Measuring biodiversity
Counting species is the simplest measure of diversity, but it ignores how individuals are spread among them. A meadow with ten species where one makes up 90% of the plants is less diverse, in practice, than one with ten equally common species. Diversity indices combine richness, the number of species, and evenness, how equal their abundances are.
Shannon index
Claude Shannon developed this measure of information in 1948, and ecologists adopted it to describe communities:
H′ = −Σ pᵢ × ln(pᵢ)
where pᵢ is the proportion of individuals belonging to species i. H′ is 0 when there is only one species and grows with both the number of species and their evenness. In many field studies it falls between about 1.5 and 3.5.
Evenness
Pielou’s evenness compares H′ with its maximum possible value for the same number of species S:
J = H′ ÷ ln(S)
J ranges from 0 to 1, where 1 means all species are equally abundant.
Simpson’s index
Simpson’s index D is the probability that two individuals drawn at random, without replacement, belong to the same species:
D = Σ nᵢ(nᵢ − 1) ÷ [N(N − 1)]
The calculator shows 1 − D, the probability that they belong to different species, which rises with diversity. Simpson’s index gives more weight to common species, while Shannon’s is more sensitive to rare ones.
Effective number of species
exp(H′) converts the Shannon index into the number of equally common species that would give the same diversity. It is easier to interpret and to compare: a community with an effective number of 4.8 is as diverse as one with about 5 equally abundant species.
Example
A survey counts 40, 25, 15, 10, 5, 3 and 2 individuals of seven species, 100 in all. The Shannon index is 1.56, the evenness 0.80, Simpson’s 1 − D is 0.75 and the effective number of species is about 4.8.
Good practice
- Compare sites only with the same sampling effort and method, since rare species appear as more individuals are counted.
- Use natural logarithms consistently; some studies use log base 2 or 10, which changes the values.
- Report richness and evenness alongside the index.