In surveys of natural animal populations the number of animals that are present and available to be detected at a sample location is often low, resulting in few or no detections. Low detection frequencies are especially common in surveys of imperiled species; however, the choice of sampling method and protocol also may influence the size of the population that is vulnerable to detection. In these circumstances, probabilities of animal occurrence and extinction will generally be estimated more accurately if the models used in data analysis account for differences in abundance among sample locations and for the dependence between site-specific abundance and detection. Simulation experiments are used to illustrate conditions wherein these types of models can be expected to outperform alternative estimators of population site occupancy and extinction. ?? 2007 by the Ecological Society of America.