Assessment and novel application of N ‐mixture models for aerial surveys of wildlife

Aerial surveys are a critical tool for inference of wildlife populations, yet are limited by current available methods to account for imperfect detection without marking animals. N ‐mixture models use count data from replicate surveys for estimation of wildlife abundance while accounting for imperfect detection. This statistical framework was recently developed but is rarely applied to aerial surveys of terrestrial wildlife. We applied an N ‐mixture model incorporating temporary emigration to a novel aerial survey design to estimate the availability, detection probability, and abundance of an unmarked population of white‐tailed deer ( Odocoileus virginianus ) in Michigan, USA, using surveys in 2014 and 2016. We assessed the selection of the sample unit size for the N ‐mixture model in a post hoc sensitivity analysis and compared all estimates to a hierarchical distance sampling (HDS) approach. Hierarchical distance sampling is an expansion of conventional distance sampling (CDS), a standard method applied to aerial survey designs for wildlife, where HDS allows for modeling spatial variation in abundance and detection probability using environmental covariates and can account for changing population demographics. We found N ‐mixture models produced similar parameter estimates to HDS with both models inferring a population increase between years, which was consistent with independently available estimates for this population (2014 N ‐mixture = 402 [CI: 303.8–515.27], and HDS = 391 [CI: 297.67–504.63]; 2016 N ‐mixture = 732 [CI: 572.89–924.22], and HDS = 708 [CI: 552.45–893.89]). Estimates from both models were sensitive to the sample unit size selected in an open population framework. We recommend using ecological (e.g., home range size) and statistical (e.g., sample size) considerations when selecting a sample unit size that reflects the movement ecology of a species and evaluating the sensitivity of parameters to sample unit size. In our study, N ‐mixture models and HDS models afforded a practical field approach and analytical methodology that resulted in precise estimation in a population of unmarked deer over time. When used with aerial surveys in terrestrial systems where distance sampling methods may be difficult to implement, N ‐mixture models can address observer error and estimate populations for conservation and management goals without marking individual animals.