We consider the species-area problem in ecology. The aim is to estimate the total number of species in a large area by extrapolating a species-area curve. Starting with a stationary random field as the background process that is decisive of species occurrence, we argue that asymptotically, the number of unseen species and the species number increment will decrease hyperbolically with increasing area. In particular, stationarity of the background process leads to a fast hyperbolic rate. Some vascular plant species richness data from Switzerland are used to motivate discussions.
Ghosh, S. (2009). The unseen species number revisited. Sankhya: the Indian Journal of Statistics 71-B: 137-150.