Mirror alpha diversity estimator

The mirror estimator (R.C. Edgar and H. Flyvbjerg, manuscript in preparation) estimates total richness including unseen OTUs by calculating an octave histogram of OTU abundances . The modal (largest) bin is identified, unless this is the singleton bin in which case it is the second largest. The total richness is then estimated to be:

Mirror = M + 2R.

Here, M is the number of OTUs in the modal bin and R is the number of OTUs in bins to the right of the modal bin.

The mirror estimator gives a good estimate if (1) the distribution is symmetrical around a peak value and (2) the peak is found in the observed bins, not in the unobserved OTUs. In particular, it will give a good estimate if the distribution is approximately log-normal and the peak is visible. If the distribution is log-normal and the peak is not visible because it is to the left of the y axis, then the estimate can be considered as a lower bound on the total richness.