### Abstract:

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.