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Monitoring animal populations is central to wildlife and fisheries management, and the use of N-mixture models toward these efforts has markedly increased in recent years. Nevertheless, relatively little work has evaluated estimator performance when basic assumptions are violated. Moreover, diagnostics to identify when bias in parameter estimates from N-mixture models is likely is largely unexplored. We simulated count data sets using 837 combinations of detection probability, number of sample units, number of survey occasions, and type and extent of heterogeneity in abundance or detectability. We fit Poisson N-mixture models to these data, quantified the bias associated with each combination, and evaluated if the parametric bootstrap goodness-of-fit (GOF) test can be used to indicate bias in parameter estimates. We also explored if assumption violations can be diagnosed prior to fitting N-mixture models. In doing so, we propose a new model diagnostic, which we term the quasi-coefficient of variation (QCV). N-mixture models performed well when assumptions were met and detection probabilities were moderate (i.e., ≥0.3), and the performance of the estimator improved with increasing survey occasions and sample units. However, the magnitude of bias in estimated mean abundance with even slight amounts of unmodeled heterogeneity was substantial. The parametric bootstrap GOF test did not perform well as a diagnostic for bias in parameter estimates when detectability and sample sizes were low. The results indicate the QCV is useful to diagnose potential bias and that potential bias associated with unidirectional trends in abundance or detectability can be diagnosed using Poisson regression. This study represents the most thorough assessment to date of assumption violations and diagnostics when fitting N-mixture models using the most commonly implemented error distribution. Unbiased estimates of population state variables are needed to properly inform management decision making. Therefore, we also discuss alternative approaches to yield unbiased estimates of population state variables using similar data types, and we stress that there is no substitute for an effective sample design that is grounded upon well-defined management objectives. [ABSTRACT FROM AUTHOR]

• Multistate occupancy 'abundance' models can differentiate sites with relatively high and low abundance. • For detecting population trends, the same sites should be surveyed from year to year (fixed-sites). • Multistate occupancy 'abundance' models reliably detect population declines of at least 45% if a fixed-site design is used. • Multistate occupancy 'abundance' models offer advantages compared to assumption sensitive N-mixture models for modeling abundance. • Multistate occupancy 'abundance' models refine the basic occupancy model to improve abundance estimates. Detecting spatiotemporal changes in the abundances of organisms is key to effectively conserving species. While indices of abundance have long been used, there has been a shift toward model-based estimators that account for the detection process. Popular approaches including traditional occupancy models and N-mixture models entail tradeoffs. The traditional occupancy approach requires the researcher coarsen the characterization of abundance to the probability that a site is occupied or unoccupied. Conversely, N-mixture models make use of variation in counts, but perform poorly when individuals have low detectability or move into or out of sites between visits. Multistate occupancy models that differentiate relatively abundant from non-abundant states have the potential to fill this gap but have been underexplored. We conducted a simulation study to test whether multistate occupancy models could capture spatial abundance patterns and detect population declines in the face of low individual detection probability (p ≤ 0.3) and unmodeled heterogeneity (e.g., that arising from individual movement). We considered 10,773 scenarios to examine the effects of differing amounts of heterogeneity as well as alternative study designs, population parameters, and modeling choices. We tracked bias in the proportion of sites estimated to be in the abundant state for single-season models, and power to detect a declining trend across multiple years. We also evaluated data diagnostic metrics to provide guidance to users. Multistate occupancy models were able to differentiate sites with higher abundances from sites with lower abundances when there were at least medium levels of spatial heterogeneity in true abundances. If different sites were randomly selected each year, power to detect even large population declines (65%) was poor (power < 0.8). However, if the same sites were surveyed each year, and a dynamic multistate occupancy was used, multistate occupancy models could detect (power ≥ 0.8) relatively small declines (5-40%) in 20% of scenarios, and frequently detect large declines of 45-60% (mean power = 0.92). Conservation decisions rely on detecting change reliably, rarely needing absolute abundance information. Multistate occupancy models can improve our ability to detect changing abundance while accommodating low individual detection probability and heterogeneity in count monitoring data. [ABSTRACT FROM AUTHOR]