Obtaining accurate estimates of animal abundance is made difficult by the fact that most animal species are detected imperfectly. Early attempts at building likelihood models that account for unknown detection probability impose a simplifying assumption unrealistic for many populations, however: no births, deaths, migration or emigration can occur in the population throughout the study (i.e., population closure). In this dissertation, I develop likelihood models that account for unknown detection and do not require assuming population closure. In fact, the proposed models yield a statistical test for population closure. The basic idea utilizes a procedure in three steps: (1) condition the probability of the observed data on the (unobserved) period- specific abundances; (2) multiply this conditional probability by the (prior) likelihood for the period abundances; and (3) remove (via summation) the period- specific abundances from the joint likelihood, leaving the marginal likelihood of the observed data. The utility of this procedure is two-fold: step (1) allows detection probability to be more accurately estimated, and step (2) allows population dynamics such as entering migration rate and survival probability to be modeled. The main difficulty of this procedure arises in the summation in step (3), although it is greatly simplified by assuming abundances in one period depend only the most previous period (i.e., abundances have the Markov property). I apply this procedure to form abundance and site occupancy rate estimators for both the setting where observed point counts are available and the setting where only the presence or absence of an animal species is ob- served. Although the two settings yield very different likelihood models and estimators, the basic procedure forming these estimators is constant in both. / Graduation date: 2012