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

Abstract

Abstract 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 Białowieża 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.