Nabin, the index is exactly that, an index. The original formula included log base e, or the natural log. Consequently, values in the literature are naturally based (:- ) on that rather than on the common log (log base 10), which is more commonly used (:- ) in some applications but not this. There is nothing magic about using one or the other in a given case, but one should use the same formula as others do to be consistent with the literature. If the literature were a mix of values using one, then the other, we'd have no means for comparison across studies.
David ---- Nabin Baral <[email protected]> wrote: > Dear Members: Happy New Year 2011. I am wondering about whats 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 -- David McNeely
