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

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.

King Rail ( Rallus elegans ) response to audio playback: implications for population estimation, monitoring methodology, and trapping approach

“…Population density has been estimated for other marsh birds (e.g., Harms and Dinsmore 2012, Wiest et al 2016, 2019, Vanausdall et al 2022) despite the high potential for these oftensecretive species to remain undetected at or immediately adjacent to the observer, which is a violation of a distance sampling assumption (Buckland et al 1993). N-mixture models can produce reliable population density estimates via repeated surveys at locations, though are known to overestimate population size where densities are low (Neubauer et al 2022), as is often true for King Rails. By using a correction factor, a distance sampling approach could feasibly yield an accurate King Rail population density estimate without employing the double-observer method (Thomas et al 2010), similar to approaches used for taxa such as cetaceans (e.g., Andriolo et al 2006) that often remain undetected at or immediately adjacent to an observer.…”

Liming and spring salamander abundance

“…Researchers have found limitations with N‐mixture models (Barker et al 2017, Link et al 2018), which show that small violations can lead to large biases in estimation. Recently, Neubauer et al (2022) found that the strength and direction of these biases in abundance estimation depend upon the presence of unmodeled heterogeneity in detection probability, which is more severe with low detection probability. It is probable that our research, given the low detection probability, has some abundance estimation bias.…”

“…N‐mixture models allow for the estimation of abundance (λ) and detection probability ($$p$$) without the explicit identification of individuals within the population. While some studies have found limitations of N‐mixture models (Barker et al 2017, Link et al 2018), other recent work suggests that these models are a valid alternative to intensive population monitoring for abundance estimation (Keever et al 2017, Kidwai et al 2019, Neubauer et al 2022). We combined counts of spring salamanders in each stream location, regardless of method (added counts across methods [LLB, VES, FS] for each UPS, DS1, and DS2 location, which includes 3 separate counts of abundance) for all 11 streams.…”

Urban oasis? Abundant dice snake (Natrix tessellata) populations along artificial lakeside habitats in urban landscapes

“…The model also enabled us to include environmental metrics as covariates; therefore both parameters (abundance and detection) could be expressed as functions of environmental covariates through a log or logit link, respectively. Previous studies have demonstrated that N-mixture models offer reliable estimates of abundance aligning with outcomes from alternative methods such as capturemark-recaptures (Ficetola et al 2018;Neubauer et al 2022).…”