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

Abstract

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 Nmixture 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

Optimally designing drone‐based surveys for wildlife abundance estimation with N‐mixture models

“…However, despite these raised concerns, studies comparing N‐mixture models with more traditional and well‐established approaches (i.e. capture‐recapture models or distance sampling) have generally shown similar results (Christensen et al, 2021; Ficetola et al, 2018; Keever et al, 2017; Kéry, 2018). In the context of drone‐based surveys, the impact of these findings would be expected to be more concerning for the availability process (non‐modelled heterogeneity in unavailability).…”

“…To reduce the effects of spatial temporary emigration, one could plan sampling design to (i) shorten the time interval between repeated visits (but avoiding temporal autocorrelation) and (ii) define site size as relatively large in comparison with the expected area used by the individuals during sampling. Christensen et al (2021) proposed a post hoc sensitivity analysis to define the best length to split flight lines into sites and found that the ideal size is similar to the home range size reported to the target species. Auxiliary data from telemetry or some marked individuals can provide information to segregate the two components of temporary emigration (spatial and temporal; Brack et al, 2018).…”

“…Hierarchical N‐mixture models have been suggested to model abundance from spatiotemporally replicated aerial counts since they are a valuable framework for studying unmarked populations while accounting for the sources of imperfect detection (Brack et al, 2018; Christensen et al, 2021; Martin et al, 2015; Williams et al, 2017). In such approach, count data obtained for each visit (i.e.…”

Comparing N-mixture models and GLMMs for relative abundance estimation in a citizen science dataset

“…Without access to known truth, we could not investigate whether the estimates produced reflect true relationships between covariates and species abundance, so we cannot say whether either N-mixture models or GLMMs estimated parameters accurately in that sense. We suggest that practitioners interested in modeling relative abundance from count data consider the assumptions of both models, including known features of N-mixture model robustness in practice and theory 10 , 11 , 13 , 14 , 16 – 18 , 20 – 23 , along with other practical trade-offs. If both GLMMs and N-mixture models are potentially appropriate, we recommend the model selection and goodness-of-fit checking procedure outlined in this paper for choosing the most parsimonious model with adequate fit.…”

“…Additionally, Kéry 19 identified estimation instability, likely attributable to a likelihood maximum in the limit of zero detection 18 , but recommended the use of N-mixture models when estimation instability does not occur 19 . Several studies have found that the N-mixture model produces estimates of absolute abundance that agree with more rigorous sampling methods 20 – 23 though this finding is not universal 24 . Still, established sensitivities and computational pathologies are grounds for caution in recommending N-mixture models when data do not strictly conform to modeling assumptions.…”