The Agony of Choice: Comparing Abundance Estimates from Multiple N-Mixture Model Variants Fitted to a Reptile Community Dataset
Ecological surveys rarely achieve perfect detection of target species, and failure to account for imperfect detection produces erroneous estimates of abundance. N-mixture models account for variation in detectability by separating the observation process from the ecological process that determines true site-level abundance, making these models theoretically well suited to studies of inconspicuous species, such as reptiles. Multiple N-mixture model variants have been published in different fields of ecology, but little is known about their ability to provide ecologically realistic abundance estimates from real-world observation data, especially for reptiles, which routinely have very low detection probabilities. Using a dataset of reptile observations from southeastern Zimbabwe, we compared estimates of five N-mixture model variants. For each species, we assessed the goodness-of-fit of each variant, proximity of each variant's site-level abundance estimates to an ecologically realistic range of values, and congruence between these estimates. We were able to fit acceptable models only for the most frequently detected species in our dataset (9 of 25 species). We found that model fit varied significantly according to model variant as well as species occupancy and detection probability, and that model variant pairs were rarely congruent in their abundance estimates. Importantly, our results demonstrate that fitting a single N-mixture model variant to data sampled from an ecologically diverse community can yield artifactual variation in abundance estimates. Further case studies in reptile spatial ecology will help to identify circumstances in which a priori matching of species and method of abundance estimation may be possible. Until then, rigorous but adaptive survey design may be a more reliable means of avoiding bias than accounting for it statistically. We provide a framework for application of multiple N-mixture model variants in faunal ecology to guide analytical decision-making.Abstract

Map of the survey area in the Malilangwe Wildlife Reserve, with an inset showing the location of the reserve within Zimbabwe. Tree cover data from Reiner et al. (2023).

Histograms of site-level abundance estimates for example species representing different levels of detectability. Species names are followed by expected number of occupied sites (Eocc), mean occupancy estimate from the occupancy model (ψ), and mean detection probability estimate from the occupancy model (P). Light gray rectangles represent predicted range of ecologically reasonable abundance estimates at sites where the species is present. The bar height at zero represents estimated number of unoccupied sites. The asterisk on the plot for Platysaurus intermedius rhodesianus indicates abundance estimates beyond the x-axis limit (283–665). Species image credits: K. M. van Wyk and T. J. Ping (Lygodactylus capensis).

Paired correlation plot of log10-transformed abundance estimates from all N-mixture model variants for the nine most frequently detected species, grouped by occupancy (ψ) and detection probability (P). We define low ψ and P as < 0.33, moderate ψ and P as 0.33–0.67, and high ψ and P as > 0.67.
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