The diversity of species in a particular area depends not only the number of species found, but also in their numbers. Ecologists call the number of species in an area its richness, and the relative abundance of species its evenness. They are both measures of diversity. A game reserve with one antelope and one zebra when compared with another with one antelope and ten zebra, therefore, have same species richness but different species evenness.
Since any particular area can have all kinds of species living together, ecologists limit the taxonomy of interest when calculating species evenness. For example, the taxonomy of interest in a game reserve can be diversity of animals, plants or flowers.
Determine the species richness "S" by counting the number of species of taxonomy of interest. Suppose there are 10 orchids, 20 roses and 100 marigolds in a garden. The species richness of flowers in this garden equals three.
Take natural logarithms of species richness "ln(S)." In this example, ln(3) equals 1.099.
Calculate the proportion of each species "P(i)" by dividing the number of that species by the total number of all species. The proportion of orchids is 10 divided by 140, which equals 0.072. Similarly, the proportion of roses and marigolds are 0.143 and 0.714 respectively.
Calculate Shannon's diversity index "H" by using the formula H = - Summation[P(i) * lnP(i)]. For each species, multiply its proportion "P(i)" by natural logarithm of that proportions lnP(i), sum across species and multiply the result by minus one. For orchids, P(i) * lnP(i) equals -0.189. The equivalent for roses and marigolds are -0.278 and -0.240. Summing them gives -0.707. Multiplying by -1 eliminates the negative. Thus, in this example, Shannon's diversity index "H" equals 0.707.
Divide Shannon's diversity index H by natural logarithm of species richness ln(S) to calculate the species evenness. In the example, 0.707 divided by 1.099 equals 0.64. Note that species evenness ranges from zero to one, with zero signifying no evenness and one, a complete evenness.