cs without resorting to samples. Or we may have obtained a nonrandom sample (thus nonrepre- aentativc 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 abun- dances from a larger community .or subcommunity of

interest, then we may appropriately use the Shannon" diversity indcx (Shannon 1 1948 I):

Toconvertto

H ' = -Sp, log 17,. ( 1 5 )

- - - - --

To Convert from

2 e 10

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 en- gineers (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 consult- ing Table 5B.3. In Appendix D. Table D. I gives loga- rithms 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 ) + 0.294( -0.532) + 0. I 18( -0.928 ) ]

= -[-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 con- verting 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 Shannon- Wicncr indcx. Ibr C. E. Shannon's cqua~ion received somc inspira- lion from N. Wicncr and some clarilication from W. W. Weaver (Pcrkins. 19821. Shannon did not apply his mcasurc lo ecological systems.

Species Diversity 181

-3 Table 5B.4 Values of ni log n, (or N log N ) for Use in Equation 16. *

" I f values for r l , (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 .

182 Analysis of Communities

conveniently used with this equation. For the above data from Table 5B.2.

H' = [85 log 85 - (50 log 50 + 25 log 25 + I0 log 10)]/85

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 representa- tives of each species in the entire community. So. typi- cally. our observed value of s is biased. an underestimate of the number of species in the entire community. How- ever, 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 abun- dances, 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 ex- press 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 sub- colnmunity. tlo not use H' ( Pielou. 1966a. 1966b. 1967. 1975); instead use the Brillouin (1962) index:

where 11 (capital Greek pi) means to take the product. just as E ~neans to take the sum: thus, we can write Equation 18 as

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,

H = [log 85! - (log 50! + log 25! + log 10!)]/85

= [ I 28.450 - (64.483 + 25.19 1 + 6.560)]/85

= 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 proba- bly 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 interpre- tations 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 individ- uals' distribution among the species. Separate measures of these two components of diversity are often desirable. Richness can be expressed simply as the number of spe- cies. 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 ~naximum possible diversity I'or a collection of N individuals in a total of s species exists when thc N indi- viduals are distributed as evenly as possible among the s species, that is. when each n, = Nl's. The maximum pos- sible values of D,, d,. A,. H. and If' are as follows:

a,,,<,.V = .s. (24)

H,,,, = [log N! - (s - r) log c! - r log ( c + 1 ) !]IN, ( 2 5 )