Dear Nabin,
Originally, Shannon wrote his formula to count bins (group of 8 values) in
an communication context. This is the reason why he used log2. His formula
has been applied in different context where log with different bases has
been chosen according to some specific or historical reasons.
Consequently, there is no theoretical reason to prefer log10 or ln
transformation. In an ecological context, you can see the log(pi) part of
Shannon's formula as a rarity function. Hence, Shannon index can be seen
as a mean rarity of your community. All diversity indices are on the same
base. For example, Simpson's D is a mean proportion in your community.
There is a lot of things to say about diversity indices and discussions
around data transformations implied are just one point.
You can also use the number equivalent of Shannon index which can be
obtain by exp(shannon). This give the theoretical number of species of
your community if the community was perfectly even. I think this is easier
to interpret for ecologist and avoid some bias when comparing shannon's
index values.
Hope this help
Nicolas
Le Sun, 02 Jan 2011 19:01:59 +0100, Nabin Baral <[email protected]> a
écrit:
Dear Members: Happy New Year 2011. I am wondering about what?s the
difference between natural log (ln) and log to the base 10 (log) while
calculating the Shannon diversity index.
H = - summation [i=1 to s] (pi log pi) for i = 1...n.
Where, i = proportion of the population of group i (i.e. relative
abundance), and s = the total number of groups.
What if I use natural log (ln) in the above formula? Is one method better
than the other?
In my understanding log is generally taken to shrink the large numbers.
Because in the above formula the proportion can range from 0 to 1 (which
is
already a small number, and standardized too), I am wondering about the
logic of multiplying the ?proportion? by its ?logarithmic proportion?.
I would greatly appreciate your thoughts.
Sincerely,
Nabin
--
Nicolas PERU, PhD
33-(0)4 72 43 28 94
06-88-15-23-10
Laboratoire d'Ecologie des Hydrosystèmes Fluviaux
Université Claude Bernard - Lyon 1
43 Bld du 11 novembre 1918
Rdc Bât Forel
69622 VILLEURBANNE cedex FRANCE
