Environmental scientists are often interested in evaluating both species richness and species evenness, so they have come up with indices of species diversity that take both measures into account. One commonly used index is Shannon’s index of diversity. To calculate this index, we must know the total number of species in a community (n) and, for each species, the proportion of the individuals in the community that represent that species ( p_i). Once we have this information, we can calculate Shannon’s index (H) by taking the product of each proportion ( p_i) and its natural logarithm [ln ( p_i)] and then summing these products, as indicated by the summation symbol ( ∑ ):

The minus sign makes the index a positive number. Higher values of H indicate higher diversity.

Imagine a community of 100 individuals that are evenly divided among four species, so that the proportions ( p_i) of the species all equal 0.25. We can calculate Shannon’s index as follows:

H = −[(0.25 × ln 0.25) + (0.25 × ln 0.25) + (0.25 × ln 0.25) × (0.25 × ln 0.25)]

H = −[(−0.35) + (−0.35) + (−0.35) + (−0.35)]

H = 1.40

Now imagine another community of 100 individuals that also contains four species, but in which one species is represented by 94 individuals and the other three species are each represented by 2 individuals. We can calculate Shannon’s index to see how this difference in species evenness affects the value of the index:

H = −[(0.94 × ln 0.94) + (0.02 × ln 0.02) + (0.02 × ln 0.02) + (0.02 × ln 0.02)]

H = −[(−0.06) + (−0.08) + (−0.08) + (−0.08)]

H = 0.30

Because this value of H is 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 individuals does not affect Shannon’s index of diversity; only the number of species and the proportion of individuals within each species matter.

Your Turn Imagine a third community of 100 individuals in which those individuals are distributed evenly among all the species, but there are only two species, not four. Calculate Shannon’s index to see how this difference in species richness affects the value of the index.