A conditionally-unbiased estimator of population size based on plant-capture in continuous time

This paper proposes an estimator of the unknown size of a target population to which has been added a planted population of known size. The augmented population is observed for a fixed time and individuals are sighted according to independent Poisson processes. These processes may be time-inhomogeneous, but, within each population, the intensity function is the same for all individuals. When the two populations have the same intensity function, known results on factorial series distributions suggest that the proposed estimator is approximately unbiased and provide a useful estimator of standard deviation. Except for short sampling times, computational results confirm that the proposed population-size estimator is nearly unbiased, and indicate that it gives a better overall performance than existing estimators in the literature. The robustness of this performance is investigated in situations in which it cannot be assumed that the behaviour of the plants matches that of individuals from the target population.