Shannoneven versus Pielou

Since there’s nothing better on Black Friday than to sit warm and snug at home and process data, I have a question concerning the calculation of evenness in a sample set.

I’ve used the summary.single command with the various calculators to get the Inverse Simpson index, Chao index, Shannon Diversity Index, and Shannoneven calculations, as well as sobs and nseqs, on a dataset. I used the subsampled.shared file for all these calculations based on the advice of my colleagues but have the same calculations for non-subsampled data. I’ve done this at the level of OTU, genus, order and phylum. So far so good.

Now then: there’s no explanation for shannoneven in the Mothur wiki but from what is provided it appears to be a measure of evenness. I am comparing this to Pielou’s index for evenness (1-2), described as

J’ = H’ / ln(sobs)

Where H’ is the Shannon diversity index and J’ is the Pielou index. J’ is supposed to get around some of the issues of using the Shannon index, but of course has issues of its own.

When I compare J’ to the values provided by shannoneven in Mothur, they are close but NOT the same. It could be that the value of H’ I am using from the Shannon calculation in Mothur is not as demanded by Pielou, but I thought they were. So a few simple questions –

1. what is shannoneven calculating exactly?

2. to describe evenness in a dataset, which is preferred; shannoneven, Pielou, or neither? I could calculate using Simpson’s dominance formula (3) as described by Mulder (4) but I’m not sure this is right either.

3. to describe evenness appropriately in a dataset, should I sub-sample first?

4. finally, the Shannon diversity index as calculated by Mothur describes diversity and not evenness. If I’m required to use one and only one measure of alpha diversity, is there a reason to use the Shannon over (say) the Inverse Simpson index? Does using both add anything to my understanding? I’m an ecological rookie on this one.

Many thanks in advance and happy Black Friday to all!

Refs

1 – Pielou, J. Theoret. Biol. 13:131-144, 1966
2 – Jost, Diversity 2:207-232, 2010
3 – Simpson, Nature 163:688, 1949
4 – Mulder et al, Okios 107:50-67, 2004

More on this and some egg on my face: when I compared J’ to the values provided by shannoneven in Mothur, they are close but NOT the same for the sub-sampled data.

But they ARE the same for non sub-sampled data (to 8 decimal places for each calculation which is good enough). I assumed but didn’t check, but now I have. My fault.

So shannoneven = Pielou J’ for non subsampled data, and that answers that question.

This gets me back to asking whether I should use subsampled data in comparing evenness.

Thoughts?