Unseen species problem

The unseen species problem is a statistical statement of a problem that arises in ecology and other fields. Given a sample from a population, where each individual in the sample is classified by kind or species, the problem is to answer these related questions:

1. How many species are there in the population, including "unseen species" that do not appear in the sample?
2. For each species, seen or unseen, what is the prevalence in the population; that is, what fraction of the population belongs to each species?
3. If additional samples are collected from the same species, how many more species do we expect to discover? The answer to this question might be expressed in the form of a species discovery curve.
4. How many additional samples are needed to achieve a desired level of coverage (fraction of species observed)?

Solutions to these problems are usually based on the assumption that each member of the population is equally likely to appear in the sample.