Environmental scientists are often interested in evaluating both species richness and species evenness, so they have come up with miles species diversity that take both measures into account. One commonly used index is Shannon's index of biodiversity. To calculate this index,
we must know the total number of species in the community (s) and, for each species, the proportion of the individuals in the community that
represents that species (p). Once we have the information, we can calculate Shannon's index of diversity (H) by taking the product of each
proportion (0) and its natural log (In ()) and then summing these products, as indicated by the summation symbol (E):
H-- pin(p)
where
H = the Shannon index value
P, = the proportion of individuals found in the ith species
In = the natural logarithm
S = the number of species in the community
The minus sign makes the index a positive number. Higher values of Hindicate higher diversity
Note: the book uses "n" and the formula I found online uses "s" for the number of species in the community.
Imagine a community of 100 individuals that are evenly divided among four species, so that the proportions () of the species all equal 0.25.
We can calculate Shannon's index as follows:
• H = -((0.25 x In 0.25) + (0.25 x In 0.25) + (0.25 x In 0.25) + (0.25 x in 0.25)]
• H-[(-0.35)+(-0.35) + (-0.35) + (-0.35)]
• 1.40
Now imagine another community of 100 individuals that also contains four species, but in which one species is represented by 94 indiviudals
and the other three species are each represented by 2 indivudals. We can calculate Shannon's index to see how this difference in species
evenness affects the value of the index:
• H = -[(0.94 x in 0.94)+ (0.02 x In 0.02) + (0.02 x In 0.02) + (0.02 x in 0.02)]
• H=-[(-0.06) + (-0.08) + (-0.08) + (-0.08)]
• 0.30
Because this value of His lower than the value we calculated for the first community, we can conclude that the second community has lower
diversity. Note that the total number of indiiduals does not affect Shannon's index of diversity, only the the number of species and the
proportion of individual within each species matters.
Your Turn
Imagine a third community of 100 individual in which those indviduals are distributed evenly among all the species, but there are only two
species, not four. Calculate shannon's index to see how different in species richness affects the value of the index
Shannon's index. He
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