In this disseration, we estimate abundance from removal-sampled animal wildlife point-count surveys, focusing on models to account for heterogeneous detection probabilities. In contrast to many published models, our research treats individual times to detection as continuous-time responses. Adopting this method enables us to ask questions that are impractical under existing discrete-time models. We accomplish our analyses by using a parametric survival analysis approach within the N-mixture class of hierarchical animal abundance models. In Chapter 2, we construct models for removal-sampled data that allow detection rates to change systematically over the course of each observation period. Most studies assume detection rates are constant, but our analysis demonstrates this assumption to be very informative, leading to biased and overly precise estimates. Non-constant models prove less biased with better coverage statistics over a range of simulated datasets. In Chapter 3, we extend the continuous-time modeling approach to distance-removal sampled surveys. We introduce a new model that successfully integrates two subtly different existing mechanisms for modeling distance-removal surveys: one that focuses on detecting available individuals and one that focuses on detecting availability cues (e.g. bird calls). We articulate the distinctions between the two and place them within current terminology for availability and perceptibility. Our new model accurately estimates abundance and detection from datasets simulated via either mechanism, but models that assume only one mechanism are often not robust to misspecification. In Chapter 4, we apply our model from Chapter 3 to six avian species monitored in removal- and distance-sampled point-count surveys in Iowa agricultural fields. We articulate several ways in which the model does not match data characteristics, and we identify priorities for developing this model in order to make it more flexible and feasible.