Assessing trends in population size of three unmarked species: A comparison of a multi‐species N‐mixture model and random encounter models

Estimation of changes in abundances and densities is essential for the research, management, and conservation of animal populations. Recently, technological advances have facilitated the surveillance of animal populations through the adoption of passive sensors, such as camera traps (CT). Several methods, including the random encounter model (REM), have been developed for estimating densities of unmarked populations but require additional information. Hierarchical abundance models, such as the N‐mixture model (NMM), can estimate abundances without performing additional fieldwork but do not explicitly estimate the area effectively sampled. This obscures the interpretation of its densities and requires its users to focus on relative measures of abundance instead. Hence, the main objective of our study is to evaluate if REM and NMM yield consistent results qualitatively. Therefore, we compare relative trends: (i) between species, (ii) between years and (iii) across years obtained from annual density/abundance estimates of three species (fox, wild boar and red deer) in central Spain monitored by a camera trapping network for five consecutive winter periods. We reveal that NMM and REM provided density estimates in the same order of magnitude for wild boar, but not for foxes and red deer. Assuming a Poisson detection process in the NMM was important to control for inflation of abundance estimates for frequently detected species. Both methods consistently ranked density/abundance across species (between species trend), but did not always agree on relative ranks of yearly estimates within a single population (between years trend), nor on its linear population trends across years (across years trend). Our results suggest that relative trends are generally consistent when the range of variability is large, but can become inconsistent when the range of variability is smaller.