number of species
Suppose a given alpha diversity metric has value X
for a given set of abundances. The effective number of species is then the
number of species in a community with equal abundances that
would give X for this metric.
This definition can be applied to any metric, regardless
of whether it is expressed as a number of species or a more obscure value
such as entropy.
Using an effective number of species is compelling
because it has a natural interpretation and makes all metrics comparable to
each other, while metrics using different units such as entropy have no
obvious connection to a number of species.
For example, I found 3,268 OTUs in a soil
community had a Shannon entropy of 3.68 bits. 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 the math given in Chao et al. (2010), I
found 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, relatively few high-abundance clusters accounted for most of the reads.
Jost's web page discussing the concept of effective number of species.
Chui and Jost (2010)