Conditional and unconditional estimators of population size

Estimators for the population sizes of animal species are similar to Horvitz-Thompson estimators — they involve dividing counts of detected animals by the probabilities of detection. Knowing detection probabilities for different subpopulations allows one to estimate each sub-population size with such an estimator, and to add the results for an estimator of the total population. In the case where the proportions of animals belonging to the different sub-populations are also known, this paper shows that using those proportions to arrive at a common average detection probability will, when used in conjunction with the total number of animals detected, result in a better estimator. We provide two examples where the inferior estimator may seem sensible.