Estimating how many species remain unseen from a finite sample is a classic problem in ecology and other fields. A new paper on arXiv (2610.22604) examines the statistical foundations of this task, focusing on rare-event occupancy statistics.
The authors emphasize that singletons—species observed exactly once in a sample—are particularly influential. These rare events carry much of the information needed to estimate the "missing mass" (the total probability of unseen species) and the count of unseen species.
However, the abstract also notes that in small-sample regimes, these singleton-based statistics can be highly variable. That variability poses a challenge for classical estimation methods, which may struggle to produce stable results when samples are limited.