Jost diversity index and the effective number of species

**See also
**Single sample diversity (alpha
diversity)

For an excellent introduction to diversity and a discussion of several popular metrics, see Lou Jost's web site.

**Effective number of species
**The
effective number of species is described by
Chao, Chui and Jost (2010) and is defined as follows. Suppose a given metric has value

Using an effective number of species is compelling because it has a natural interpretation and makes all metrics comparable to each other, while "raw" metrics such as entropy have no obvious connection to a number of species, and different raw metrics cannot be compared.

For example, I created OTUs for a soil community with 3,268 OTUs which had a Shannon entropy of 3.68. With 39 even abundances, the Shannon entropy is 3.66 and with 40 even abundances, the entropy is 3.39, so we can see that the effective number of species should be more than 39 and less than 40. Using Jost's formula, we find that the effective number of species for a Shannon entropy of 3.66 is 39.7. This indicates that while the community had many OTUs, there were relatively few high-abundance clusters that accounted for most of the reads.

**Jost index
**In the same 2010 paper, Choa, Chui and Jost describe a family of metrics
based on "Hill numbers" with a single
parameter (