N-mixture models estimate abundance reliably: A field test on Marsh Tit using time-for-space substitution

Lay Summary center dot We performed a field test of binomial N-mixture models using a 33-year dataset of a Marsh Tit (Poecile palustris) counts in Bialowieza Forest, Poland, by comparing abundance estimates from the model to the true number of breeding pairs. center dot The models produced highly reliable estimates: 88% of 132 comparisons included the true number of pairs within confidence intervals but showed a clear tendency to overestimate abundance at low densities and underestimate it at high densities. center dot Countersinging increased with abundance and violated independence in detections-one of the model's assumptions. Despite this violation, simulations indicated that even if density dependence was not accounted for in the submodel for detection, model estimates showed high agreement with abundances at particular sites, except for extreme situations (low detection probability coupled with low or high abundance). center dot While our study validates the performance of binmix models, future studies are needed to understand why and how the possible biases can arise. Imperfect detection in field studies on animal abundance, including birds, is common and can be corrected for in various ways. The binomial N-mixture (hereafter binmix) model developed for this task is widely used in ecological studies owing to its simplicity: it requires replicated count results as the input. However, it may overestimate abundance and be sensitive to even small violations of its assumptions. We used a 33-year dataset on the Marsh Tit (Poecile palustris), a sedentary forest passerine, from Bialowieza Forest, Poland, to validate inference from binmix models by comparing model-estimated abundances to the true number of breeding pairs within the plots, determined by exhaustive population study. The abundance estimates, derived from 6 springtime (April and May) counts of males on each plot in each year, were highly reliable: 116 out of 132 year-plot estimates (88%) included the true number of pairs within the 95% confidence intervals. Over- and under-estimations were thus rare and similarly frequent (9 and 12 cases, respectively), with a tendency to overestimate at low densities and underestimate at high densities. Marsh Tits sing rarely but the frequency of countersinging increases with abundance, leading to nonindependence in detections. When accounted for in a submodel for detection, the per-survey number of countersinging events positively affected detection probability but only weakly affected abundance estimates. Simulations further demonstrate that this property, overestimation at low densities and underestimation at high densities, may be a systematic bias of binmix model even if density-dependent detection is absent. While the behavior of binmix models in specific situations requires more study, we conclude that these models are a valid tool to estimate abundance reliably when intensive population monitoring is not feasible.