Chapter 16 Handout on Diversity Index Calculation

BIOL 4120

Principles of Ecology

Harned Hall 301

(615) 963 - 5782

 

The equations for each calculation are given in both the notes and in the textbook. As they are fairly simple and no new notation is introduced, the equations will not be given here. To follow the tables, have the equations in front of you or go back to the webpage for Chapters 15&16.

Simpson's Index and Berger-Parker index

Notice that the three communities differ

  • I is the base community
  • II is the same richness and same evenness but the sample size is doubled
  • III adds two rare species
Simpson and Berger/Parker Indices 
Sample I ni*(ni-1) /N*(N-1)   
Species            
A 24

552

0.193

   
B 20

380

0.133

   
C 7

42

0.015

   
D 3

6

0.002

   
            Simpson's =
Total 54    0.342

2.92
N*(N-1) 2862       Berger-Parker=
           

2.25
Sample II         
A 48

2256

0.195

   
B 40

1560

0.135

   
C 14

182

0.016

   
D 6

30

0.003

   
            Simpson's =
Total 108    0.349

2.87
N*(N-1) 11556       Berger-Parker=
           

2.25
Sample III         
A 24

552

0.167

   
B 20

380

0.115

   
C 7

42

0.013

   
D 3

6

0.002

   
E 3

6

0.002

   
F 1

0

0.000

   
            Simpson's =
Total 58    0.298

3.35
N*(N-1) 3306       Berger-Parker=
           

2.42

Both of these indices are the reciprocal of the book's formulations

Note that:

  • The Simpson index varies slightly with sample size
    • This is the effect of the correction for finite community size
  • Adding rare species increases the Simpson index but hardly changes the B-P index

Shannon Index

The three communities are the same as above

Shannon Index Calculation 
Sample I pi Ln(pi) pi*ln(pi)
Species            
A 24 0.44 -0.81 -0.36
B 20 0.37 -0.99 -0.37
C 7 0.13 -2.04 -0.26
D 3 0.06 -2.89 -0.16
              
Total 54 1

H'=

 1.15
              
              
Sample II         
A 48 0.44 -0.81 -0.36
B 40 0.37 -0.99 -0.37
C 14 0.13 -2.04 -0.26
D 6 0.06 -2.89 -0.16
              
Total 108 1

H'=

 1.15
              
              
Sample III         
A 24 0.41 -0.88 -0.37
B 20 0.34 -1.06 -0.37
C 7 0.12 -2.11 -0.26
D 3 0.05 -2.96 -0.15
E 3 0.05 -2.96 -0.15
F 1 0.02 -4.06 -0.07
              
Total 58 1

H'=

 1.36

Note that:

Note that the index is invariant with respect to sample size, but rare species add to it

Brillouin Index

Brillouin Index Calculation 
Sample I ln(n!)      
Species          ln(N!) =
A 24 54.8    164.3
B 20 42.3      
C 7 8.5    ln(N!) - sum =
D 3 1.8    56.9
              
Total 54 107.4    divide by N =
        

HB =

 1.05
              
Sample II       ln(N!) =
A 48 140.7    400.9
B 40 110.3      
C 14 25.2    ln(N!) - sum =
D 6 6.6    118.2
              
Total 108 282.8    divide by N =
        

HB =

 1.09
              
Sample III         
A 24 54.8    ln(N!) =
B 20 42.3    180.5
C 7 8.5      
D 3 1.8    ln(N!) - sum =
E 3 1.8    71.2
F 1 0.0      
            divide by N =
Total 58 109.2

HB =

 1.23

Note that:

Note that the sample size affects the magnitude of the index, unlike the Shannon index

Last Updated April 10, 2006