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|a The closure assumption of many abundance models, that individual animals are present throughout the survey season, often is inconsistent with field data. The effects of closure-assumption violations on estimators of abundance and associations between abundance and covariates are not fully understood. Furthermore, one's definition of abundance affects these estimates. We used simulated data on breeding birds to explore how permanent, non-random immigration and emigration that violate the closure assumption affect estimates from N-mixture abundance models and naïve models (models that do not account for imperfect detection). This is the first work to evaluate the effect of permanent immigration and emigration on estimates from N-mixture models, and to compare these effects among definitions of abundance (initial, season-long, and superpopulation). We also collected and analyzed point-count data on breeding bird species in the Great Basin (USA) to evaluate the frequency of within-season movement. When detection probability was high (ρ ≥ 0.65), estimators of superpopulation abundance from N-mixture and naïve models were relatively unbiased. By comparison, in many cases, even relatively small violations of the closure assumption biased estimates of initial and season-long abundance by > 20%. Naïve abundance models generally were less biased than N-mixture models when ρ ≥ 0.65, but highly biased when ρ ≤ 0.4. In both model types, estimators of the association between abundance and an environmental covariate were minimally biased. The magnitudes of assumption violations tested in our simulations were consistent with those in our field data. Movement of individuals (availability) strongly affected detection probability of nearly all species and, in 7 of 34 species-region combinations, was temporally heterogeneous, suggesting that closure-assumption violations are common in our study system. Our results highlight that permanent movement of individuals within a season may be a substantial source of bias in studies of breeding birds that are based on count data, and that the definition of abundance affects the magnitude of these biases. © 2021 The Authors
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