Population estimation by a one-release, two-capture experiment

We suggest here easy-to-use equations for population estimation for a single mark-release experiment in which individuals are captured at two points in time without being re-released. Two models are considered. Both models adopt an assumption that the survival rate of marked individuals is constant. In Model A, the total number of individuals including marked and non-marked individuals is assumed to be constant. The proportion of captured individuals need not be constant in this model. In Model B, the probability that an individual is captured is assumed to be constant. The total number of individuals need not be constant in this model. Maximum likelihood estimates and the unbiased estimates are derived in explicit form for both Model A and Model B. The relation with classical methods, such as Jackson's positive method and Itô's modified positive method, is examined. Numerical simulation indicates that the unbiased estimates work better than do other methods in both Model A and Model B.