Who needs closure? Estimating abundance with a Markovian availability model for geographically open removal sampling

Removal sampling is an important method for estimating abundance, but nearly all removal models assume closure during sampling. Yet, closure may be difficult to assume, evaluate, or enforce in many settings. To address situations where populations are geographically open between each removal sample, we incorporated a Markovian availability process into an N-mixture model framework. This model relates local abundance available for sampling to a superpopulation through recruitment of new individuals to the sampling area. To test the model, we (1) conducted parameter identifiability analysis, (2) fit the model to removal data generated from a random walk movement model, and (3) analyzed a case study of empirical removal data. Parameters were increasingly identifiable as capture probability exceeded 0.25 and removal samples increased from 3 to 6. Abundance estimates were unbiased when parameters were identifiable, except for scenarios that simulated a behavioral response to sampling. For our case study, the model estimated negligible recruitment for benthic-oriented fishes, indicating closure, but we found evidence against closure for juvenile Chinook salmon, a highly mobile species. Our removal model allows researchers to formally test closure assumptions, to estimate the degree of closure, and to estimate abundance without bias when closure is violated.