Shannon and Wiener Diversity Index
Dr. James T. Cronin, Assistant Professor
A. H = - SUM(pilnpi)
H = diversity index
SUM = summation
pi = proportion of total sample represented by species i
B. Calculation for a hypothetical community #1
|
Species (i) |
Number in sample |
pi |
ln(pi) |
(pi)ln(pi) |
|
1 |
60 |
0.60 |
-0.51 |
-0.31 |
|
2 |
10 |
0.10 |
-2.30 |
-0.23 |
|
3 |
25 |
0.25 |
-1.39 |
-0.35 |
|
4 |
1 |
0.01 |
-4.61 |
-0.05 |
|
5 |
4 |
0.04 |
-3.22 |
-0.13 |
|
|
SUM = 100 |
|
|
SUM = -1.07 |
H = 1.07
C. Rare species carry less weight
1. compare value of species 1 versus species 5
2. index accounts for differential abundance
D. Diversity for community with more even abundances (#2)
|
Species (i) |
Number in sample |
pi |
ln(pi) |
(pi)ln(pi) |
|
1 |
20 |
0.20 |
-1.61 |
-0.32 |
|
2 |
20 |
0.20 |
-1.61 |
-0.32 |
|
3 |
20 |
0.20 |
-1.61 |
-0.32 |
|
4 |
20 |
0.20 |
-1.61 |
-0.32 |
|
5 |
20 |
0.20 |
-1.61 |
-0.32 |
|
|
SUM = 100 |
|
|
SUM = -1.61 |
H = 1.61
E. Shannon-Weiner Index is sensitive to:
1. species richness
2. abundance of individuals
F. Maximum diversity possible: Hmax = ln(S)
1. occurs when communities are comprised of equal number of species
2. community #2 is at maximal diversity
G. Evenness measures equitability of species
1. useful descriptive measure of community
2. Evenness: E = H/Hmax
3. ranges between 0 - 1 (can’t equal 0)
4. communities
#1 = 1.07/1.61 = 0.66
#2 = 1.61/1.61 = 1