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\begin{document}

\title{Assessing trends in population size of three unmarked species: A
comparison of a multi-species N-mixture Model and Random Encounter
Models}



\author[1]{Martijn Bollen}%
\author[2]{Pablo Palencia}%
\author[2]{Joaquín Vicente}%
\author[2]{Pelayo Acevedo}%
\author[2]{Lucía Del Río}%
\author[3]{Thomas Neyens}%
\author[1]{Natalie Beenaerts}%
\author[4]{Jim Casaer}%
\affil[1]{Centre for Environmental Sciences}%
\affil[2]{Instituto de Investigacion en Recursos Cinegeticos}%
\affil[3]{Data Science Institute}%
\affil[4]{Research Institute for Nature and Forest}%


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  \date{May 29, 2024}


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\begin{abstract}
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 field work. Hierarchical abundance models, such as
the N-mixture model (NMM), can estimate densities 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. We compare
relative trends in density/ abundance for three species (wild boar, red
deer, and fox) based on the REM and NMM. The NMM applied here is adapted
to overcome two issues potentially leading to poor abundance estimates:
(i) we specify a joint observation model, based on a beta distribution,
for all species within a community to strengthen the inference on
infrequently detected species, and (ii) we model species-specific counts
as a Poisson process, relaxing the assumption that each individual can
only be detected once per survey. 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 density estimates for
frequently detected species. Both methods correctly identified species
ranking of abundance/density but did not always agree on relative ranks
of yearly estimates within a single population, nor on its linear
population trends. Our results suggest that relative population trends
are better preserved between NMM and REM compared to absolute densities.
Thus practitioners working with counts-only data should resort to
relative abundances, rather than absolute densities.%
\end{abstract}%



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