A hierarchical Bayesian approach for estimating the number of groups and group sizes in group-living animals using passive detectors

Abstract

Mammals that live in groups play critical roles in ecosystems and are significant conservation and management targets. However, efficiently and reliably estimating both the number of groups and group sizes for monitoring their population status presents challenges. Point-count surveys, such as camera trapping, face difficulties in estimating these variables because multiple groups are detected repeatedly at the same observation station. In such cases, the observed group sizes should conform to finite mixture distributions—that is, probability distributions with varying parameters may be combined, and the number of distributions involved remains uncertain. We developed a hierarchical Bayesian model to simultaneously estimate these variables while accounting for imperfect detection based on point-count survey data. Specifically, we extend the N-mixture model to estimate group size by introducing a mixture structure for each group observation using a truncated stick-breaking (TSB) prior. Additionally, by incorporating the Royle–Nichols model as a sub-model, we estimate the number of potentially detectable clusters at a given point, enabling effective truncation of the prior distribution for cluster assignment probability by the TSB prior. Monte Carlo simulations revealed that while the conventional N-mixture model overestimated group sizes by 56.1%, the mixture models using TSB prior reduced this bias to − 5.2%. Further inclusion of information from the Royle-Nichols model improved accuracy, resulting in a minimal bias of + 0.6% in group size estimates. The estimation of the number of groups showed a 35.0% positive bias when using the TSB prior alone but incorporating auxiliary information by the RN model reduced this bias to − 2.1%. Using a random walk model that simulated movements of group-living animals, we demonstrated that our model provided robust group size estimates even under model misspecification, when the individual detection probability exceeded 0.5 and mortality remained below 13%. The model slightly underestimated the number of groups but maintained acceptable accuracy. Field surveys using camera trap data from juvenile wild boars yielded satisfactory goodness of fit. Our model is robust to changes in group membership during surveys, offering an underlying structure for future refinement to address more realistic situations.