What is Species richness, diversity index?

The species richness $S$ of a community is the number of species in it. Richness alone ignores abundance: a wood with a hundred oaks and one of each of nine other trees is less diverse than one with ten of each. The Shannon index

where $p_i$ is the fraction of individuals belonging to species $i$, rises with both richness and evenness; it is $\ln S$ when all species are equally abundant and near zero when one dominates. The evenness is $H/\ln S$. Diversity generally rises from the poles to the tropics, with area, with time since the last disturbance, and with the productivity of the site up to a point.