On the nature of one–inflation in microbial diversity studies

The phenomenon of one–inflation is gaining more and more attention in the recent literature on species abundance and capture–recapture analysis. When analysing frequency count distribution, the excess of singletons is often ascribed to the erroneous inclusion of spurious cases. Various works propose to estimate the true number of singletons relying on the higher, supposedly error–free, counts (“discounting” approach). We argument that, in the case of microbial diversity studies, the generating process of the spurious singletons can be described in terms of false negative record linkage errors. Errors in sequencing the RNA genomes result in chimeric sequences that cannot be associated to the correct species, and constitute missing links that are added to the true singletons. In this scenario, none of the observed frequency counts is assumed to be error–free, and we propose an ABC algorithm to estimate the true frequency counts. The number of true singletons estimated in this way may differ considerably from the discounting approach. This implies different estimates of the diversity as measured, e.g., by Shannon’s index. However, curiously, the total population count estimates under the two approaches coincide.