Introduction: A diversity index is a mathematical measure of
species diversity in a community. Diversity indices provide more information
about community composition than simply species richness (i.e., the number
of species present); they also take the relative abundances of different
species into account (for an illustration of this point, see below,
or introduction to SIMPSON'S D AND E).
Importance: Diversity indices provide important information about rarity and commonness of species in a community. The ability to quantify diversity in this way is an important tool for biologists trying to understand community structure.
Question: How do we measure diversity?
Variables:
H  Shannon's diversity index 
S  total number of species in the community (richness) 
p_{i}  proportion of S made up of the ith species 
E_{H}  equitability (evenness) 
Methods: The Shannon diversity index (H) is another index that is commonly used to characterize species diversity in a community. Like Simpson's index, Shannon's index accounts for both abundance and evenness of the species present. The proportion of species i relative to the total number of species (p_{i}) is calculated, and then multiplied by the natural logarithm of this proportion (lnp_{i}). The resulting product is summed across species, and multiplied by 1:
Shannon's equitability (E_{H}) can
be calculated by dividing H by H_{max} (here H_{max}
= lnS). Equitability assumes a value between 0 and 1 with 1 being
complete evenness.
Example:
The graph below shows H and E_{H}
for four hypothetical communities, each consisting of 100 individuals.
The communities are composed of 5, 10, 20 and 50 species, respectively.
For each community H and E_{H} have been calculated
for the case in which individuals are distributed evenly among the different
species (i.e., each species makes up an equal proportion of S),
and for the case in which one species has 90% of the individuals, and the
remaining individuals are distributed evenly. For example, in a community
with 10 species in which the species contain equal numbers of individuals,
p
=
0.1 for each species. In a community with 10 species in which one species
has 90% of the individuals, p = 0.9 for the dominant species, and
p
= 0.01 for the other nine species. The diamonds represent
H and
E_{H}values
for the first case (equal proportions), and the triangles represent values
for H and E_{H} for the second case (unequal proportions).
For the first case, E_{H} is always equal to one (complete evenness, or equitability), but H increases dramatically as the number of species increases, as we would expect. For the second case, in which one species makes up 90% of the community, the picture is a little different. Here we can see that although H does increase with increasing numbers of species, it does so much more slowly than in the first case. Additionally, E_{H} decreases as species number increases (since one species always makes up 90% of the community in the second case of this hypothetical example, the remaining species make up some fraction of 10% of the community; as species number increases this fraction becomes smaller and evenness decreases). H and E_{H} clearly give more information about these communities than would species number (richness) alone.
The following table contains data from a study of Costa Rican ant diversity (Roth et al. 1994). The authors measured diversity in four different habitats ranging very low levels of human disturbance (primary rain forest) to very high levels of human disturbance (banana plantations) to assess the impacts of different levels of disturbance on biological diversity. For each habitat studied we will use data collected from one site within that habitat. The numbers below represent relative proportions of each species (from Roth et al. 1994 [family names have been omitted]).
Formicidae 




Acromyrmex sp. 1 
0.013


A. volcanus 
0.006


A. araneoides 
0.117

0.140


Atta cephalotes 
0.010


Carabarella sp. 1 
0.004


Cardiocondyla sp. 1 
0.011


Crematogaster sp. 2 
0.021

0.024


Cyphomyrmex sp. 1 
0.011


Erebomyrma nevermanni 
0.004

0.021


Pheidole sp. 1 
0.021

0.035

0.019


Pheidole sp. 2 
0.008

0.045

0.013


Pheidole sp. 3 
0.058

0.021


Pheidole sp. 5 
0.054

0.010


Pheidole sp. 7 
0.006


Pheidole sp. 9 
0.021


Pheidole sp. 10 
0.004


Pheidole sp. 11 
0.024


Pheidole sp. 12 
0.004

0.003


Pheidole sp. 15 
0.163


Pheidole sp. 16 
0.003


Pheidole sp. 19 
0.004

0.017


Pheidole sp. 22 
0.067


Pheidole sp. 23 
0.004


Pheidole sp. 24 
0.017

0.011


Pheidole sp. 25 
0.157


Pheidole sp. 26 
0.005


Pheidole sp. 27 
0.003


Pheidole sp. 28 
0.003


Pheidole sp. 31 
0.010


Pheidole sp. 34 
0.005


Pheidole sp. 36 
0.125

0.007


P. annectans 
0.079

0.028

0.005


P. longiscapa 
0.050

0.003


P. punctatissima 
0.005


P. nr. subarmata 
0.003


P. subarmata 
0.043


P. fiorii 
0.075


Sericomyrmex sp. 1 
0.006


Solenopsis sp. 1 
0.004

0.006


Solenopsis sp. 3 
0.004

0.077


Solenopsis sp. 4 
0.017


Solenopsis sp. 5 
0.004


Solenopsis sp. 6 
0.004


Solenopsis sp. 7 
0.038


Solenopsis sp. 8 
0.042


Solenopsis sp. 9 
0.035


S. geminata 
0.031

0.101

0.830


Tetramorium bicarinatum 
0.005


Trachymyrmex sp. 1 
0.003

0.019


Trachymyrmex sp. 2  
Trachymyrmex sp. 3 
0.004

0.007


Wasmannia sp. 1 
0.011


W. auropunctata 
0.050

0.021

0.006


Pseudomyrmex sp. 1  
Ectatomma gibbum 
0.004


E. ruidum 
0.004

0.038

0.753


E. tuberculatum  
Gnamptogenys sp. 2  
Gnamptogenys sp. 3  
Gnamptogenys sp. 4  
G. bispinosa  
Hypoponera sp. 1 
0.004

0.010


Hypoponera sp. 2 
0.007


Hypoponera sp. 3 
0.005


Hypoponera sp. 4 
0.011


Odontomachus bauri  
O. brunneus 
0.004


O. chelifer 
0.021


O. erythrocephalus 
0.017

0.006

0.043


O. hastatus  
O. laticeps 
0.008

0.010


O. opaciventris  
Pachycondyla apicalis 
0.017

0.007


P. constricta 
0.006


P. harpax 
0.0125

0.031

0.013


P. obscuricornis 
0.003

0.006


P. villosa  
Paraponera clavata 
0.019


Brachymyrmex sp. 1  
Brachymyrmex sp. 2  
Campanotus sp. 1  
Paratrechina sp. 1 
0.033

0.063


Paratrechina sp. 2  
Tapinoma melanocephalum  
total # of species per site:

37

36

16

14

To calculate Shannon's H for the primary forest site we can use the equation given above: H = (1) * (0.117 * ln 0.117) + (0.004 * ln 0.004) + (0.021 * ln 0.021) + (0.004 * ln 0.004) + (0.021 * ln 0.021) + (0.008 * ln 0.008) + (0.058 * ln 0.058) + (0.054 * ln 0.054) + (0.021 * ln 0.021) + (0.004 * ln 0.004) + (0.004 * ln 0.004) + (0.163 * ln 0.163) + (0.004 * ln 0.004) + (0.067 * ln 0.067) + (0.004 * ln 0.004) + (0.017 * ln 0.017) + (0.125 * ln 0.125) + (0.079 * ln 0.079) + (0.050 * ln 0.050) + (0.075 * ln 0.075) + (0.004 * ln 0.004) + (0.004 * ln 0.004) + (0.017 * ln 0.017) + (0.004 * ln 0.004) + (0.004 * ln 0.004) + (0.004 * ln 0.004) + (0.050 * ln 0.050) + (0.004 * ln 0.004) + (0.004 * ln 0.004) + (0.004 * ln 0.004) + (0.004 * ln 0.004) + (0.021 * ln 0.021) + (0.017 * ln 0.017) + (0.008 * ln 0.008) + (0.017 * ln 0.017) + (0.0125 * ln 0.0125) + (0.033 * ln 0.033) = 3.1823. Evenness is then E_{H} = 3.1823 / ln 37 = 0.8813 (37 being S, the total number of species at this site). Using the same equations, Shannon's H for the banana plantation is 0.8322, and E_{H} = 0.3153.
Interpretation: We can see from our results that the diversity and evenness in this site from the undisturbed habitat (primary rain forest) are much higher than in the site from the highly disturbed habitat (banana plantation). The primary rain forest not only has a greater number of species present, but the individuals in the community are distributed more equitably among these species. In the banana plantation there are 23 fewer species and over 80% of the individuals belong to one species, Solenopsis geminata (the most common species in the primary rain forest, on the other hand, makes up about 16% of the community [Pheidole sp. 15]).
Conclusions: Different levels of disturbance have different effects on ant diversity. If our goal is to preserve biodiversity in a given area, we need to be able to understand how diversity is impacted by different management strategies. Because diversity indices provide more information than simply the number of species present (i.e., they account for some species being rare and others being common), they serve as valuable tools that enable biologists to quantify diversity in a community and describe its numerical structure.
Additional Questions:
1. Calculate H and E_{H} for both the abandoned and productive cacao plantation sites. Are they more similar to one another or to the more or less disturbed habitats?
2. What do you notice about the species compositions of these four habitats (i.e., do most species occur in all four habitats, in only one habitat, etc.)?
Extra credit: Calculate Simpson'sD and E_{D} for the primary forest and abandoned cacao plantation sites. Do these values lead to the same conclusions drawn from your calculations of Shannon's indices?
Sources: Begon, M., J. L. Harper, and C. R. Townsend. 1996. Ecology: Individuals, Populations, and Communities, 3rd edition. Blackwell Science Ltd., Cambridge, MA.
Magurran, A. E. 1988. Ecological Diversity and its Measurement. Princeton University Press, Princeton, NJ.
Rosenzweig, M. L. 1995. Species Diversity in Space and Time. Cambridge University Press, New York, NY.
Roth, D. S., I. Perfecto, and B. Rathcke. 1994. The effects of management systems on groundforaging ant diversity in Costa Rica. Ecological Applications 4(3):423436.
copyright 2000 M. Beals, L. Gross, and S. Harrell