Species Diversity

Biological communities vary in the number of species they contain and a knowledge of this number is important in understanding the structure of the community. The number of species in a community is referred to as species richness. The relative abundance of species is also important. For example, two communities may both contain the same number of species but one community may be dominated by one species while the other community may contain large numbers of all species. The relative abundance of rare and common species is called evenness. Communities dominated by one or a few species have a low evenness while those that have a more even distribution of species have a high evenness. Species diversity, includes both species richness and evenness. Communities with a large number of species that are evenly distributed are the most diverse and communities with few species that are dominated by one species are the least diverse.

For some ecological investigations, it may be useful to measure diversity of one taxonomic group. For example, if a plant ecologist were interested in studying species of plants, they would measure plant diversity and exclude other kinds of organisms.

A number of different measures of species diversity have been proposed. This exercise explores two methods for measuring species diversity of communities: Simpson's Index and the Shannon-Weiner Index.

Simpson Index

If a community with high diversity was randomly-sampled twice, there is a good chance that the two samples will contain different species. However, if a low-diversity community were sampled twice, it is likely that both of the samples will contain many of the same species. Simpson (1949) derived a formula based on the expected outcome of two random samples.





     Equation 1

where N = the total number of individuals of all species

           ni = the number of individuals of species i


We will illustrate using Simpson's index on a hypothetical community with three species.

Table 1. A hypothetical community with 3 species.

 Species  No. of Individuals 

For this community, N = 32 + 18 + 12 = 62. The calculations using equation 1 are shown below.


62 X 61


(32 X 31) + (18 X 17) + (12 X 11)





 = 2.64

Shannon-Weiner Index

The Shannon-Weiner index was developed from information theory and is based on measuring uncertainty. The degree of uncertainty of predicting the species of a random sample is related to the diversity of a community. If a community is dominated by one species (low diversity), the uncertainty of prediction is low; a randomly-sampled species is most likely going to be the dominant species. However, if diversity is high, uncertainty is high.

The index of diversity is 

H' = - pi ln pi      Equation 2

Where pi = the proportion of individuals of species i.

Notice that there is a negative sign in front of the summation sign.

This index is often calculated using natural logarithms (base e) but other bases can be used. The ln key on a calculator calculates logarithms to base e; the log key calculates to base 10. In our calculations, we will use natural logarithms (the ln key on your calculator).

Equation 2 can be rearranged to produce an equation that is easier for performing the calculations.

H' = 

N ln N - (ni ln ni)



     Equation 3

Equations 2 and 3 are equivalent; you can use either one. Equation 3 requires fewer calculations. Both are illustrated below.

Example Using Equation 2

We will use equation 2 to calculate diversity of the community in Table 1.

You must first calculate pi for each species. This is done in column 3 below. Next, calculate ln pi. This is done in column 4. Remember, use the ln key on your calculator.

 Species  No. of Individuals pi ln pi 


 __   =  0.52 




 __   =  0.29 




 __   =  0.19 



We can now calculate diversity using equation 2.

H' = - (0.52 X -0.65) + (0.29 X -1.24) + (0.19 X -1.66)

H' = -(-0.338) + (-0.360) + (-0.315) 

H' = -(-1.01) = 1.01

Example Using Equation 3

First, calculate N.

N = 32 + 18 + 12 = 62.


H' = 

62 ln 62 - ((32 ln 32) + (18 ln 18) + (12 ln 12))




H'  = 

255.88 - (110.90 + 52.03 + 29.82)




H'  = 

255.88 - (192.75)




H'  = 

255.88 - (192.75)



 = 1.02


The difference between the answer above (1.02) and the answer calculated using equation 2 (1.01) is due to rounding error. It is not significant.


1. Use Simpson's index (equation 1) to calculate species diversity for the three communities shown in the table below. Show your work for Community A. It is not necessary to show your work for Communities B and C.


Number of Individuals

  Community A   Community B   Community C  

2. Use the Shannon-Weiner index to calculate species diversity for the the three communities shown in the table above. Use either equation 2 or equation 3. Equation 3 is easier. Show your work for Community A. It is not necessary to show your work for Communities B and C.

3. Do the two methods of calculating species diversity (questions #1 and 2 above) give you the same answer? Do they show the same pattern?

4. Communities A and B each have the same species richness (5 species each). Which has the highest species diversity? Why?

5. Communities B and C both have high evenness. Which has the highest species diversity? Why?